jcuny/These_linjie_JC
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

Renvois toute la these pour commencer

Browse Source
This commit is contained in:
jcuny 2021-06-14 03:58:27 +02:00
parent a735d32918
commit 6fb21febf1
192 changed files with 287411 additions and 0 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

BIN
thesis/.DS_Store vendored Normal file
View File

Binary file not shown.

BIN
thesis/0_frontmatter/.DS_Store vendored Normal file
View File

Binary file not shown.

30
thesis/0_frontmatter/abstract.aux Normal file
View File

@ -0,0 +1,30 @@
\relax
\providecommand\hyper@newdestlabel[2]{}
\@setckpt{0_frontmatter/abstract}{
\setcounter{page}{5}
\setcounter{equation}{0}
\setcounter{enumi}{0}
\setcounter{enumii}{0}
\setcounter{enumiii}{0}
\setcounter{enumiv}{0}
\setcounter{footnote}{0}
\setcounter{mpfootnote}{0}
\setcounter{part}{0}
\setcounter{chapter}{0}
\setcounter{section}{0}
\setcounter{subsection}{0}
\setcounter{subsubsection}{0}
\setcounter{paragraph}{0}
\setcounter{subparagraph}{0}
\setcounter{figure}{0}
\setcounter{table}{0}
\setcounter{ContinuedFloat}{0}
\setcounter{pp@next@reset}{1}
\setcounter{@fnserial}{0}
\setcounter{NAT@ctr}{0}
\setcounter{Item}{0}
\setcounter{Hfootnote}{0}
\setcounter{bookmark@seq@number}{0}
\setcounter{parentequation}{0}
\setcounter{section@level}{0}
}

97
thesis/0_frontmatter/abstract.log Normal file
View File

@ -0,0 +1,97 @@
This is pdfTeX, Version 3.14159265-2.6-1.40.20 (TeX Live 2019) (preloaded format=pdflatex 2019.10.4) 2 SEP 2020 15:33
entering extended mode
restricted \write18 enabled.
%&-line parsing enabled.
**abstract.tex
(./abstract.tex
LaTeX2e <2018-12-01>
! LaTeX Error: Environment abstracts undefined.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
l.6 \begin{abstracts}
%this creates the heading for the abstract page
Your command was ignored.
Type I <command> <return> to replace it with another command,
or <return> to continue without it.
! LaTeX Error: Missing \begin{document}.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
l.8 a
bstract or summary here, if needed.
You're in trouble here. Try typing <return> to proceed.
If that doesn't work, type X <return> to quit.
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no . in font nullfont!
Overfull \hbox (20.0pt too wide) in paragraph at lines 8--9
[]
[]
! LaTeX Error: \begin{document} ended by \end{abstracts}.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
l.10 \end{abstracts}
Your command was ignored.
Type I <command> <return> to replace it with another command,
or <return> to continue without it.
)
! Emergency stop.
<*> abstract.tex
*** (job aborted, no legal \end found)
Here is how much of TeX's memory you used:
6 strings out of 492616
143 string characters out of 6129481
57212 words of memory out of 5000000
4026 multiletter control sequences out of 15000+600000
3640 words of font info for 14 fonts, out of 8000000 for 9000
1141 hyphenation exceptions out of 8191
6i,0n,6p,100b,19s stack positions out of 5000i,500n,10000p,200000b,80000s
! ==> Fatal error occurred, no output PDF file produced!

41
thesis/0_frontmatter/abstract.tex Normal file
View File

@ -0,0 +1,41 @@
% Thesis Abstract -----------------------------------------------------
%\begin{abstractslong} %uncommenting this line, gives a different abstract heading
\begin{abstracts} %this creates the heading for the
This thesis aims at studying in details the behavior of complex molecular clusters and focuses on two main aspects. First, the description of low-energy isomers of ammonium/ammonia water clusters and protonated uracil water clusters through an extensive exploration of potential energy surfaces (PES) using a combination of global and local optimization schemes. Structural, solvation and thermodynamics properties of the newly identified low-energy isomers were characterized. Second, the dynamical simulations of collision-induced dissociation of protonated uracil water clusters and pyrene dimer cation were carried out to explore collision trajectories, dissociation mechanism, energy partition, mass spectra, and collision cross-sections to complement experimental measurements conducted on these species.
Global optimization of (H$_2$O)$_{1-10}$NH$_4^+$ and (H$_2$O)$_{1-10}$NH$_3$ clusters is conducted at the self-consistent-charge density-functional based tight-binding (SCC-DFTB) level of theory, for which improved N-H parameters are proposed, in combination with the parallel-tempering molecular dynamics (PTMD) approach. Low-energy isomers of (H$_2$O)$_{1-10}$NH$_4^+$ and (H$_2$O)$_{1-10}$NH$_3$ are further optimized at MP2 level in order to evaluate the reliability of our modified N-H parameters. Both structures and binding energies obtained with SCC-DFTB are in line with the results at MP2/Def2TZVP level, which demonstrates the ability of SCC-DFTB to describe the PES of molecular species and represents a first step towards the modeling of complex aggregates of atmospheric interest.
Focus on protonated uracil water clusters aims at providing a detailed description of recent collision-induced dissociation (CID) experiments. First, stable isomers of (H$_2$O)$_{1-7, 11, 12}$UH$^+$
are calculated using the same methodology as described above. Then, dynamical simulations of the collisions between various (H$_2$O)$_{1-7, 11, 12}$UH$^+$ isomers and argon is conducted at a constant collision energy at the SCC-DFTB level. Simulated proportion of formed neutral vs. protonated uracil containing clusters, fragmentation cross-section as well as mass spectra are consistent with the experimental data which highlights the accuracy of our simulations. They allow to probe which fragments are formed on the short time scale and rationalize the location of the excess proton on these fragments.This latter property is highly influenced by the nature of the aggregate undergoing the collision. Analyses of proportion of time-dependent fragments and mass spectra demonstrate that, up to 7 water molecules, a shattering mechanism occurs after collision whereas for n=11,12 a statistical mechanism is more likely to participate. These simulations appear as a useful tool to complement CID experiments of hydrated molecular species.
Dynamical simulation of CID experiments of pyrene dimer cation for different collision energies between 2.5 and 30 eV is also presented. The dynamical simulations allow to understand the dissociation processes. The agreement between the simulated and measured mass spectra suggests that the main processes are captured by this approach. It appears that most of the dissociation occurs on a short timescale (less than 3 ps). At low collision energies, the dissociation cross-section increases with collision energies whereas it remains almost constant for collision energies greater than 10 to 15 eV. Analysis of the kinetic energy partition is used to get insights into the collision/dissociation processes at the atomic scale. The simulated time of flight mass spectra of the parent and dissociated products are obtained from the combination of molecular dynamics simulations and phase space theory to address the short and long timescales dissociation, respectively.
Keywords:
SCC-DFTB, CID, molecular dynamics, ammonium/ammonia water clusters, uracil water clusters,
% \break
\break
\textbf{Résumé de la thèse}
Cette thèse vise à étudier en détails le comportement d’agrégats moléculaires complexes et se concentre sur deux aspects principaux. Tout d’abord, la description des isomères de faible énergie des clusters d'ammonium et ammoniac et des clusters d’uracile/eau protonés à travers l’exploration des surfaces d'énergie potentielle (PES) en utilisant une combinaison d’approches d'optimisation globales et locales. Les propriétés structurelles, de solvatation et thermodynamiques des isomères de basse énergie nouvellement identifiés ont été caractérisées. Par la suite, des simulations dynamiques de la dissociation induite par collision des agrégats d’uracile/eau protonés et du dimère de pyrène ont été réalisées et analysées en termes de : mécanisme de dissociation, répartition d'énergie, spectres de masse et sections efficaces de collision pour complémenter des mesures expérimentales récentes menées sur ces espèces.
L'optimisation globale des clusters (H$_2$O)$_{1-10}$NH$_4^+$ et (H$_2$O)$_{1-10}$NH$_3$ a été réalisée au niveau de théorie SCC-DFTB (pour self-consistent-charge density-functional based tight-binding), pour laquelle des paramètres NH améliorés ont été proposés, en combinaison avec l'approche d’exploration PTMD (pour parallel-tempering molecular dynamics). Les isomères de basse énergie nouvellement déterminés ont été optimisés au niveau MP2 afin d'évaluer la fiabilité de nos paramètres N-H modifiés. Les structures et les énergies de liaison obtenues avec la méthode SCC-DFTB sont en très bon accord avec les résultats de niveau MP2/Def2TZVP, ce qui démontre la capacité de l’approche SCC-DFTB à décrire la PES de ces espèces moléculaires et représente ainsi une première étape vers la modélisation d'agrégats complexes d’intérêt atmosphérique.
L’intérêt porté aux agrégats uracile/eau protonés vise à fournir une description détaillée d’expériences récentes de dissociation induite par collision (CID). Premièrement, les isomères stables des agrégats (H$_2$O)$_{1-7, 11, 12}$UH$^+$ sont calculés en utilisant la même méthodologie que celle décrite ci-dessus. Ensuite, des simulations dynamiques des collisions entre divers isomères (H$_2$O)$_{1-7, 11, 12}$UH$^+$ et un atome d’argon sont réalisées à énergie de collision constante au niveau SCC-DFTB. La proportion simulée de d’agrégats neutres contenant l’uracile par rapport à celle d’agrégats chargés contenant l’uracile, la section efficace de fragmentation ainsi que les spectres de masse sont cohérents avec les données expérimentales ce qui met en évidence la précision de nos simulations. Ces dernières permettent de sonder en details les fragments qui se forment aux temps courts et de rationaliser la localisation du proton en excès sur ces fragments. Cette dernière propriété est fortement influencée par la nature de l'agrégat soumis à la collision. L’analyses de la proportion des fragments en fonction du temps et des spectres de masse démontrent que, jusqu'à 7 molécules d'eau, un mécanisme de dissociation direct en mis en jeu après la collision alors que pour 11 et 12 molécules, un mécanisme statistique est plus susceptible d’intervenir. Ces simulations, uniques jusqu’à présent, apparaissent comme un outil indispensable pour comprendre et interpréter les expériences CID d'espèces moléculaires hydratées.
Enfin, des simulations d'expériences CID du dimère de pyrène à différentes énergies de collision, entre 2,5 et 30 eV, sont également présentées. Les simulations permettent de comprendre les processus de dissociation mis en jeu. L'accord entre les spectres de masse simulés et mesurés suggère que les principaux processus sont bien pris en compte par cette approche. Il semble que la majeure partie de la dissociation se produise sur une courte échelle de temps (moins de 3 ps). Aux faibles énergies de collision, la section efficace de dissociation augmente avec les énergies de collision alors qu'elle reste presque constante pour des énergies de collision comprises entre 10 et 15 eV. L'analyse de la répartition d'énergie cinétique est utilisée pour obtenir des informations sur les processus de collision/dissociation à l'échelle atomique. Les spectres de masse simulés des clusters parents et dissociés sont obtenus à partir en combinant simulations de dynamique moléculaire et théorie de l'espace des phases pour traiter respectivement la dissociation aux courtes et longues échelles de temps.
Mots clés :
SCC-DFTB, CID, dynamique moléculaire, agrégats d'ammonium/ammoniac, agrégats d’uracile eau protonés
\end{abstracts}
%\end{abstractlongs}
% ----------------------------------------------------------------------

31
thesis/0_frontmatter/acknowledgement.aux Normal file
View File

@ -0,0 +1,31 @@
\relax
\providecommand\hyper@newdestlabel[2]{}
\FN@pp@footnotehinttrue
\@setckpt{0_frontmatter/acknowledgement}{
\setcounter{page}{7}
\setcounter{equation}{0}
\setcounter{enumi}{0}
\setcounter{enumii}{0}
\setcounter{enumiii}{0}
\setcounter{enumiv}{0}
\setcounter{footnote}{0}
\setcounter{mpfootnote}{0}
\setcounter{part}{0}
\setcounter{chapter}{0}
\setcounter{section}{0}
\setcounter{subsection}{0}
\setcounter{subsubsection}{0}
\setcounter{paragraph}{0}
\setcounter{subparagraph}{0}
\setcounter{figure}{0}
\setcounter{table}{0}
\setcounter{ContinuedFloat}{0}
\setcounter{pp@next@reset}{1}
\setcounter{@fnserial}{0}
\setcounter{NAT@ctr}{0}
\setcounter{Item}{0}
\setcounter{Hfootnote}{0}
\setcounter{bookmark@seq@number}{0}
\setcounter{parentequation}{0}
\setcounter{section@level}{0}
}

94
thesis/0_frontmatter/acknowledgement.log Normal file
View File

@ -0,0 +1,94 @@
This is pdfTeX, Version 3.14159265-2.6-1.40.20 (TeX Live 2019) (preloaded format=pdflatex 2019.10.4) 2 SEP 2020 15:34
entering extended mode
restricted \write18 enabled.
%&-line parsing enabled.
**acknowledgement.tex
(./acknowledgement.tex
LaTeX2e <2018-12-01>
! LaTeX Error: Environment acknowledgements undefined.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
l.5 \begin{acknowledgements}
%this creates the heading for the acknowle...
Your command was ignored.
Type I <command> <return> to replace it with another command,
or <return> to continue without it.
! LaTeX Error: Missing \begin{document}.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
l.7 I
would like to acknowledge ....
You're in trouble here. Try typing <return> to proceed.
If that doesn't work, type X <return> to quit.
Missing character: There is no I in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no . in font nullfont!
Overfull \hbox (20.0pt too wide) in paragraph at lines 7--8
[]
[]
! LaTeX Error: \begin{document} ended by \end{acknowledgements}.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
l.9 \end{acknowledgements}
Your command was ignored.
Type I <command> <return> to replace it with another command,
or <return> to continue without it.
)
! Emergency stop.
<*> acknowledgement.tex
*** (job aborted, no legal \end found)
Here is how much of TeX's memory you used:
6 strings out of 492616
178 string characters out of 6129481
57254 words of memory out of 5000000
4026 multiletter control sequences out of 15000+600000
3640 words of font info for 14 fonts, out of 8000000 for 9000
1141 hyphenation exceptions out of 8191
6i,0n,6p,119b,19s stack positions out of 5000i,500n,10000p,200000b,80000s
! ==> Fatal error occurred, no output PDF file produced!

14
thesis/0_frontmatter/acknowledgement.tex Normal file
View File

@ -0,0 +1,14 @@
% Thesis Acknowledgements ------------------------------------------------
%\begin{acknowledgementslong} %uncommenting this line, gives a different acknowledgements heading
\begin{acknowledgements} %this creates the heading for the acknowlegments
I would like to acknowledge ....
\end{acknowledgements}
%\end{acknowledgmentslong}
% ------------------------------------------------------------------------

31
thesis/0_frontmatter/dedication.aux Normal file
View File

@ -0,0 +1,31 @@
\relax
\providecommand\hyper@newdestlabel[2]{}
\FN@pp@footnotehinttrue
\@setckpt{0_frontmatter/dedication}{
\setcounter{page}{6}
\setcounter{equation}{0}
\setcounter{enumi}{0}
\setcounter{enumii}{0}
\setcounter{enumiii}{0}
\setcounter{enumiv}{0}
\setcounter{footnote}{0}
\setcounter{mpfootnote}{0}
\setcounter{part}{0}
\setcounter{chapter}{0}
\setcounter{section}{0}
\setcounter{subsection}{0}
\setcounter{subsubsection}{0}
\setcounter{paragraph}{0}
\setcounter{subparagraph}{0}
\setcounter{figure}{0}
\setcounter{table}{0}
\setcounter{ContinuedFloat}{0}
\setcounter{pp@next@reset}{1}
\setcounter{@fnserial}{0}
\setcounter{NAT@ctr}{0}
\setcounter{Item}{0}
\setcounter{Hfootnote}{0}
\setcounter{bookmark@seq@number}{0}
\setcounter{parentequation}{0}
\setcounter{section@level}{0}
}

9
thesis/0_frontmatter/dedication.tex Normal file
View File

@ -0,0 +1,9 @@
% Thesis Dedictation ---------------------------------------------------
\begin{dedication} %this creates the heading for the dedication page
To ...
\end{dedication}
% ----------------------------------------------------------------------

BIN
thesis/0_frontmatter/figures/.xvpics/CUc_LJ.eps Normal file
View File

Binary file not shown.

BIN
thesis/0_frontmatter/figures/.xvpics/CUnibig1.eps Normal file
View File

Binary file not shown.

BIN
thesis/0_frontmatter/figures/.xvpics/CUnibig1.png Normal file
View File

Binary file not shown.

BIN
thesis/0_frontmatter/figures/.xvpics/CUnibig2.eps Normal file
View File

Binary file not shown.

BIN
thesis/0_frontmatter/figures/.xvpics/CUnibig2.png Normal file
View File

Binary file not shown.

10719
thesis/0_frontmatter/figures/logo.eps Normal file
View File

File diff suppressed because it is too large Load Diff

BIN
thesis/0_frontmatter/figures/logo.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 5.9 KiB

BIN
thesis/0_frontmatter/figures/upc-logo.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 24 KiB

30
thesis/0_frontmatter/glossary.aux Normal file
View File

@ -0,0 +1,30 @@
\relax
\providecommand\hyper@newdestlabel[2]{}
\@setckpt{0_frontmatter/glossary}{
\setcounter{page}{10}
\setcounter{equation}{0}
\setcounter{enumi}{0}
\setcounter{enumii}{0}
\setcounter{enumiii}{0}
\setcounter{enumiv}{0}
\setcounter{footnote}{0}
\setcounter{mpfootnote}{0}
\setcounter{part}{0}
\setcounter{chapter}{0}
\setcounter{section}{0}
\setcounter{subsection}{0}
\setcounter{subsubsection}{0}
\setcounter{paragraph}{0}
\setcounter{subparagraph}{0}
\setcounter{figure}{0}
\setcounter{table}{0}
\setcounter{ContinuedFloat}{0}
\setcounter{pp@next@reset}{1}
\setcounter{@fnserial}{0}
\setcounter{NAT@ctr}{0}
\setcounter{Item}{0}
\setcounter{Hfootnote}{0}
\setcounter{bookmark@seq@number}{0}
\setcounter{parentequation}{0}
\setcounter{section@level}{0}
}

41
thesis/0_frontmatter/glossary.tex Normal file
View File

@ -0,0 +1,41 @@
% this file is called up by thesis.tex
% content in this file will be fed into the main document
% Glossary entries are defined with the command \nomenclature{1}{2}
% 1 = Entry name, e.g. abbreviation; 2 = Explanation
% You can place all explanations in this separate file or declare them in the middle of the text. Either way they will be collected in the glossary.
% required to print nomenclature name to page header
\markboth{\MakeUppercase{\nomname}}{\MakeUppercase{\nomname}}
% ----------------------- contents from here ------------------------
\nomenclature{PAH}{polycyclic aromatic hydrocarbons; p. 4}
\nomenclature{PES}{potential energy surface; page 5}
\nomenclature{MD}{molecular dynamics; p. 30}
\nomenclature{FF}{force field; p. 17}
\nomenclature{BO}{Born-Op­pen­heimer; p. 18}
\nomenclature{HF}{Hartree-Fock; p. 20 }
\nomenclature{KS}{Kohn-Sham p. 20}
\nomenclature{DFT}{densituy functional theory p.}
\nomenclature{DFTB}{}
\nomenclature{SCC-DFTB}{Density Functional based Tight-Binding p. XX}
\nomenclature{PTMD}{Parallel-tempering molecular dynamics p. XX}
\nomenclature{QM}{quantum chemical; p. }
\nomenclature{MM}{molecular mechanics p. }
\nomenclature{CAD}{collisionally activated dissociation p, 84}
\nomenclature{CID}{collision‐induced dissociation p, 84}
\nomenclature{}{}
\nomenclature{}{}
\nomenclature{}{}
\nomenclature{}{}
\nomenclature{}{}
\nomenclature{}{}
\nomenclature{}{}
\nomenclature{}{}
\nomenclature{}{}
\nomenclature{}{}
\nomenclature{}{}
\nomenclature{}{}

BIN
thesis/1_GeneIntro/.DS_Store vendored Normal file
View File

Binary file not shown.

176
thesis/1_GeneIntro/GeneIntro-copy.tex Normal file
View File

@ -0,0 +1,176 @@
%this file is c\emph{•}alled up by thesis.tex
% content in this file will be fed into the main document
%%\chapter{Aims of the project} % top level followed by section, subsection
\ifpdf
\graphicspath{{1_GeneIntro/figures/PNG/}{1_GeneIntro/figures/PDF/}{1_GeneIntro/figures/}}
\else
\graphicspath{{1_GeneIntro/figures/EPS/}{1_GeneIntro/figures/}}
\fi
\chapter{General Introduction}
%The work of this thesis is focused on two aspects. First, to obtain the low-lying energy isomers of ammonium/ammonia water clusters and protonated uracil water clusters through exploring the potential energy surfaces using the combination of global and local optimizations. Then the structural, solvation, thermodynamics properties of the low-lying energy isomers were characterized. Second, the molecular dynamics simulations of collision-induced dissociation of protonated uracil water clusters and pyrene dimer cation were carried out to explore the collision trajectories, dissociation mechanism, energy partition, mass spectra, cross-section and do on.
%\section{Molecular Clusters}
The term cluster was coined by Cotton in the early 1960s to refer to compounds containing metal–metal bonds such as [Re$_2$Cl$_8$]$^{2-}$
and [Re$_2$Br$_8$]$^{2-}$.\cite{Cotton1964} More generally, in chemistry, the term cluster refers to an ensemble of bound atoms or molecules,
that can be isolated or incorporated in a larger chemical compounds, for instance in a material. A cluster is intermediate in size between a single
molecule or atom and a nanoparticle which can be composed of up to a few nanometers in diameter. Clusters are also intermediate in terms of
properties between a single molecule or atom and the corresponding bulk compound. Although there is no strict definition of the size range
for a species to be referred to as a cluster, a rule of thumb is that a cluster can be composed of 3 to 3$\times$10$^7$ components. \cite{Cluster}
%Two-atom particle is sometimes also considered as a cluster.
Cluster chemistry developed contemporaneously along several independent research lines and several families of compounds can be referred to as
clusters. Among them, one can mention \textbf{ transition metal carbonyl clusters},\cite{Dahl1963} \textbf{transition metal halide clusters},\cite{Fucugauchi1994}
\textbf{transition metal organic carbon clusters} (organometallic),\cite{Sutton2016} \textbf{metalloid clusters},\cite{Schnepf2002}
\textbf{intermetalloid clusters},\cite{Fassler2004, Stegmaier2011} as well as \textbf{atomic clusters} composed of non-metal atoms \cite{Farges1981, Kroto1991c60, Blase2008, Siedschlag2004}
and \textbf{molecular clusters}. \cite{Rapacioli2005stacked, Zhen2018}.
%The cluster can be either pure formed (from a single atomic species) or mixed (formed from different atomic species).
%It can classified according to the nature of predominantly bond (metallic, covalent or ionic bond).
\blue{\textbf{Transition metal carbonyl cluster} is a compound containing a core that consists of two or more metal atoms linked in part by metal-metal bonds and embraced by carbon monoxide (CO) ligand groups exclusively or predominantly.
\textbf{Transition metal halide cluster} is a compound that contains two or more metal atoms (prevalent for the heavy metals) linked in part by metal-metal bonds and embraced by halide ligand. Some representative species for transition metal carbonyl and halide clusters are Mn$_2$(CO)$_{10}$,\cite{Dahl1963} Ni(CO)$_4$,\cite{Braga1993}
Fe(CO)$_5$,\cite{Braga1993} Re$_3$Cl$_{12}^{3-}$,\cite{Colton1965} (Mo$_6$Cl$_8$)Cl$_4$,\cite{Fucugauchi1994} Nb$_3$Cl$_8$,\cite{Yoon2020}}
\sout{\textbf{Transition metal carbonyl} and \textbf{halide clusters}, among which some representative species are Mn$_2$(CO)$_{10}$,\cite{Dahl1963} Ni(CO)$_4$,\cite{Braga1993}
Fe(CO)$_5$,\cite{Braga1993} Re$_3$Cl$_{12}^{3-}$,\cite{Colton1965} (Mo$_6$Cl$_8$)Cl$_4$,\cite{Fucugauchi1994} Nb$_3$Cl$_8$.\cite{Yoon2020}
have benefited from single-crystal X-ray diffraction} \red{because .... In this paragraph you are giving some randum facts about clusters but
it is not clear why, if you want to give details OK, but be precis and give more context For the other one you describe what are they main charactyeristic,
but not for these ones, why}. \textbf{Organometallic clusters} contain metal-metal bonds as well as at least an organic ligand directly bonded to a
metal atom. It can be neutral or ionic. One typical representative for the organometallic cluster is [Co$_3$(CCH$_3$)(CO)$_9$].\cite{Sutton2016}
\textbf{Metalloid cluster} are ligand-stabilized clusters that metal atoms possess more direct element-element than element-ligand contacts such
as [Al$_{69}$(N(SiMe$_3$)$_2$)$_{18}$]$^{3-}$ and [Ga$_{84}$(N(SiMe$_3$)$_2$)$_{20}$]$^{4-}$.\cite{Schnepf2002} The suffix ``oid" designates
such cluster possesses atom arrangements that appear in bulk intermetallic compounds with high coordination numbers of the atoms at a molecular
scale. \textbf{Intermetalloid} clusters consisting in at least two different (semi) metallic elements, and possess more direct metal-metal contacts
than metal-ligand contacts. This kind of cluster often appears as discrete units in intermetallic compounds separated from each other by electropositive
atoms for instance $[$Sn@Cu$_{12}$@Sn$_{20}]^{12-}$.\cite{Stegmaier2011, Fassler2004}
%Clusters can also be observed in the gas-phase by means of mass spectrometry but usually they are not stable.
Finally, \textbf{clusters composed of non-metal atoms or molecules} are usually found in gas-phase for instance \textbf{fullerenes}, \cite{Kroto1991c60} \red{citation} \textbf{rare-gas clusters},\cite{Farges1981, Siedschlag2004} \red{citation} \textbf{water cluster},\cite{Berden1996, Buck2000} \red{citation} and \textbf{PAHs cluster}.\cite{Rapacioli2005stacked, Zhen2018}
%\cite{Farges1981, Kroto1991c60, Blase2008, Siedschlag2004, Rapacioli2005stacked, Zhen2018, Berden1996, Buck2000} \
These various kinds of clusters, which list has no mean to be non-exhaustive, can be differentiated by the bounding mode, \textit{i.e.} the interaction,
between the cluster constituents. They can be of different natures:
\begin{itemize}
\item[$\bullet$] \textbf{Van der Waals interactions.} %rises from attraction between induced electric dipoles and repulsion between electron cores of closed electronic configurations.
This is the main interaction in the rare-gas clusters such as argon clusters.\red{citations}
\item[$\bullet$] \textbf{Hydrogen-bond interaction,} which is of paramount important in a variety of molecular clusters,
in particular those containing water molecules.
\item[$\bullet$] \textbf{Covalent interaction,} as found in fullerenes\red{citation}, or more generally pure carbonaceous aggregates, and other atomic aggregates
made of non-metallic atoms.
%which is from the stable balance of attractive and repulsive forces between atoms, when they share electron pairs.
\item[$\bullet$] \textbf{Electrostatic interaction.} as found in \red{Linjie found in the litterature some clusters held together by electrostatic interaction}
%that stems from the valence electrons which almost entirely transferred among closest neighbors to yield two equal but opposite electric charge distributions that mutually attract.
\item[$\bullet$] Electrostatic attractive force. For instance, the metal clusters are together by electrostatic attractive force. \red{LMinjie, do not know what is this
Electrostatic attractive force, I want reference here to metalic bound or metalic interecatiuon and some examples.}
%rising from long range valence electron sharing (over many successive adjacent atoms) and partially directional.
\end{itemize}
%Fullerene is a cluster composed of 60 carbon atoms arranged as the vertices of a truncated icosahedron.\cite{Kroto1991c60}
%Rare-gas clusters are ideal microclusters, for which a reliable theoretical treatment may be reached due to the applicability of a simple pair potential. \cite{Farges1981, Siedschlag}
%such as the Lennard-Jones potential.
%Such naked clusters that are not stabilized by ligands are usually produced by ablation of a bulk metal or metal-containing compound or laser induced evaporation. These approaches produce a broad size distributed clusters. Their reactivity, ionization potential and HOMO-LUMO gap usually show a pronounced size dependence such as certain aluminium clusters and gold clusters. The laser ablation experiments can also generate isolated compounds, and the premier cases are the clusters of carbon \textit{i.e.}, the fullerenes for instance C$_{60}$ and C$_{84}$.
Properties of clusters stem from both their size and composition. Clusters can thus exhibit very specific physical and chemical properties
that are strongly influence by their structure, which them self are strongly determined by the number of atoms or molecules they are made of.
In particular, the properties of a given clusters can be significantly different from the properties of the corresponding bulk material.\red{citation + exemple here}
Furthermore, when a given cluster of a well defined composition switches between different stable configurations, chemical and physical
properties can also be strongly impacted.\red{here also, citation + example} This becomes all the more true as the chemical complexity of the cluster
increases, \textit{i.e.} when its is constituted of more than one chemical element, for instance several types of molecules for a molecular clusters or
different atoms for an atomic cluster. Depending on the cluster type, see above, intermolecular interactions can be rather weak.\red{citation}
This is true for atomic or molecular clusters which cohesion is governed by Van der Waals and/or hydrogen-bond interactions. In that case, its
potential energy surface (PES), or energy landscape, can be extremely complex and a very large variety of local minima displaying equivalent stabilities.
In that case, the structural properties of such an aggregate result from a fine equilibrium between different contributions such as \red{which ones}.
Although properties of clusters generally differ from those of the corresponding bulk materials, a gradual transition occurs between the properties
of the clusters and those of the corresponding bulk as cluster size increases increase.\red{citation} This transition can be rough or continuous depending
on the considered species and properties.\red{citation + exemple} Consequently, the study of clusters allow to bridge the gap between single
molecule or atom properties and bulk materials, which can be of help to reveal microscopic aspects which are hardly observable in the bulk only.
The field of cluster research can be traced back to 1857 when Faraday gave his lecture entitled ``Experimental Relation of (Colloidal) Gold to Light" which paved the way for modern work on both metal clusters and the interaction of photons with clusters.\cite{Faraday1857} Clusters research have drawn interest and undergone a dramatic growth for several reasons. One is the matter of technique. Now some techniques made it possible for the investigation of clusters both experimentally and theoretically in several scientific fields, for instance the astrophysics, atmospheric physico-chemistry, biochemistry, environmental science.
With the help of mass spectrometer, the well-defined clusters were observed in a supersonic expansion.
The advent of the laser provided a new dimension, enabling detailed spectroscopic observations through probing the systems of different size and degree of solvation.
Others are reasons of purpose. Clusters may offer ways to make new kinds of materials together, to carry out chemical reactions in new ways and to get new kinds of understanding of bulk matter by learning how the bulk properties emerge from properties of clusters as the cluster grow larger and larger.
The behavior study of clusters has been giving new insights into phase transition, e.g. the adsorption to the surface, condensation of gas mixtures and evaporation, precipitation, solidification of liquid mixtures and melting of solids, which makes it a big interest standpoint.\cite{Galvez2019, Xu2020, Tian2018, Deng2018, Rapacioli2019}
The study of clusters helps to understand the nucleation phenomena, for instance the formation of nanoscale materials and aerocolloids, ultrafine particles.\cite{Castleman1978, Castleman1978the, Zhong2000, Pinkard2018}
Cluster in gas-phase state study can provide detailed structural, energetic, and spectroscopic information which is hard to extract from the bulk measurement.\cite{Asuka2013, Luo2016, Wang2016, Jiang2019}
Clusters containing organic/inorganic molecules and some water molecules can be viewed as an intermediate state of matter between the dilute gas phase and solution and the study of them allows the effects of solvation on the chemistry of gas-phase molecules and ions to be explored.\cite{Meot1984, Castleman1994, Castleman1996, Farrar1988, Mayer2002}
%\subsection{Water clusters with impurities}
\textbf{Water clusters}
Water is ubiquitous in our environment. In view of the importance of water to all life and its complex properties, a significant amount of experimental \cite{Woutersen1997, Ruan2004, Brubach2005, Bergmann2007, Pokapanich2009, Sun2010, Harada2017, Yamazoe2019} and theoretical \cite{Silvestrelli1999, Laage2006, Bryantsev2009, Silvestrelli2017} studies have been performed about this fundamental substance since the first realistic interaction potential of water was proposed in 1933. \cite{Bernal1933, Shields2010} Water clusters are intermediate systems between gas phase and condensed phases. The study of water clusters is of fundamental importance to understand properties of liquid water and ice and offers the opportunity to understand how the properties of bulk water emerge and how the properties of water change with size.\cite{Gregory1996} The research about water clusters focusing on the determination of the most stable structures, the corresponding stabilization energies, and the harmonic vibrational frequencies etc has been done.\cite{Teeter1984, Pedulla1998, James2005, Prell2009, Brown2017, Malloum2021} There have been many $ab initio$ studies of small water clusters, and the global potential energy minima of (H$_2$O)$_{1-5}$ are not in doub. \cite{Wales1998}
The water complexes are plentiful in the atmosphere, which plays a crucial role in the evolution of climate. \cite{Bigg1975, Vaida2000, Aloisio2000, Ramanathan2001, Mccurdy2002, Hartt2008, Vaida2011}
It is known that water clusters can absorb significant amounts of energy,\cite{Kjaergaard2003} and these clusters are not yet included in climate models due to the lack of data about their formation. \cite{Vaida2003} Detailed computational thermodynamics can be useful in modeling the aerosol growth by determining the equilibrium constants for cluster formation.\cite{Morrell2010}
Hydrogen bonding is arguably the most extensively studied among all the noncovalent interactions. Hydrogen bonding governs many chemical
and biological processes in nature and living organisms.\cite{Pimentel1960, Jeffrey1997}
The hydrogen bonding has been known for about one hundred years, \cite{Latimer1920} but new researches involving hydrogen bonding species continues to generate interesting results.
An important property of water is its ability to form
hydrogen bonds.
Commonly it is asserted that each hydrogen bond between water molecules stabilizes a structure by about 5 kcal.mol$^{-1}$. \cite{Eisenberg2005} Therefore, water clusters that differ only by the direction of hydrogen bonds, but otherwise have the same number of H-bonds and placement of oxygen atoms should have approximately the same energy. \cite{Kuo2003} The stability of water clusters, based on the arrangement of individual molecules in different phases has been widely explored. \cite{Ludwig2001, Buckingham2008} A lot of theoretical studies have focused on understanding hydrogen bonding in small water clusters (H$_2$O)$_{2-6}$. \cite{Lee2000, Maheshwary2001, Santra2008, Buckingham2008, Hanninen2009, Neela2010} In one of the carefully conducted computational studies, it was shown that the most stable geometries of water clusters H$_2$O)$_{8-20}$ arise from a fusion of tetrameric or pentameric rings. \cite{Maheshwary2001, Neela2010}
Molecular clusters with a controlled number of solvent molecules are ideal model systems for providing a fundamental understanding of solute-solvent and solvent-solvent interactions at the molecular level.\cite{Wang2010}
The study of the stability of water clusters containing inorganic/organic ions or neutral molecules for instance the Cl$^{-}$(H$_2$O)$_n$, Na$^+$(H$_2$O)$_n$, H$_2$PO$_4^{-}$, NH$_4^+$(H$_2$O)$_n$, NH$_3$(H$_2$O)$_n$, C$_6$H$_6$O(H$_2$O)$_n$, H$_2$SO$_4$(H$_2$O)$_n$,
HSO$_4^{-}$(H$_2$O)$_n$, (CO)$_m$(H$_2$O)$_n$, ((CH$_3$)$_2$NH$_2^+$)$_m$(HSO$_4^{-}$)$_m$(H$_2$O)$_n$, C$_4$H$_5$N$_2$O$_2^+$(H$_2$O)$_n$, (C$_5$H$_5$N)$_m$H$^+$(H$_2$O)$_n$, and so on is the foundation for the study of other properties of these systems such as the spectroscopic study. \cite{Berden1996, Buck2000, Huneycutt2003, Schermann2007, Caleman2007, Rozenberg2009, Ryding2011, Depalma2014, Korchagina2016, Korchagina2017M, Korchagina2017, Braud2019}
Many significant efforts have been devoted to the experimental characterization of the chemical composition and behavior of atmospheric particles
since 1970s. \cite{Hogan1975, Arnold1977, Arnold1982, Heymsfield1986} Among these studies, the ion composition measurements demonstrated the existence of charged molecular aggregates in the stratosphere,\cite{Arnold1977, Arnold1982} especially the negatively charged species such as nitrate- and sulfate-containing water clusters.
These grown atmospheric particles initiate the process of acid cloud formation and participate in reactions leading to the destruction of the ozone layers in polar regions, \cite{Koop1996, Carslaw1997} which makes it meaningful to study the corresponding charged water clusters. \cite{Korchagina2016}
In addition, charged clusters can be sorted easily by electrostatic, magnetic or time-of-flight mass analysis to yield mass spectra, which contributes to the exploration of charged clusters.
Understanding the hydrated proton is of paramount importance for the knowledge of fundamental processes in biology and chemistry, and the investigation of protonated water clusters has been proven to be essential for understanding the nature of protons in solution. \cite{Kunst1980, Torrent2011}
In the work of this thesis, the stability of ammonium/ammonia water clusters and protonated uracil water clusters were explored.
%\subsection{PAHs Clusters}
\textbf{PAHs clusters}
Polycyclic aromatic hydrocarbon clusters are abundant in the interstellar medium, which lock up about 10\% - 20\% of the carbon element in the universe and are considered as the possible starting material for the earliest forms of life. \cite{Hoover2014, Tielens2008} They are one of the main pollutants in the environment. They act as part of the soot particles in combustion science. In addition, they act as the prototypes for the design of new organic solar cell devices. PAHs can be transformed, through hydrogenation, oxygenation, and hydroxylation, to become more complex organic compounds, which makes it an interesting choice to study the PAH clusters.
In order to characterize the stability of polycyclic aromatic hydrocarbons, the involution of them has been explored a lot in experiment after absorption of photons, collision with high or low energetic particles or in a very high pressure environment. The collision details of polycyclic aromatic hydrocarbon cluster with projectile are always not possible to obtain from the experimental data. In addition, the experimental studies are complicated and associated facilities are expensive, which sometimes prevent all desired measurements to be carried out. Therefore, further theoretical studies should be conducted to bring us to make a deeper interpretation of the experimental measurements and complement the experiments.
%\section{CID of molecular clusters}
\textbf{CID of molecular clusters}
The structure, energetics and reactivity of a variety of molecular cluster can be explored by collision-induced dissociation. \cite{Dawson1982, Graul1989, Wei1991, Liu2006, Goebbert2006, Coates2018}. By colliding a molecule, or a molecular cluster with a non-reactive noble gas atom or a small molecule such as N$_2$, it is possible to monitor the parent ions and collision products then the spectra of the parent and product ions can provide a wealth of information about the structure from which one can infer, for instance, dissociation mechanisms \cite{Nelson1994, Molina2015} or bond and hydration enthalpies \cite{Carl2007}. The collision-induced dissociation also has been used to understand the impact of high-energy radiations on living cells and DNA or RNA \cite{Liu2006, Nguyen2011, Shuck2014}, as well as low-energy collisions on of biological molecules. \cite{Castrovilli2017,Bera2018}.
Extracting energetics or collision process from collision-induced dissociation is not an easy task and it often requires the theoretical calculations to complement. Two main methodologies can be conducted. The first one is to make an exhaustive description of the potential energy surface connecting both parent ions and products.
%Energetic information on both minima and transition states can then be introduced in Rice-Ramsperger-Kassel-Marcus \cite{Klippenstein1992, Baer1996} and/or Kinetic Monte Carlo simulations \cite{Metropolis1949, Voter2007}.
The second approach is to perform molecular dynamics simulations to explicitly model the collision trajectory of the target ion and the projectile, the energy redistribution, the subsequent reorganizations and fragmentations.
A potential is needed to correctly describe the potential energy surface of the system and its reactivity. The method chosen need to reach a balance between the desired precision and the computational cost.
%The question appeared during the theoretical study of molecular clusters is to chose the calculation method.
For the dynamical simulations of system composed of several tens of atoms, the full configuration interaction and wave function based methods allow to calculate the energy, but do not allow to achieve sufficient simulations to describe their dynamic behavior at finite temperature.
It is difficult for the exhaustive exploration of potential energy surfaces of system with tens of atoms or for carrying out dynamical simulations for several hundred picoseconds using DFT method.
The density-functional based tight-binding method (DFTB) method can perform molecular dynamical simulations of systems containing several tens of atoms for simulation time of several hundred picoseconds.
The force field methods can achieve dynamical simulations of system with tens of atoms for several hundred nanoseconds, but it can poorly describe the formation or breaking of covalent bonds.
Therefore, the DFTB approach seems to be well suited to the study of molecular clusters investigated in this thesis work.
For the work of this thesis, it is concentrated on the structure, solvation, thermodynamics study of ammonia containing water clusters, ammonium containing water clusters, which help to understand the nucleation phenomena and the formation of aerosols. The uracil included water clusters were also studied, which can provide a benchmark to observe how the properties of biological molecules change from isolated gas-phase to hydrated species. The polycyclic aromatic hydrocarbon (PAH) clusters are abundant in the universe.\cite{Carey2005, Hudgins2005, Clavin2015}
The dynamics study of the dissociation of the simplest pyrene aggregates, pyrene dimer, to interpret the CID experiments of PAHs with noble gas to have a better understanding of the physics of this kind of cluster.
The first chapter introduces the object of this thesis work. A generality about clusters and the clusters studied in this thesis are introduced. Then the collision-induced dissociation of molecular clusters is briefly described.
The second chapter is devoted to the introduction the fundamental concepts used in theoretical chemistry for the solution of the electronic problem, which describes the main approaches traditionally employed.
The method, density functional based tight binding (DFTB), applied in this thesis work is also described. The different methods to explore the potential energy surface are presented in this chapter.
In the third chapter, the study on the structure and stability of ammonium/ammonia water clusters,
%mixed ammonium/ammonia and sulfate containing water clusters,
and protonated uracil water clusters were presented.
Comparing the results calculated using DFTB method with the corresponding ones using MP2 method or the ones in the literature, it shows the DFTB method can provide a quite good result for the optimization of these clusters.
The fourth chapter presents the study on the molecular dynamics simulations of collision-induced dissociation of protonated uracil water clusters. The theoretical proportion of formed neutral uracil molecule \textit{vs.} protonated water cluster as well as total fragmentation cross sections are consistent with
the experimental data which highlights the accuracy of the simulations. The molecular dynamic simulations allow to probe which fragments are formed on the short time scale and rationalize the location of the excess proton on these fragments. We demonstrate that the location of the excess proton is highly influenced by the nature of the aggregate undergoing the collision. The analyses show that, up to seven water molecules in the cluster, a shattering mechanism occurs after collision whereas for the cluster with twelve water molecules has a chance to rearrange prior to complete dissociation. In addition, the dymical simulations of the collision-induced dissociation of pyrene dimer cation at different collision energies are described in this chapter. It appears that most of the dissociation occurs on a short timescale (less than 3 ps). The dynamical simulations allow to visualise the dissociation processes.
At low collision energies, the dissociation cross section increases with collision energies whereas it remains almost constant for collision energies greater than 10-15~eV. The analysis of the kinetic energy partition is used to get insights into the collision/dissociation processes at the atomic scale.
The simulated time of flight mass spectra of parent and dissociated products are obtained from the combination of molecular dynamics simulations and phase space theory to address the short and long timescales dissociation, respectively. The agreement between the simulated and measured mass spectra suggests that the main processes are captured by this approach.
Finally, the conclusions of the work of this thesis as well as a number of perspectives are displayed in chapter 5.
% ---------------------------------------------------------------------------

334
thesis/1_GeneIntro/GeneIntro.aux Normal file
View File

@ -0,0 +1,334 @@
\relax
\providecommand\hyper@newdestlabel[2]{}
\citation{Cotton1964}
\citation{Haberland2013}
\citation{Schmid1988,Hakkinen2002}
\citation{Dahl1963}
\citation{Fucugauchi1994}
\citation{Sutton2016}
\citation{Schnepf2002}
\citation{Fassler2004,Stegmaier2011}
\citation{Farges1981,Kroto1991c60,Blase2008,Siedschlag2004}
\citation{Rapacioli2005stacked,Zhen2018}
\citation{Schmid1988}
\citation{Dahl1963}
\citation{Dyson2000}
\citation{Dyson2000}
\citation{Colton1965}
\citation{Fucugauchi1994}
\citation{Yoon2020}
\citation{Sutton2016}
\citation{Schnepf2002}
\citation{Stegmaier2011,Fassler2004}
\citation{Kroto1991c60}
\citation{Farges1981,Siedschlag2004}
\citation{Berden1996,Buck2000}
\citation{Rapacioli2005stacked,Zhen2018}
\FN@pp@footnotehinttrue
\@writefile{toc}{\contentsline {chapter}{\numberline {1}General Introduction}{1}{chapter.1}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{chap:general_intro}{{1}{1}{General Introduction}{chapter.1}{}}
\@writefile{brf}{\backcite{Cotton1964}{{1}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Haberland2013}{{1}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Schmid1988}{{1}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Hakkinen2002}{{1}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Dahl1963}{{1}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Fucugauchi1994}{{1}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Sutton2016}{{1}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Schnepf2002}{{1}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Fassler2004}{{1}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Stegmaier2011}{{1}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Farges1981}{{1}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Kroto1991c60}{{1}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Blase2008}{{1}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Siedschlag2004}{{1}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Rapacioli2005stacked}{{1}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Zhen2018}{{1}{1}{chapter.1}}}
\citation{Harris1984}
\citation{Kroto1991c60}
\citation{Hakkinen2002}
\citation{Ayuela1993}
\citation{Calvo2018}
\@writefile{brf}{\backcite{Schmid1988}{{2}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Dahl1963}{{2}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Dyson2000}{{2}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Dyson2000}{{2}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Colton1965}{{2}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Fucugauchi1994}{{2}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Yoon2020}{{2}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Sutton2016}{{2}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Schnepf2002}{{2}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Fassler2004}{{2}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Stegmaier2011}{{2}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Kroto1991c60}{{2}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Farges1981}{{2}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Siedschlag2004}{{2}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Berden1996}{{2}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Buck2000}{{2}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Rapacioli2005stacked}{{2}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Zhen2018}{{2}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Harris1984}{{2}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Kroto1991c60}{{2}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Hakkinen2002}{{2}{1}{chapter.1}}}
\citation{Alonso2000}
\citation{Margenau2013}
\citation{Kimura1991}
\citation{Jortner1992}
\citation{Hakkinen2002}
\citation{Boulon2014}
\citation{Schmidt2012}
\citation{Hock2009}
\citation{Boulon2014}
\citation{Schmidt2012}
\citation{Hock2009}
\citation{Boulon2014}
\citation{Faraday1857}
\citation{Zhen2018}
\citation{Kulmala2000}
\citation{Wang2008}
\citation{Depalma2014}
\citation{Katakuse1985}
\citation{Posthumus2009}
\citation{Castleman2009}
\citation{Henglein1989}
\citation{Jortner1992}
\citation{Korobeishchikov2005}
\citation{Xu2020}
\citation{Tian2018}
\citation{Deng2018}
\citation{Rapacioli2019}
\citation{Castleman1978,Castleman1978the,Zhong2000,Pinkard2018}
\citation{Asuka2013,Luo2016,Wang2016,Jiang2019}
\citation{Meot1984,Castleman1994,Castleman1996,Farrar1988,Mayer2002}
\@writefile{brf}{\backcite{Ayuela1993}{{3}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Calvo2018}{{3}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Alonso2000}{{3}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Margenau2013}{{3}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Kimura1991}{{3}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Jortner1992}{{3}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Hakkinen2002}{{3}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Boulon2014}{{3}{1}{chapter.1}}}
\@writefile{brf}{\backcite{Faraday1857}{{3}{1}{figure.caption.3}}}
\citation{Wales1997,Wales1998,Wales1999,James2005}
\citation{Boulon2014}
\citation{Korchagina2017}
\citation{Hada2003,Chakraborty2020,Zamith2020threshold,Zheng2021}
\citation{Tibshirani2005}
\@writefile{lof}{\contentsline {figure}{\numberline {1.1}{\ignorespaces Transition temperature of (H$_{2}$O)$_{n}$H$^{+}$ clusters (red squares) and (H$_{2}$O)$_{n-1}$OH$^{-}$ (blue circles) as a function of $n$. The results obtained by M. Schmidt \textit {et al.} on (H$_{2}$O)$_{n}$H$^{+}$ are also presented (black circles)\cite {Schmidt2012} as well as those by C. Hock \textit {et al.} on (H$_{2}$O)$_{n}^{-}$ clusters (black stars).\cite {Hock2009} Figure extracted from reference~\cite {Boulon2014}.\relax }}{4}{figure.caption.3}}
\@writefile{brf}{\backcite{Schmidt2012}{{4}{1.1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Hock2009}{{4}{1.1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Boulon2014}{{4}{1.1}{figure.caption.3}}}
\providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}}
\newlabel{T_trans}{{1.1}{4}{Transition temperature of (H$_{2}$O)$_{n}$H$^{+}$ clusters (red squares) and (H$_{2}$O)$_{n-1}$OH$^{-}$ (blue circles) as a function of $n$. The results obtained by M. Schmidt \textit {et al.} on (H$_{2}$O)$_{n}$H$^{+}$ are also presented (black circles)\cite {Schmidt2012} as well as those by C. Hock \textit {et al.} on (H$_{2}$O)$_{n}^{-}$ clusters (black stars).\cite {Hock2009} Figure extracted from reference~\cite {Boulon2014}.\relax }{figure.caption.3}{}}
\@writefile{brf}{\backcite{Zhen2018}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Kulmala2000}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Wang2008}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Depalma2014}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Katakuse1985}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Posthumus2009}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Castleman2009}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Henglein1989}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Jortner1992}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Korobeishchikov2005}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Xu2020}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Tian2018}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Deng2018}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Rapacioli2019}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Castleman1978}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Castleman1978the}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Zhong2000}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Pinkard2018}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Asuka2013}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Luo2016}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Wang2016}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Jiang2019}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Meot1984}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Castleman1994}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Castleman1996}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Farrar1988}{{4}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Mayer2002}{{4}{1}{figure.caption.3}}}
\citation{Woutersen1997,Ruan2004,Brubach2005,Bergmann2007,Pokapanich2009,Sun2010,Harada2017,Yamazoe2019}
\citation{Silvestrelli1999,Laage2006,Bryantsev2009,Silvestrelli2017}
\citation{Bernal1933,Shields2010}
\citation{Gregory1996}
\citation{Kunst1980,Torrent2011}
\citation{Wang2010}
\citation{Bigg1975,Vaida2000,Aloisio2000,Ramanathan2001,Mccurdy2002,Hartt2008,Vaida2011}
\citation{Kjaergaard2003}
\citation{Vaida2003}
\citation{Klan2001,Amiaud2007,Kahan2010,Minissale2019}
\@writefile{brf}{\backcite{Wales1997}{{5}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Wales1998}{{5}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Wales1999}{{5}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{James2005}{{5}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Boulon2014}{{5}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Korchagina2017}{{5}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Hada2003}{{5}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Chakraborty2020}{{5}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Zamith2020threshold}{{5}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Zheng2021}{{5}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Tibshirani2005}{{5}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Woutersen1997}{{5}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Ruan2004}{{5}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Brubach2005}{{5}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Bergmann2007}{{5}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Pokapanich2009}{{5}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Sun2010}{{5}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Harada2017}{{5}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Yamazoe2019}{{5}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Silvestrelli1999}{{5}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Laage2006}{{5}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Bryantsev2009}{{5}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Silvestrelli2017}{{5}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Bernal1933}{{5}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Shields2010}{{5}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Gregory1996}{{5}{1}{figure.caption.3}}}
\citation{Perez2012}
\@writefile{brf}{\backcite{Kunst1980}{{6}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Torrent2011}{{6}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Wang2010}{{6}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Bigg1975}{{6}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Vaida2000}{{6}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Aloisio2000}{{6}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Ramanathan2001}{{6}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Mccurdy2002}{{6}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Hartt2008}{{6}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Vaida2011}{{6}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Kjaergaard2003}{{6}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Vaida2003}{{6}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Klan2001}{{6}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Amiaud2007}{{6}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Kahan2010}{{6}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Minissale2019}{{6}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Perez2012}{{6}{1}{figure.caption.3}}}
\citation{Huneycutt2003}
\citation{Caleman2007}
\citation{Berden1996}
\citation{Rozenberg2009,Korchagina2016}
\citation{Korchagina2016}
\citation{Depalma2014}
\citation{Braud2019}
\citation{Ryding2011}
\citation{Koop1996,Carslaw1997}
\citation{Arnold1977,Arnold1982}
\citation{Korchagina2016}
\citation{Payzant1973,Berden1996}
\citation{Kulmala1995,Kirkby2011,Dunne2016}
\@writefile{brf}{\backcite{Huneycutt2003}{{7}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Caleman2007}{{7}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Berden1996}{{7}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Rozenberg2009}{{7}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Korchagina2016}{{7}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Korchagina2016}{{7}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Depalma2014}{{7}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Braud2019}{{7}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Ryding2011}{{7}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Koop1996}{{7}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Carslaw1997}{{7}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Arnold1977}{{7}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Arnold1982}{{7}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Korchagina2016}{{7}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Berden1996}{{7}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Payzant1973}{{7}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Kulmala1995}{{7}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Kirkby2011}{{7}{1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Dunne2016}{{7}{1}{figure.caption.3}}}
\citation{Leger1984,Allamandola1985}
\citation{Leger1984,Puget1989,Tielens2008}
\citation{Tielens2005,Tielens2008}
\citation{Rapacioli2006,Montillaud2014}
\citation{Rapacioli2009,Joblin2017}
\citation{Rapacioli2009}
\citation{Finlayson1986}
\citation{Callen2008}
\citation{Eaves2015,Violi2007}
\citation{Scholz2013,Darghouth2015}
\citation{Rapacioli2006,Holm2010,Simon2017formation,Zhen2018,Chen2018,Zamith2020threshold}
\citation{Schmidt2006,Holm2010,Gatchell2015,Joblin2017,Gatchell2017,Zamith2019thermal}
\@writefile{lof}{\contentsline {figure}{\numberline {1.2}{\ignorespaces Examples of several PAH molecules.\relax }}{8}{figure.caption.4}}
\newlabel{PAHs_sample}{{1.2}{8}{Examples of several PAH molecules.\relax }{figure.caption.4}{}}
\@writefile{brf}{\backcite{Leger1984}{{8}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Allamandola1985}{{8}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Leger1984}{{8}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Puget1989}{{8}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Tielens2008}{{8}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Tielens2008}{{8}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Tielens2005}{{8}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Rapacioli2006}{{8}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Montillaud2014}{{8}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Rapacioli2009}{{8}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Joblin2017}{{8}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Rapacioli2009}{{8}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Finlayson1986}{{8}{1}{figure.caption.4}}}
\citation{Dawson1982,Graul1989,Wei1991,Liu2006,Goebbert2006,Coates2018}
\citation{Nelson1994,Molina2015}
\citation{Carl2007}
\citation{Liu2006,Nguyen2011,Shuck2014}
\citation{Castrovilli2017,Bera2018}
\citation{Klippenstein1992,Baer1996}
\citation{Metropolis1949,Voter2007}
\@writefile{brf}{\backcite{Callen2008}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Eaves2015}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Violi2007}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Scholz2013}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Darghouth2015}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Zhen2018}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Zamith2020threshold}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Rapacioli2006}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Holm2010}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Simon2017formation}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Chen2018}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Joblin2017}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Holm2010}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Schmidt2006}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Gatchell2015}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Gatchell2017}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Zamith2019thermal}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Dawson1982}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Graul1989}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Wei1991}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Liu2006}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Goebbert2006}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Coates2018}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Nelson1994}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Molina2015}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Carl2007}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Liu2006}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Nguyen2011}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Shuck2014}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Castrovilli2017}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Bera2018}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Klippenstein1992}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Baer1996}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Metropolis1949}{{9}{1}{figure.caption.4}}}
\@writefile{brf}{\backcite{Voter2007}{{9}{1}{figure.caption.4}}}
\FN@pp@footnotehinttrue
\@setckpt{1_GeneIntro/GeneIntro}{
\setcounter{page}{12}
\setcounter{equation}{0}
\setcounter{enumi}{0}
\setcounter{enumii}{0}
\setcounter{enumiii}{0}
\setcounter{enumiv}{0}
\setcounter{footnote}{0}
\setcounter{mpfootnote}{0}
\setcounter{part}{0}
\setcounter{chapter}{1}
\setcounter{section}{0}
\setcounter{subsection}{0}
\setcounter{subsubsection}{0}
\setcounter{paragraph}{0}
\setcounter{subparagraph}{0}
\setcounter{figure}{2}
\setcounter{table}{0}
\setcounter{ContinuedFloat}{0}
\setcounter{pp@next@reset}{1}
\setcounter{@fnserial}{0}
\setcounter{NAT@ctr}{0}
\setcounter{Item}{0}
\setcounter{Hfootnote}{0}
\setcounter{bookmark@seq@number}{2}
\setcounter{parentequation}{0}
\setcounter{section@level}{0}
}

0
thesis/1_GeneIntro/GeneIntro.bbl Normal file
View File

47
thesis/1_GeneIntro/GeneIntro.blg Normal file
View File

@ -0,0 +1,47 @@
This is BibTeX, Version 0.99d (TeX Live 2019)
Capacity: max_strings=100000, hash_size=100000, hash_prime=85009
The top-level auxiliary file: GeneIntro.aux
I found no \bibdata command---while reading file GeneIntro.aux
I found no \bibstyle command---while reading file GeneIntro.aux
You've used 119 entries,
0 wiz_defined-function locations,
321 strings with 3006 characters,
and the built_in function-call counts, 0 in all, are:
= -- 0
> -- 0
< -- 0
+ -- 0
- -- 0
* -- 0
:= -- 0
add.period$ -- 0
call.type$ -- 0
change.case$ -- 0
chr.to.int$ -- 0
cite$ -- 0
duplicate$ -- 0
empty$ -- 0
format.name$ -- 0
if$ -- 0
int.to.chr$ -- 0
int.to.str$ -- 0
missing$ -- 0
newline$ -- 0
num.names$ -- 0
pop$ -- 0
preamble$ -- 0
purify$ -- 0
quote$ -- 0
skip$ -- 0
stack$ -- 0
substring$ -- 0
swap$ -- 0
text.length$ -- 0
text.prefix$ -- 0
top$ -- 0
type$ -- 0
warning$ -- 0
while$ -- 0
width$ -- 0
write$ -- 0
(There were 2 error messages)

27054
thesis/1_GeneIntro/GeneIntro.log Normal file
View File

File diff suppressed because it is too large Load Diff

385
thesis/1_GeneIntro/GeneIntro.tex Normal file
View File

@ -0,0 +1,385 @@
%this file is c\emph{•}alled up by thesis.tex
% content in this file will be fed into the main document
%%\chapter{Aims of the project} % top level followed by section, subsection
\ifpdf
\graphicspath{{1_GeneIntro/figures/PNG/}{1_GeneIntro/figures/PDF/}{1_GeneIntro/figures/}}
\else
\graphicspath{{1_GeneIntro/figures/EPS/}{1_GeneIntro/figures/}}
\fi
\chapter{General Introduction} \label{chap:general_intro}
%\section{Molecular Clusters}
The term \textit{cluster} was coined by Cotton in the early 1960s to refer to compounds containing metal-metal bonds such as [Re$_2$Cl$_8$]$^{2-}$
and [Re$_2$Br$_8$]$^{2-}$.\cite{Cotton1964} He defined metal atom cluster compounds as "\textit{those containing a finite group of metal atoms
which are held together entirely, mainly, or at least to a significant extent, by bonds directly between the metal atoms even though some non-metal
atoms may be associated intimately with the cluster}". Subsequently, the study of clusters, also referred to as aggregates, has greatly diversified
and the definition of the term \textit{cluster} has evolved considerably from that given by Cotton. Indeed, in chemistry, the term cluster now refers to
an ensemble of bound atoms or molecules that can be isolated or incorporated within a larger chemical compounds, for instance within a solid-state compounds.
A cluster is intermediate in size between a single molecule or atom and a nanoparticle. A hundred billion \textit{particles} (here the term particle referred
to the constituents of the cluster, which can be either atoms, ions, molecules or a mix) held together behave in most ways like bulk matter whereas
small clusters contain no more than a few hundred or a thousand particles and a large cluster designates something containing about a few thousands
of particles.\cite{Haberland2013} Clusters are also intermediate in terms of properties between a single molecule or atom and the corresponding bulk
compound.
Cluster chemistry developed contemporaneously along several independent research lines and several families of compounds can be referred to as
clusters. Among them, one can mention \textbf{naked metal clusters},\cite{Schmid1988, Hakkinen2002} metal cluster compounds such as
\textbf{transition metal carbonyl clusters},\cite{Dahl1963} \textbf{transition metal halide clusters},\cite{Fucugauchi1994}
\textbf{transition metal organic carbon clusters} (organometallic),\cite{Sutton2016} \textbf{metalloid clusters},\cite{Schnepf2002}
\textbf{intermetalloid clusters},\cite{Fassler2004, Stegmaier2011} as well as \textbf{atomic clusters} composed of non-metal atoms \cite{Farges1981, Kroto1991c60, Blase2008, Siedschlag2004} and \textbf{molecular clusters}.\cite{Rapacioli2005stacked, Zhen2018}
\textbf{Naked metal clusters} encompass only metal atoms that are held together by metallic bond for instance Rh$_{13}$ and Au$_{13}$.\cite{Schmid1988}
\textbf{Transition metal carbonyl clusters} are compounds containing a core that consists of two or more metal atoms linked in part by metal-metal
bonds and embraced by carbon monoxide (CO) ligand groups exclusively or predominantly. Similarly, \textbf{transition metal halide clusters} are compounds
that contains two or more metal atoms (prevalent for heavy metals) linked in part by metal-metal bonds and embraced by halide ligands. Some
representative species for transition metal carbonyl and halide clusters are Mn$_2$(CO)$_{10}$,\cite{Dahl1963} Fe$_2$(CO)$_9$,\cite{Dyson2000}
[Rh$_6$(CO)$_{15}$]$^{2-}$,\cite{Dyson2000}
Re$_3$Cl$_{12}^{3-}$,\cite{Colton1965} (Mo$_6$Cl$_8$)Cl$_4$,\cite{Fucugauchi1994} Nb$_3$Cl$_8$,\cite{Yoon2020}
\textbf{Organometallic clusters} contain metal-metal bonds as well as at least one organic ligand directly bonded to a
metal atom. It can be neutral or ionic. One example of organometallic cluster is [Co$_3$(CCH$_3$)(CO)$_9$].\cite{Sutton2016}
\textbf{Metalloid clusters} are ligand-stabilized clusters that metal atoms possess more direct element-element contacts than
element-ligand contacts such as [Al$_{69}$(N(SiMe$_3$)$_2$)$_{18}$]$^{3-}$ and [Ga$_{84}$(N(SiMe$_3$)$_2$)$_{20}$]$^{4-}$.\cite{Schnepf2002}
The suffix ``oid" highlights that such clusters possess atom arrangements that appear in bulk intermetallic compounds with high
coordination numbers of the atoms at a molecular scale. \textbf{Intermetalloid} clusters consist in at least two different (semi)
metallic elements, and possesses more direct metal-metal contacts than metal-ligand contacts. This kind of cluster often appears
as discrete units in intermetallic compounds separated from each other by electropositive atoms for instance
$[$Sn@Cu$_{12}$@Sn$_{20}]^{12-}$.\cite{Stegmaier2011, Fassler2004}
%Clusters can also be observed in the gas-phase by means of mass spectrometry but usually they are not stable.
Finally, \textbf{clusters composed of non-metal atoms or molecules} are usually found in gas-phase for instance \textbf{fullerenes},
\cite{Kroto1991c60} \textbf{rare-gas clusters},\cite{Farges1981, Siedschlag2004} \textbf{water clusters},\cite{Berden1996, Buck2000}
and \textbf{PAHs (Polycyclic aromatic hydrocarbons) clusters}.\cite{Rapacioli2005stacked, Zhen2018}
These various kinds of clusters, which list has no mean to be exhaustive, can be differentiated by the bounding mode, \textit{i.e.} the nature
of the interaction, between the cluster particles. They can be of different natures:
\begin{itemize}
\item[$\bullet$] \textbf{Van der Waals interactions}, which is the main interaction in the rare-gas clusters such as argon clusters.\cite{Harris1984}
\item[$\bullet$] \textbf{Hydrogen-bond interaction}, which is of paramount importance in a variety of molecular clusters, in particular
those containing water molecules.
\item[$\bullet$] \textbf{Covalent bond}, as found in fullerenes,\cite{Kroto1991c60} or more generally pure carbonaceous aggregates,
and other atomic aggregates made of non-metallic atoms.
%which is from the stable balance of attractive and repulsive forces between atoms, when they share electron pairs.
\item[$\bullet$] \textbf{Metallic bond}, as found in Cu, Ag, and Au clusters.\cite{Hakkinen2002}
\item[$\bullet$] \textbf{Ionic bond}, which exists in ionic clusters such as NaCl\cite{Ayuela1993} or NaF clusters.\cite{ Calvo2018}
\end{itemize}
%Fullerene is a cluster composed of 60 carbon atoms arranged as the vertices of a truncated icosahedron.\cite{Kroto1991c60}
%Rare-gas clusters are ideal microclusters, for which a reliable theoretical treatment may be reached due to the applicability of a simple pair potential. \cite{Farges1981, Siedschlag}
%such as the Lennard-Jones potential.
%Such naked clusters that are not stabilized by ligands are usually produced by ablation of a bulk metal or metal-containing compound or laser induced evaporation. These approaches produce a broad size distributed clusters. Their reactivity, ionization potential and HOMO-LUMO gap usually show a pronounced size dependence such as certain aluminium clusters and gold clusters. The laser ablation experiments can also generate isolated compounds, and the premier cases are the clusters of carbon \textit{i.e.}, the fullerenes for instance C$_{60}$ and C$_{84}$.
Properties of clusters stem from both their size and composition. Clusters can thus exhibit very specific physical and chemical properties
that are strongly influences by their structures, which themselves are strongly determined by the number of atoms or molecules they are
made of. Furthermore, when a given cluster of a well defined composition switches between different stable configurations, chemical
and physical properties can also be strongly impacted. For instance, for different conformational isomers of small Ni and Fe clusters, compact
structures are more stable than open structures and the photoabsorption spectra of two isomers of Ni$_4$ are different.\cite{Alonso2000}
This becomes all the more true as the chemical complexity of the cluster increases, \textit{i.e.} when it is constituted of more than one chemical
element, for instance several types of molecules for a molecular cluster or
different atoms for an atomic cluster. Depending on the cluster type, see above, intermolecular interactions can be rather weak.\cite{Margenau2013}
This is true for atomic or molecular clusters which cohesion is governed by Van der Waals and/or hydrogen-bond interactions. In that case, the
potential energy surface (PES), or energy landscape, can be extremely complex and a large variety of local minima displaying equivalent stabilities
exist. The properties of a given cluster can significantly differ from the properties of the corresponding bulk material. For instance, the magnetic moment
of small iron particles at room temperature is smaller than that of the bulk.\cite{Kimura1991} However, a gradual transition occurs between the properties
of the clusters and those of the corresponding bulk as cluster size increases.\cite{Jortner1992} This transition can be rough or continuous depending
on the considered species and properties. For instance, Landman \textit{et al.} reported that anionic gold clusters favor planar structures
up to $\sim$13 atoms.\cite{Hakkinen2002} L'Hermite \textit{et al.} also reported that the transition temperature extracted from he
heat capacity curve of protonated water clusters (H$_{2}$O)$_{n}$H$^{+}$ has a strong size dependence as seen in Figure~\ref{T_trans}.\cite{Boulon2014}
Consequently, the study of clusters allow to bridge the gap between single molecule or atom properties and bulk materials, which can be of help
to reveal microscopic aspects which are hardly observable in the bulk only.
\begin{figure}[h]
\begin{center}
\includegraphics[width=12cm]{T_trans.png}
\caption{Transition temperature of (H$_{2}$O)$_{n}$H$^{+}$ clusters (red squares) and (H$_{2}$O)$_{n-1}$OH$^{-}$
(blue circles) as a function of $n$. The results obtained by M. Schmidt \textit{et al.} on (H$_{2}$O)$_{n}$H$^{+}$ are also
presented (black circles)\cite{Schmidt2012} as well as those by C. Hock \textit{et al.} on (H$_{2}$O)$_{n}^{-}$ clusters
%<<<<<<< HEAD
%(black stars \sout{noires}).\cite{Hock2009} \red{ref does not} Figure extracted from reference~\cite{Boulon2014}.} \label{T_trans}
%=======
(black stars).\cite{Hock2009} Figure extracted from reference~\cite{Boulon2014}.} \label{T_trans}
%>>>>>>> 92023a10c3aa8b7dc4ace43987c1d571fb99a738
\end{center}
\end{figure}
The field of cluster research can be traced back to 1857 when M. Faraday gave his lecture entitled ``\textit{Experimental Relation of (Colloidal) Gold to Light}"
which paved the way for modern work on both metal clusters and the interaction of photons with clusters.\cite{Faraday1857} Cluster research
have since drawn a lot of interest and the field has undergone a dramatic growth which can be explained by two main reasons. The first one is the
\textbf{development of efficient and accurate characterization techniques}. Indeed, experimental techniques now enable the investigation of clusters of
interest in several scientific domains such as astrophysics and astrochemistry,\cite{Zhen2018} atmospheric physico-chemistry,\cite{Kulmala2000}
biochemistry,\cite{Wang2008} and environmental science.\cite{Depalma2014} With the help of mass spectrometer, well-defined cluster sizes can
now be isolated and observed.\cite{Katakuse1985} The advent of the laser technology also provides a new dimension to the field as it enables
detailed spectroscopic observations.\cite{Posthumus2009} The second reason is related to \textbf{application of clusters}. Indeed, clusters may offer ways
to develop new kinds of materials,\cite{Castleman2009} to carry out chemical reactions in new ways,\cite{Henglein1989} and to get new kinds of
understanding of bulk matter by learning how the bulk properties emerge from properties of clusters as the cluster grows larger and
larger.\cite{Jortner1992} For instance, the study of clusters has provided new insights into phase transition, e.g. condensation of gas
mixtures,\cite{Korobeishchikov2005} evaporation,\cite{Xu2020} precipitation,\cite{Tian2018} solidification of liquid mixtures\cite{Deng2018} and
melting of solids.\cite{Rapacioli2019}
The study of clusters also helps to understand nucleation phenomena, for instance the formation of nanoscale materials and aerocolloids, as well as
ultrafine particles.\cite{Castleman1978, Castleman1978the, Zhong2000, Pinkard2018} Study of clusters in gas phase can provide detailed structural,
energetic, and spectroscopic information which are hardly accessible from measurements on the bulk.\cite{Asuka2013, Luo2016, Wang2016, Jiang2019}
Finally, clusters containing organic/inorganic molecules or ions and water molecules can be viewed as intermediates between a dilute gas phase and a
solution. Consequently, their study allows to explore the effects of solvation on the chemistry of gas-phase molecules and
ions.\cite{Meot1984, Castleman1994, Castleman1996, Farrar1988, Mayer2002}
Although it is possible to experimentally probe a large range of properties of clusters, one difficulty is to extract all the chemical and physical
information provided by these experiments. Indeed, in the "simplest case", a property determined experimentally can result from a unique
isomer of the probed species. A first major task is thus to determine the nature of this lowest energy isomer which is not straightforward.
This is where theoretical calculations come in. Indeed, a vast majority of experiments requires the contribution of theoretical calculations
in order to determine the lowest energy isomer of a given cluster. For instance, a vast amount of theoretical calculations have been
conducted to determine the low energy structures of (H$_2$O)$_n$ and (H$_2$O)$_n$H$^+$ aggregates. Among them, we can mention
the studies performed by D. Wales and co-workers using the basin-hopping algorithm.\cite{Wales1997,Wales1998,Wales1999,James2005}
In more difficult cases, the probe properties result from the contribution of several isomers which have to be taken into account. When
considering finite-temperature properties, an ergodic exploration of the PES also need to be performed. For instance, Boulon \textit{et al.}
reported heat capacity curves as a function of temperature of mass selected protonated water clusters and highlighted a stronger steepness
of the curve of (H$_2$O)$_{21}$H$^+$ as compared to adjacent sizes.\cite{Boulon2014} Theoretical simulations latter provided explanations
for this peculiar behavior.\cite{Korchagina2017} When considering dissociation of clusters, which can be a non-equilibrium process, theoretical
calculations allow to understand dissociation mechanisms and energy partition which are not accessible from the experiment.\cite{Hada2003, Chakraborty2020, Zamith2020threshold, Zheng2021} It is worth noting that theoretical calculations can also be useful to make predictions when the experiments are restricted by
cost or other conditions.\cite{Tibshirani2005}
Among these variety of systems and properties, the present thesis has focused on the study of two kinds of molecular clusters:
\textbf{water clusters containing an impurity} and \textbf{polycyclic aromatic hydrocarbon clusters} with a focus on the \textbf{exploration
of PES} and the modelling of \textbf{collision induced dissociation} processes. In the following, I briefly
introduce these different aspects.
\textbf{Water clusters.}
Water is ubiquitous in our environment. In view of the importance of water to life and its complex properties, a significant amount of
experimental \cite{Woutersen1997, Ruan2004, Brubach2005, Bergmann2007, Pokapanich2009, Sun2010, Harada2017, Yamazoe2019}
and theoretical \cite{Silvestrelli1999, Laage2006, Bryantsev2009, Silvestrelli2017} studies have been devoted to this fundamental
substance since the first realistic interaction potential of water was proposed in 1933.\cite{Bernal1933,Shields2010} Water clusters
are intermediate species between gas and condensed phases, their study is therefore of fundamental importance to understand
properties of liquid water and ice. They also offer the opportunity to understand how the properties of liquid water and ice emerge
from the assembling of an increasing number of water molecules.\cite{Gregory1996} They also allow to study at the molecular scale
proton transfer processes,\cite{Kunst1980, Torrent2011} finite-temperature effects as well as nuclear quantum effects. Molecular clusters
with a controlled number of solvent molecules are also ideal model systems for providing a fundamental understanding of solute-solvent
and solvent-solvent interactions at the molecular level.\cite{Wang2010} From a more applicative
point of view, they play a significant role in atmospheric sciences where the physical and chemical properties of aerosols are strongly
impacted by the properties of the water clusters they are made of.\cite{Bigg1975, Vaida2000, Aloisio2000, Ramanathan2001, Mccurdy2002, Hartt2008, Vaida2011}
In particular, water clusters can absorb a significant amounts of radiative energy,\cite{Kjaergaard2003} and therefore they have to be included
in climate models.\cite{Vaida2003} This is not actually the case due to the lack of data about their formation. They can also play a role
in astrochemistry where water ice can act as a catalyst for the formation of a large range of chemical species. \cite{Klan2001, Amiaud2007, Kahan2010, Minissale2019}
From a theoretical point of view, the study of water clusters is not straightforward as water clusters display \textbf{two major difficulties}:
\begin{itemize}
\item[$\bullet$] As stated above, the PES of aggregates can display a large number of local minima, \textit{i.e.} stable configurations,
and energy barriers. Determination of low-energy structures or ergodic exploration of PES is thus not straightforward. This is all
the more true that, for molecular aggregates, the range of considered temperatures often results in a low diffusion of molecules which
makes possible for a given aggregate to be trapped in a local minimum of the PES. One textbook case for the complexity of
water clusters is (H$_2$O)$_6$. Despite the apparent simplicity of (H$_2$O)$_6$, which is the smallest neutral water cluster
displaying a tridimensional structure, the nature of its lowest energy isomer has been a subject of debate for several years.
It is only in 2012 that C. P\'erez \textit{et al.} published an experimental paper in Science in which the authors unambiguously
identified three of its isomers: cage, prism and book and concluded that the most stable isomer is the cage.\cite{Perez2012}
The theoretical description of water clusters thus requires simulation tools specifically devoted to the exploration of
complex PES such as \textbf{molecular dynamics} or \textbf{Monte-Carlo simulations} in combination with efficient \textbf{enhanced sampling methods}.
\item[$\bullet$] Molecular scale modelling of water is also made difficult as there is no potential,
\textit{ab initio} or empirical, that makes possible to reproduce all the properties of the
different phases of water, that is applicable to large systems and that is easily transferable.
It is therefore often necessary to make a choice between computational efficiency, transferability,
and accuracy. This balance determines the nature of the questions that can be addressed.
Furthermore, the aforementioned \textbf{enhanced sampling methods} generally require to
repeat a large amount of calculations. Therefore, they need to be combined with computationally
efficient approaches to compute the PES. As presented in Chapter~\ref{chap:comput_method}, the method
I use within this thesis is the \textbf{self-consistent-charge density functional based tight-binding} (SCC-DFTB) method.
\end{itemize}
%Hydrogen bonding is arguably the most extensively studied among all the noncovalent interactions. Hydrogen bonding governs many chemical
%and biological processes in nature and living organisms.\cite{Pimentel1960, Jeffrey1997}
%The hydrogen bonding has been known for about one hundred years, \cite{Latimer1920} but new researches involving hydrogen bonding species continues to generate interesting results.
%An important property of water is its ability to form hydrogen bonds.
%Commonly it is asserted that each hydrogen bond between water molecules stabilizes a structure by about 5 kcal.mol$^{-1}$. \cite{Eisenberg2005} Therefore, water clusters that differ only by the direction of hydrogen bonds, but otherwise have the same number of H-bonds and placement of oxygen atoms should have approximately the same energy. \cite{Kuo2003} The stability of water clusters, based on the arrangement of individual molecules in different phases has been widely explored. \cite{Ludwig2001, Buckingham2008} A lot of theoretical studies have focused on understanding hydrogen bonding in small water clusters (H$_2$O)$_{2-6}$. \cite{Lee2000, Maheshwary2001, Santra2008, Buckingham2008, Hanninen2009, Neela2010} In one of the carefully conducted computational studies, it was shown that the most stable geometries of water clusters H$_2$O)$_{8-20}$ arise from a fusion of tetrameric or pentameric rings. \cite{Maheshwary2001, Neela2010}
%In addition to the study of pure water clusters, water clusters containing an impurity, \textit{i.e.} a inorganic/organic ion or a neutral molecule, have drastically grown over the last years. For instance, one can mention studies devoted to Cl$^{-}$(H$_2$O)$_n$,\cite{Huneycutt2003} Na$^+$(H$_2$O)$_n$, H$_2$PO$_4^{-}$(H$_2$O)$_n$,\cite{Caleman2007} NH$_4^+$(H$_2$O)$_n$, NH$_3$(H$_2$O)$_n$, C$_6$H$_6$O(H$_2$O)$_n$,\cite{Berden1996} H$_2$SO$_4$(H$_2$O)$_n$,\cite{Rozenberg2009, Korchagina2016} SO$_4^{2-}$(H$_2$O)$_n$,\cite{Korchagina2016} (CO)$_m$(H$_2$O)$_n$, ((CH$_3$)$_2$NH$_2^+$)$_m$(HSO$_4^{-}$)$_m$(H$_2$O)$_n$,\cite{Depalma2014} C$_4$H$_5$N$_2$O$_2^+$(H$_2$O)$_n$,\cite{Braud2019} (C$_5$H$_5$N)$_m$H$^+$(H$_2$O)$_n$.\cite{Ryding2011} As an important domain impacted by water clusters, many significant efforts have been devoted to the experimental and theoretical characterization of the chemical composition and behavior of atmospheric particles.\cite{Hogan1975, Arnold1977, Arnold1982, Heymsfield1986} Among these studies, ion composition measurements demonstrated the existence of charged molecular aggregates in the stratosphere,\cite{Arnold1977, Arnold1982} especially negatively charged species such as nitrate- and sulfate-containing water clusters. These grown atmospheric particles initiate the process of acid cloud formation and participate in reactions leading to the destruction of the ozone layers in polar regions.\cite{Koop1996, Carslaw1997} The study of these species is thus of high interest. In addition, charged clusters can be sorted easily by electrostatic, magnetic or time-of-flight mass analysis to yield mass spectra, which contributes to the detailed study of charged clusters. Understanding the hydrated proton is of paramount importance for the knowledge of fundamental processes in biology and chemistry, and the investigation of protonated water clusters has been proven to be essential for understanding the nature of protons in solution.\cite{Kunst1980, Torrent2011} In the work of this thesis, the stability of ammonium/ammonia water clusters and protonated uracil water clusters were explored.
Water clusters are usually combined with other inorganic/organic ions or molecules that make them relevant to astrochemistry, atmospheric chemistry
and biological sciences. Therefore, it is of paramount importance to investigate \textbf{water clusters containing an impurity}, whether it is experimentally
or theoretically. And indeed, in parallel to the study of pure water clusters, such studies have drastically grown over the last years. For instance, one can
mention studies devoted to Cl$^{-}$(H$_2$O)$_n$,\cite{Huneycutt2003} Na$^+$(H$_2$O)$_n$, H$_2$PO$_4^{-}$(H$_2$O)$_n$,\cite{Caleman2007} NH$_4^+$(H$_2$O)$_n$, NH$_3$(H$_2$O)$_n$, C$_6$H$_6$O(H$_2$O)$_n$,\cite{Berden1996} H$_2$SO$_4$(H$_2$O)$_n$,\cite{Rozenberg2009, Korchagina2016}
SO$_4^{2-}$(H$_2$O)$_n$,\cite{Korchagina2016} (CO)$_m$(H$_2$O)$_n$, \newline ((CH$_3$)$_2$NH$_2^+$)$_m$(HSO$_4^{-}$)$_m$(H$_2$O)$_n$,\cite{Depalma2014}
%<<<<<<< HEAD
%C$_4$H$_5$N$_2$O$_2^+$(H$_2$O)$_n$,\cite{Braud2019} (C$_5$H$_5$N)$_m$H$^+$(H$_2$O)$_n$.\cite{Ryding2011}
%The grown atmospheric particles can initiate the process of acid cloud formation and participate in reactions leading to the destruction of the ozone layers in polar regions.\cite{Koop1996, Carslaw1997} The studies of atmospheric particles demonstrate the existence of charged molecular aggregates in the stratosphere, \cite{Arnold1977, Arnold1982} which can be adsorbed by water clusters to form such as sulfate including water clusters\cite{Korchagina2016} and ammonium/ammonia including water clusters. \cite{Payzant1973, Berden1996} Ammonia is an important component of atmospheric nucleation together with water and sulphuric acid. \cite{Kulmala1995, Kirkby2011, Dunne2016}
%The presence of ammonia in the atmosphere together with water and its ability to form hydrogen bonds with water molecules makes it particular interesting to study the solvation of ammonia.\cite{Sunden2018}
%%%In addition, charged clusters can be sorted easily by electrostatic, magnetic or time-of-flight mass analysis to yield mass spectra, which contributes to the detailed study of charged clusters.
%Understanding the hydrated proton is of paramount importance for the knowledge of fundamental processes in biology and chemistry, and the investigation of protonated water clusters has been proven to be essential for understanding the nature of protons in solution.\cite{Kunst1980, Torrent2011}
%The necleobase uracil play a key role in the encoding and expression of genetic information in living organism. The study of the clusters composed of nucleobase molecules with water clusters is a good benchmark to observe how the nucleobase molecules properties vary from isolated gas-phase to hydrated species. In the work of this thesis, the stability of ammonium/ammonia water clusters and protonated uracil water clusters were explored.
%}
%\textbf{PAHs clusters.}
%\red{This paragraph is a bit short, I would developpe it a bit. IN particulatr give details about what as been done from theory on PAHs clusters and precise
%why PAHs cluster are importante, why not single PAH molecules. Maybe one or two picture to show what is a PAH ?} \blue{"In the beginning, I thought to make a general simple introduction about PAHs because they will also be described in chapters 4." Is it necessary to write too much here ?"}
%\blue{
%PAHs are a family of organic molecules made up of two or more aromatic carbon rings containing peripheral hydrogens. These rings result from the presence of sp$^2$ bonds between the carbon atoms, which makes these hydrocarbon molecules have aromatic behavior. Several examples of PAHs molecules are presented in Figure \ref{PAHs_sample}.
%=======
C$_4$H$_5$N$_2$O$_2^+$(H$_2$O)$_n$,\cite{Braud2019} and (C$_5$H$_5$N)$_m$H$^+$(H$_2$O)$_n$.\cite{Ryding2011}
In the domain of astrochemistry, the growth of atmospheric particles can initiate the process of acid cloud formation and participates in reactions
leading to the destruction of the ozone layers in polar regions.\cite{Koop1996, Carslaw1997} More detailed studies of atmospheric particles demonstrated
the existence of charged molecular aggregates in the stratosphere,\cite{Arnold1977,Arnold1982} in particular sulfate containing aggregates,\cite{Korchagina2016}
and ammonium/ammonia containing aggregates.\cite{Payzant1973, Berden1996} In the latter case, \textbf{ammonia has been highlighted as an
important component of atmospheric nucleation} together with water and sulphuric acid.\cite{Kulmala1995, Kirkby2011, Dunne2016} This important
role of ammonia and ammonium water clusters, and the lake of theoretical studies devoted to these species, motivated a thorough benchmark of
the SCC-DFTB approach to model these systems which is presented in Chapter~\ref{chap:structure}. In parallel, understanding the \textbf{properties of
the proton} and how it can impact the solvation properties of molecules of biological interest is of paramount importance for understanding
fundamental processes in biology and chemistry. In particular, uracil, one of the nucleobases, plays a key role in the encoding and expression of genetic
information in living organisms. The study of \textbf{water clusters containing uracil} is therefore a good playground to probe how uracil properties
vary from isolated gas-phase to hydrated species and how this is impacted by protonation. Chapters~\ref{chap:structure} and ~\ref{chap:collision}
try to address these questions.
\textbf{Polycyclic aromatic hydrocarbon clusters.}
Polycyclic aromatic hydrocarbons (PAHs) are a family of organic molecules made up of two or more aromatic carbon rings
containing peripheral hydrogen atoms. These hydrocarbon molecules have aromatic behavior resulting from the presence of sp$^2$
carbon atoms. Several examples of PAHs molecules are presented in Figure \ref{PAHs_sample}.
%>>>>>>> 92023a10c3aa8b7dc4ace43987c1d571fb99a738
\begin{figure}[h]
\begin{center}
\includegraphics[width=12cm]{PAHs_sample.png}
\caption{Examples of several PAH molecules.}
\label{PAHs_sample}
\end{center}
\end{figure}
PAHs have been investigated in various scientific fields, both experimentally and theoretically, for instance in astrophysics and astrochemistry,
environmental science, combustion science, or the search for new organic solar cell devices.
%(see Figure \ref{PAHs})
%\begin{figure}[h]
%\begin{center}
%\includegraphics[width=12cm]{PAHs.png}
%\caption{Role of PAHs.}
%\label{PAHs}
%\end{center}
%\end{figure}
The presence of PAHs in the interstellar medium was proposed in the middle of the 80s,\cite{Leger1984,Allamandola1985}
and they have since played an important role in the astrophysical context. In particular, the so-called unidentified infrared bands
in the gas phase of the interstellar medium are thought to be partially attributable to emission by PAHs.\cite{Leger1984, Puget1989, Tielens2008}
They have been proposed to be present in the form of a mixture of neutral, ionised, and partly dehydrogenated molecules
and to account for $\sim$10 - 20\% of the total carbon in the interstellar medium.\cite{Tielens2005, Tielens2008}
In addition, cationic PAH clusters are expected to be abundant in photo-dissociation regions\cite{Rapacioli2006, Montillaud2014}
since the ionization energy of the clusters is lower than that of neutral PAHs and decreases with the cluster
size,\cite{Rapacioli2009, Joblin2017} leading to the efficient formation of cationic clusters. These charged species are
expected to survive longer than their neutral counterparts due to higher dissociation energies, as predicted by calculations.\cite{Rapacioli2009}
PAHs are also found in the atmosphere as highly toxic molecules. Their significant abundance arises from their efficient formation
as by-products of natural processes, biomass burning, or human activities such as combustion of fossil fuels.\cite{Finlayson1986}
In the atmosphere, PAHs with more than three rings can be adsorbed by various particles, for instance carbonaceous aerosols,
ferric oxides, and icy particles.\cite{Callen2008} The role of \textbf{PAH clusters} in the process of soot nucleation is a major
topic in the context of combustion and leads to consider the competition between clustering, evaporation, and oligomerization.\cite{Eaves2015, Violi2007}
Finally, PAH stacks provide possible compounds to define new organic solar cell junctions.\cite{Scholz2013, Darghouth2015}
Due to the importance of PAHs as mentioned above, the stability of PAH clusters have been extensively studied experimentally
and theoretically. \cite{Rapacioli2006, Holm2010, Simon2017formation, Zhen2018, Chen2018, Zamith2020threshold} IN particular,
their evolution following absorption of photons, collision with high or low energetic particles as well as their behaviour in very high
pressure environments has been thoroughly studied.\cite{Schmidt2006, Holm2010, Gatchell2015, Joblin2017, Gatchell2017, Zamith2019thermal}
Chapter~\ref{chap:collision} provides thorough theoretical analysis of the \textbf{collision-induced dissociation} of the simplest pyrene cluster,
\textit{i.e.} the \textbf{pyrene dimer cation} in order to complement recent experiments.
\textbf{Collision-induced dissociation of molecular clusters.}
The structure, energetics and reactivity of a variety of molecular clusters can be explored by collision-induced
dissociation.\cite{Dawson1982, Graul1989, Wei1991, Liu2006, Goebbert2006, Coates2018} By colliding a molecule
or a molecular cluster with a non-reactive noble gas atom or a small molecule such as N$_2$, it is possible to monitor
the parent ions and collision products by means of mass spectrometry that can provide a wealth of structural information
from which one can infer, for instance, dissociation mechanisms,\cite{Nelson1994, Molina2015}
or bond and hydration enthalpies.\cite{Carl2007} Collision-induced dissociation has also been used to understand the
impact of high-energy radiations on living cells and DNA or RNA,\cite{Liu2006, Nguyen2011, Shuck2014} as well as
the impact of low-energy collisions on biological molecules.\cite{Castrovilli2017,Bera2018}
Extracting energetics or collision process from collision-induced dissociation is not straightforward and it often needs to
be \textbf{complemented by theoretical calculations}. Two main methodologies can be conducted. The first one is to
make an exhaustive description of the PES connecting both parent ions and products. Energetic information on both
minima and transition states can then be introduced in Rice-Ramsperger-Kassel-Marcus \cite{Klippenstein1992, Baer1996}
and/or Kinetic Monte Carlo simulations.\cite{Metropolis1949, Voter2007}
The second approach is to perform \textbf{molecular dynamics simulations to explicitly model the collision trajectory} of
the target ion and the projectile, the energy redistribution, the subsequent reorganizations and fragmentations. A potential
is needed to describe the PES of the system and its reactivity in both methodology. For the latter one, the potential needs to
reach a very good balance between accuracy and computational efficiency as this methodology requires the propagation of
tens, hundreds or even thousands of trajectories. With this in view, it appears that wave-function based methods do not
allow to reach a sufficient amount of simulations to describe dynamical behavior at finite temperature. Unfortunately,
the same is true for density-functional theory (DFT). Force-field approaches can easily handle molecular dynamics simulations
of system with hundred of atoms for several hundred nanoseconds, but they can poorly describe formation or breaking
of covalent bonds and they are poorly transferable. In between DFT and force-field methods, semi-empirical approaches
provide interesting alternatives. In particular, the \textbf{SCC-DFTB}
method allows to perform molecular dynamical simulations of systems containing several tens or hundreds of atoms for
simulation time of several hundred picoseconds. This approach has thus been used in the present thesis to model
collision-induced dissociation experiments.
To summarize, the goal of this thesis is to go a step further into the theoretical description of the properties of molecular clusters
in the view to complement complex experimental measurements. It has focused on two different types of molecular clusters. First,
we have focused on water clusters containing an impurity, \textit{i.e.} an additional ion or molecule. We have first focused our
studies on \textbf{ammonium and ammonia water clusters} in order to thoroughly explore their PES to characterize in details
low-energy isomers for various cluster sizes. We then tackle the study of \textbf{protonated uracil water clusters} through two
aspects: characterize low-energy isomers and model collision-induced dissociation experiments to probe dissociation mechanism
in relation with recent experimental measurements. Finally, we address the study of the \textbf{pyrene dimer cation} to explore collision
trajectories, dissociation mechanism, energy partition, mass spectra, and cross-section.
To introduce, develop, and conclude on these different subjects, this manuscript is organised as follow:
%<<<<<<< HEAD
%In order to characterize the stability of PAHs, their evolution \sout{involution} \red{what is involution ?} has been explored extensively in experiments after absorption of photons, collision with high or low energetic particles or in a very high pressure environments. \cite{Schmidt2006, Holm2010, Gatchell2015, Joblin2017, Gatchell2017, Zamith2019thermal}
%The collision details of PAHs cluster with projectile can hardly be obtained from experimental data. In addition, the experimental studies are complex and associated facilities are expensive, which sometimes prevent all desired measurements to be carried out. Therefore, further theoretical studies should be conducted to bring us to make a deeper interpretation of the experimental measurements and complement the experiments. Pyrene C$_{16}$H$_{10}$, is a planar PAH molecule composed of the compact arrangement of four fused benzene rings. In the work of this thesis, the collision-induced dissociation of the simplest pyrene clusters, pyrene dimer, was studied. }
%=======
\begin{itemize}
\item[$\bullet$] The \textbf{first chapter} introduces the objectives of this thesis. Generalities about clusters, in particular molecular clusters,
and collision-induced
dissociation are provided.
%>>>>>>> 92023a10c3aa8b7dc4ace43987c1d571fb99a738
\item[$\bullet$] The \textbf{second chapter} is devoted to the introduction of the fundamental concepts used in theoretical chemistry to solve
the electronic structure problem and to explore the PES. It describes the main approaches used along this thesis and their
foundations. The \textbf{SCC-DFTB} approach, which is the main method used along this thesis,
is described in details as well as the \textbf{parallel-tempering molecular dynamics} approach to explore PES.
\item[$\bullet$] The \textbf{third chapter} focuses on the thorough exploration of the PES of ammonium and ammonia water clusters, as well as
protonated uracil water clusters, in the view to discuss their structural and energetic properties. Along this chapter, the results obtained at the SCC-DFTB
level are compared to MP2 results and discuss in the light of the actual literature.
\item[$\bullet$] The \textbf{fourth chapter} presents molecular dynamics simulations of collision-induced dissociation of protonated
uracil water clusters and pyrene dimer cation. In the former case, the theoretical proportion of formed neutral uracil aggregates \textit{vs.}
protonated water cluster as well as total fragmentation cross sections are compared to the experimental results by S. Zamith and J.-M. L'Hermite.
The molecular dynamics simulations allow to probe the nature of the formed fragments one the short time scale and to rationalize the
location of the excess proton on these fragments. The simulation of the collision-induced dissociation of the pyrene dimer cation at
different collision energies is then addressed in this chapter.
\item[$\bullet$] Finally, the conclusions of this thesis as well as a number of perspectives are presented in the \textbf{fifth chapter}.
\end{itemize}
%<<<<<<< HEAD
%\textbf{Collision-induced dissociation of molecular clusters.}
%The structure, energetics and reactivity of a variety of molecular cluster can be explored by collision-induced dissociation.\cite{Dawson1982, Graul1989, Wei1991, Liu2006, Goebbert2006, Coates2018}. By colliding a molecule or a molecular cluster with a non-reactive noble gas atom or a small molecule such as N$_2$, it is possible to monitor the parent ions and collision products then the spectra of the parent and product ions can provide a wealth of information about the structure from which one can infer, for instance, dissociation mechanisms \cite{Nelson1994, Molina2015} or bond and hydration enthalpies.\cite{Carl2007} Collision induced dissociation has also been used to understand the impact of high-energy radiations on living cells and DNA or RNA,\cite{Liu2006, Nguyen2011, Shuck2014} as well as low-energy collisions on biological molecules.\cite{Castrovilli2017,Bera2018}
%Extracting energetics or collision process from collision-induced dissociation is not an easy task and it often need to be complemented by theoretical calculations. Two main methodologies can be conducted. The first one is to make an exhaustive description of the potential energy surface connecting both parent ions and products. Energetic information on both minima and transition states can then be introduced in Rice-Ramsperger-Kassel-Marcus \cite{Klippenstein1992, Baer1996} and/or Kinetic Monte Carlo simulations.\cite{Metropolis1949, Voter2007} The second approach is to perform molecular dynamics simulations to explicitly model the collision trajectory of the target ion and the projectile, the energy redistribution, the subsequent reorganizations and fragmentations. A potential is needed to describe the PES of the system and its reactivity. For the second methodology, the potential needs to reach a very good balance between accuracy and computational cost as this methodology requires the propagation of tens, hundreds or even thousands trajectories. With this in view, it appears that wave-function based methods do not allow to reach a sufficient amount of simulations to describe dynamical behavior at finite temperature. Unfortunately, the same is true for density-functional theory (DFT). Force-field approaches can easily handle molecular dynamics simulations of system with hundred of atoms for several hundred nanoseconds, but they can poorly describe formation or breaking of covalent bonds and they are poorly transferable. In between DFT and force-field methods, semi-empirical methods provides interesting alternatives. In particular, the \textbf{self-consistent-charge density functional based tight-binding} method allows to perform molecular dynamical simulations of systems containing several tens or hundreds of atoms for simulation time of several hundred picoseconds. This approach has thus been used in the present thesis to model collision-induced dissociation experiments.
%The present thesis focuses on the structure, solvation, thermodynamics study of ammonia containing water clusters, ammonium containing water clusters, which help to understand the nucleation phenomena and the formation of aerosols. The uracil included water clusters were also studied, which can provide a benchmark to observe how the properties of biological molecules change from isolated gas-phase to hydrated species. The polycyclic aromatic hydrocarbon (PAH) clusters are abundant in the universe.\cite{Carey2005, Hudgins2005, Clavin2015}
%The dynamics study of the dissociation of the simplest pyrene aggregates, pyrene dimer, to interpret the ollision-induced dissociation experiments of PAHs with noble gas to have a better understanding of the physics of this kind of cluster.
%The first chapter introduces the object of this thesis. A generality about clusters and the clusters studied in this thesis are introduced. Then the collision-induced dissociation of molecular clusters is briefly described.
%The second chapter is devoted to the introduction the fundamental concepts used in theoretical chemistry for the solution of the electronic problem, which describes the main approaches traditionally employed.
%The method, density functional based tight binding (DFTB), applied in this thesis is also described. The different methods to explore the potential energy surface are presented in this chapter.
%In the third chapter, the study on the structure and stability of ammonium/ammonia water clusters,
%%%%mixed ammonium/ammonia and sulfate containing water clusters,
%and protonated uracil water clusters were presented.
%Comparing the results calculated using DFTB method with the corresponding ones using MP2 method or the ones in the literature, it shows the DFTB method can provide a quite good result for the optimization of these clusters.
%The fourth chapter presents the study on the molecular dynamics simulations of collision-induced dissociation of protonated uracil water clusters. The theoretical proportion of formed neutral uracil molecule \textit{vs.} protonated water cluster as well as total fragmentation cross sections are consistent with the experimental data which highlights the accuracy of the simulations. The molecular dynamic simulations allow to probe which fragments are formed on the short time scale and rationalize the location of the excess proton on these fragments.
%We demonstrate that the location of the excess proton is highly influenced by the nature of the aggregate undergoing the collision. The analyses show that, up to seven water molecules in the cluster, a shattering mechanism occurs after collision whereas for the cluster with twelve water molecules has a chance to rearrange prior to complete dissociation.
%In addition, the dymical simulations of the collision-induced dissociation of pyrene dimer cation at different collision energies are described in this chapter. It appears that most of the dissociation occurs on a short timescale (less than 3 ps). The dynamical simulations allow to visualise the dissociation processes.
%At low collision energies, the dissociation cross section increases with collision energies whereas it remains almost constant for collision energies greater than 10-15~eV. The analysis of the kinetic energy partition is used to get insights into the collision/dissociation processes at the atomic scale.
%The simulated time of flight mass spectra of parent and dissociated products are obtained from the combination of molecular dynamics simulations and phase space theory to address the short and long timescales dissociation, respectively.
%The agreement between the simulated and measured mass spectra suggests that the main processes are captured by this approach.
%Finally, the conclusions of the work of this thesis as well as a number of perspectives are displayed in chapter 5.
%=======
%>>>>>>> 92023a10c3aa8b7dc4ace43987c1d571fb99a738
% ---------------------------------------------------------------------------

BIN
thesis/1_GeneIntro/figures/.DS_Store vendored Normal file
View File

Binary file not shown.

BIN
thesis/1_GeneIntro/figures/PAHs.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 341 KiB

BIN
thesis/1_GeneIntro/figures/PAHs_sample.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 259 KiB

BIN
thesis/1_GeneIntro/figures/T_trans.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 108 KiB

BIN
thesis/2_Introduction/.DS_Store vendored Normal file
View File

Binary file not shown.

BIN
thesis/2_Introduction/figures/.DS_Store vendored Normal file
View File

Binary file not shown.

BIN
thesis/2_Introduction/figures/PES.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 920 KiB

BIN
thesis/2_Introduction/figures/PTMD.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 275 KiB

BIN
thesis/2_Introduction/figures/PTMD_schema.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 93 KiB

BIN
thesis/2_Introduction/figures/methods.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 212 KiB

BIN
thesis/2_Introduction/figures/variables.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 33 KiB

433
thesis/2_Introduction/introduction.aux Normal file
View File

@ -0,0 +1,433 @@
\relax
\providecommand\hyper@newdestlabel[2]{}
\FN@pp@footnotehinttrue
\citation{Brown2009}
\@writefile{toc}{\contentsline {chapter}{\numberline {2}Computational Methods}{13}{chapter.2}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{chap:comput_method}{{2}{13}{Computational Methods}{chapter.2}{}}
\@writefile{brf}{\backcite{Brown2009}{{13}{2}{chapter.2}}}
\citation{MCTDH}
\@writefile{lof}{\contentsline {figure}{\numberline {2.1}{\ignorespaces Comparison of the computational efficiency, \textit {i.e.} system sizes and simulation times, of various computational chemistry methods. The \textit {y}-axis indicates the length of time accessible from classical molecular simulations for average system sizes tackle by each method. The \textit {x}-axis indicates the approximative maximum system size tractable by each method in a single-point energy calculation.\relax }}{14}{figure.caption.5}}
\newlabel{methods}{{2.1}{14}{Comparison of the computational efficiency, \textit {i.e.} system sizes and simulation times, of various computational chemistry methods. The \textit {y}-axis indicates the length of time accessible from classical molecular simulations for average system sizes tackle by each method. The \textit {x}-axis indicates the approximative maximum system size tractable by each method in a single-point energy calculation.\relax }{figure.caption.5}{}}
\@writefile{brf}{\backcite{MCTDH}{{14}{2}{figure.caption.5}}}
\citation{Griffiths2018}
\@writefile{toc}{\contentsline {section}{\numberline {2.1}Schr{\"o}dinger Equation}{15}{section.2.1}}
\@writefile{brf}{\backcite{Griffiths2018}{{15}{2.1}{section.2.1}}}
\newlabel{TDSE}{{2.1}{15}{Schr{\"o}dinger Equation}{equation.2.1.1}{}}
\newlabel{TISE}{{2.2}{15}{Schr{\"o}dinger Equation}{equation.2.1.2}{}}
\newlabel{waveFunc}{{2.3}{15}{Schr{\"o}dinger Equation}{equation.2.1.3}{}}
\newlabel{operatorH}{{2.4}{16}{Schr{\"o}dinger Equation}{equation.2.1.4}{}}
\newlabel{laplace}{{2.5}{16}{Schr{\"o}dinger Equation}{equation.2.1.5}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2.2}Born-Oppenheimer Approximation}{16}{section.2.2}}
\newlabel{BO_approx}{{2.2}{16}{Born-Oppenheimer Approximation}{section.2.2}{}}
\citation{Born1927}
\@writefile{brf}{\backcite{Born1927}{{17}{2.2}{section.2.2}}}
\newlabel{BO}{{2.6}{17}{Born-Oppenheimer Approximation}{equation.2.2.6}{}}
\newlabel{H_e}{{2.7}{17}{Born-Oppenheimer Approximation}{equation.2.2.7}{}}
\newlabel{BOSeq}{{2.8}{17}{Born-Oppenheimer Approximation}{equation.2.2.8}{}}
\citation{Born1927}
\citation{Epstein1966,Butler1998}
\citation{Puzzarini2010,Helgaker1999,Pedone2010,Fleming1986,Laane1999,Helgaker2012}
\newlabel{nucSeq}{{2.9}{18}{Born-Oppenheimer Approximation}{equation.2.2.9}{}}
\@writefile{brf}{\backcite{Born1927}{{18}{2.2}{equation.2.2.9}}}
\newlabel{ESeq}{{2.10}{18}{Born-Oppenheimer Approximation}{equation.2.2.10}{}}
\newlabel{classical}{{2.11}{18}{Born-Oppenheimer Approximation}{equation.2.2.11}{}}
\@writefile{brf}{\backcite{Epstein1966}{{18}{2.2}{equation.2.2.11}}}
\@writefile{brf}{\backcite{Butler1998}{{18}{2.2}{equation.2.2.11}}}
\@writefile{toc}{\contentsline {section}{\numberline {2.3}Computation of Electronic Energy}{18}{section.2.3}}
\newlabel{electronicEnergy}{{2.3}{18}{Computation of Electronic Energy}{section.2.3}{}}
\citation{Jensen2017}
\citation{dftb1,dftb2,Elstner1998,Elstner2014}
\citation{Cremer1993}
\citation{Singh1986,Gao1996,Mordasini1998}
\citation{Hartree1928,Hartree1947,Slater1968}
\@writefile{brf}{\backcite{Puzzarini2010}{{19}{2.3}{section.2.3}}}
\@writefile{brf}{\backcite{Helgaker1999}{{19}{2.3}{section.2.3}}}
\@writefile{brf}{\backcite{Pedone2010}{{19}{2.3}{section.2.3}}}
\@writefile{brf}{\backcite{Fleming1986}{{19}{2.3}{section.2.3}}}
\@writefile{brf}{\backcite{Laane1999}{{19}{2.3}{section.2.3}}}
\@writefile{brf}{\backcite{Helgaker2012}{{19}{2.3}{section.2.3}}}
\@writefile{brf}{\backcite{Jensen2017}{{19}{2.3}{section.2.3}}}
\@writefile{brf}{\backcite{dftb1}{{19}{2.3}{section.2.3}}}
\@writefile{brf}{\backcite{dftb2}{{19}{2.3}{section.2.3}}}
\@writefile{brf}{\backcite{Elstner1998}{{19}{2.3}{section.2.3}}}
\@writefile{brf}{\backcite{Elstner2014}{{19}{2.3}{section.2.3}}}
\@writefile{brf}{\backcite{Cremer1993}{{19}{2.3}{section.2.3}}}
\@writefile{brf}{\backcite{Singh1986}{{19}{2.3}{section.2.3}}}
\@writefile{brf}{\backcite{Gao1996}{{19}{2.3}{section.2.3}}}
\@writefile{brf}{\backcite{Mordasini1998}{{19}{2.3}{section.2.3}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.1}Wavefunction based Methods}{19}{subsection.2.3.1}}
\@writefile{brf}{\backcite{Hartree1928}{{19}{2.3.1}{subsection.2.3.1}}}
\@writefile{brf}{\backcite{Hartree1947}{{19}{2.3.1}{subsection.2.3.1}}}
\@writefile{brf}{\backcite{Slater1968}{{19}{2.3.1}{subsection.2.3.1}}}
\citation{Mcweeny1992,Szabo1996,Kohanoff2006,Helgaker2014}
\citation{Roothaan1951}
\citation{Blinder2018}
\citation{koch1999}
\citation{Moskowitz1965}
\citation{Lowdin1995}
\newlabel{HF}{{2.12}{20}{Wavefunction based Methods}{equation.2.3.12}{}}
\newlabel{HF-individual}{{2.13}{20}{Wavefunction based Methods}{equation.2.3.13}{}}
\newlabel{Hartreepotential}{{2.14}{20}{Wavefunction based Methods}{equation.2.3.14}{}}
\newlabel{HF-idensity}{{2.15}{20}{Wavefunction based Methods}{equation.2.3.15}{}}
\@writefile{brf}{\backcite{Mcweeny1992}{{20}{2.3.1}{equation.2.3.15}}}
\@writefile{brf}{\backcite{Szabo1996}{{20}{2.3.1}{equation.2.3.15}}}
\@writefile{brf}{\backcite{Kohanoff2006}{{20}{2.3.1}{equation.2.3.15}}}
\@writefile{brf}{\backcite{Helgaker2014}{{20}{2.3.1}{equation.2.3.15}}}
\@writefile{brf}{\backcite{Roothaan1951}{{20}{2.3.1}{equation.2.3.15}}}
\@writefile{brf}{\backcite{Blinder2018}{{20}{2.3.1}{equation.2.3.15}}}
\citation{Cramer2003,Jensen2017}
\citation{Head1994,Maurice1999}
\citation{Moller1934,Pople1976,Krishnan1978}
\citation{Vcivzek1966,Purvis1982,Raghavachari1989,Van2001}
\citation{Curtiss1991,Curtiss1998,Ohlinger2009}
\citation{Head1994,Magnasco2009,Dacosta2011}
\citation{Kohn1965,kohn1999nobel}
\@writefile{brf}{\backcite{koch1999}{{21}{2.3.1}{equation.2.3.15}}}
\@writefile{brf}{\backcite{Moskowitz1965}{{21}{2.3.1}{equation.2.3.15}}}
\@writefile{brf}{\backcite{Lowdin1995}{{21}{2.3.1}{equation.2.3.15}}}
\@writefile{brf}{\backcite{Jensen2017}{{21}{2.3.1}{equation.2.3.15}}}
\@writefile{brf}{\backcite{Cramer2003}{{21}{2.3.1}{equation.2.3.15}}}
\@writefile{brf}{\backcite{Head1994}{{21}{2.3.1}{equation.2.3.15}}}
\@writefile{brf}{\backcite{Maurice1999}{{21}{2.3.1}{equation.2.3.15}}}
\@writefile{brf}{\backcite{Moller1934}{{21}{2.3.1}{equation.2.3.15}}}
\@writefile{brf}{\backcite{Pople1976}{{21}{2.3.1}{equation.2.3.15}}}
\@writefile{brf}{\backcite{Krishnan1978}{{21}{2.3.1}{equation.2.3.15}}}
\@writefile{brf}{\backcite{Vcivzek1966}{{21}{2.3.1}{equation.2.3.15}}}
\@writefile{brf}{\backcite{Purvis1982}{{21}{2.3.1}{equation.2.3.15}}}
\@writefile{brf}{\backcite{Raghavachari1989}{{21}{2.3.1}{equation.2.3.15}}}
\@writefile{brf}{\backcite{Van2001}{{21}{2.3.1}{equation.2.3.15}}}
\@writefile{brf}{\backcite{Curtiss1991}{{21}{2.3.1}{equation.2.3.15}}}
\@writefile{brf}{\backcite{Curtiss1998}{{21}{2.3.1}{equation.2.3.15}}}
\@writefile{brf}{\backcite{Ohlinger2009}{{21}{2.3.1}{equation.2.3.15}}}
\@writefile{brf}{\backcite{Head1994}{{21}{2.3.1}{equation.2.3.15}}}
\@writefile{brf}{\backcite{Magnasco2009}{{21}{2.3.1}{equation.2.3.15}}}
\@writefile{brf}{\backcite{Dacosta2011}{{21}{2.3.1}{equation.2.3.15}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.2}Density Functional Theory}{21}{subsection.2.3.2}}
\citation{Thomas1927}
\citation{Fermi1928}
\citation{Hohenberg1964}
\citation{Levy1979}
\citation{Kohn1965}
\@writefile{brf}{\backcite{Kohn1965}{{22}{2.3.2}{subsection.2.3.2}}}
\@writefile{brf}{\backcite{kohn1999nobel}{{22}{2.3.2}{subsection.2.3.2}}}
\newlabel{density}{{2.16}{22}{Density Functional Theory}{equation.2.3.16}{}}
\@writefile{brf}{\backcite{Thomas1927}{{22}{2.3.2}{equation.2.3.16}}}
\@writefile{brf}{\backcite{Fermi1928}{{22}{2.3.2}{equation.2.3.16}}}
\@writefile{brf}{\backcite{Hohenberg1964}{{22}{2.3.2}{equation.2.3.16}}}
\@writefile{brf}{\backcite{Levy1979}{{22}{2.3.2}{equation.2.3.16}}}
\@writefile{brf}{\backcite{Kohn1965}{{22}{2.3.2}{equation.2.3.16}}}
\citation{Kohn1965}
\newlabel{N}{{2.17}{23}{Density Functional Theory}{equation.2.3.17}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {2.2}{\ignorespaces Interdependence of basic variables in the Hohenberg-Kohn theorem.}}{23}{figure.caption.6}}
\newlabel{variables}{{2.2}{23}{Interdependence of basic variables in the Hohenberg-Kohn theorem}{figure.caption.6}{}}
\newlabel{HK}{{2.18}{23}{Density Functional Theory}{equation.2.3.18}{}}
\@writefile{brf}{\backcite{Kohn1965}{{23}{2.3.2}{equation.2.3.18}}}
\newlabel{E_KS}{{2.19}{24}{Density Functional Theory}{equation.2.3.19}{}}
\newlabel{Tn}{{2.20}{24}{Density Functional Theory}{equation.2.3.20}{}}
\newlabel{Ehartree}{{2.21}{24}{Density Functional Theory}{equation.2.3.21}{}}
\newlabel{Exc}{{2.22}{24}{Density Functional Theory}{equation.2.3.22}{}}
\newlabel{Delta}{{2.23}{24}{Density Functional Theory}{equation.2.3.23}{}}
\newlabel{Lagrange}{{2.24}{24}{Density Functional Theory}{equation.2.3.24}{}}
\citation{Kohn1965}
\citation{Kohn1965,Herman1969,Perdew1996}
\citation{Becke1993}
\newlabel{Veff}{{2.25}{25}{Density Functional Theory}{equation.2.3.25}{}}
\newlabel{rho}{{2.26}{25}{Density Functional Theory}{equation.2.3.26}{}}
\newlabel{KS}{{2.27}{25}{Density Functional Theory}{equation.2.3.27}{}}
\newlabel{orthonormality}{{2.28}{25}{Density Functional Theory}{equation.2.3.28}{}}
\citation{Becke1988,Lee1988,Becke1993,Stephens1994}
\citation{Adamo1999}
\citation{Henderson2009,Krukau2006}
\citation{Zhao2008}
\citation{Li2018}
\citation{Foulkes1989}
\citation{Porezag1995}
\@writefile{brf}{\backcite{Kohn1965}{{26}{2.3.2}{equation.2.3.28}}}
\@writefile{brf}{\backcite{Kohn1965}{{26}{2.3.2}{equation.2.3.28}}}
\@writefile{brf}{\backcite{Herman1969}{{26}{2.3.2}{equation.2.3.28}}}
\@writefile{brf}{\backcite{Perdew1996}{{26}{2.3.2}{equation.2.3.28}}}
\@writefile{brf}{\backcite{Becke1993}{{26}{2.3.2}{equation.2.3.28}}}
\newlabel{Ehybrid}{{2.29}{26}{Density Functional Theory}{equation.2.3.29}{}}
\@writefile{brf}{\backcite{Becke1993}{{26}{2.3.2}{equation.2.3.29}}}
\@writefile{brf}{\backcite{Becke1988}{{26}{2.3.2}{equation.2.3.29}}}
\@writefile{brf}{\backcite{Lee1988}{{26}{2.3.2}{equation.2.3.29}}}
\@writefile{brf}{\backcite{Stephens1994}{{26}{2.3.2}{equation.2.3.29}}}
\@writefile{brf}{\backcite{Adamo1999}{{26}{2.3.2}{equation.2.3.29}}}
\@writefile{brf}{\backcite{Henderson2009}{{26}{2.3.2}{equation.2.3.29}}}
\@writefile{brf}{\backcite{Krukau2006}{{26}{2.3.2}{equation.2.3.29}}}
\@writefile{brf}{\backcite{Zhao2008}{{26}{2.3.2}{equation.2.3.29}}}
\@writefile{brf}{\backcite{Li2018}{{26}{2.3.2}{equation.2.3.29}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.3}Density Functional based Tight-Binding Theory}{26}{subsection.2.3.3}}
\newlabel{sec:DFTB}{{2.3.3}{26}{Density Functional based Tight-Binding Theory}{subsection.2.3.3}{}}
\citation{Elstner1998,Porezag1995,Seifert1996,Elstner1998,Elstne2007,Oliveira2009}
\citation{Gaus2011}
\@writefile{brf}{\backcite{Foulkes1989}{{27}{2.3.3}{subsection.2.3.3}}}
\@writefile{brf}{\backcite{Porezag1995}{{27}{2.3.3}{subsection.2.3.3}}}
\@writefile{brf}{\backcite{Elstner1998}{{27}{2.3.3}{subsection.2.3.3}}}
\@writefile{brf}{\backcite{Elstner1998}{{27}{2.3.3}{subsection.2.3.3}}}
\@writefile{brf}{\backcite{Porezag1995}{{27}{2.3.3}{subsection.2.3.3}}}
\@writefile{brf}{\backcite{Seifert1996}{{27}{2.3.3}{subsection.2.3.3}}}
\@writefile{brf}{\backcite{Elstne2007}{{27}{2.3.3}{subsection.2.3.3}}}
\@writefile{brf}{\backcite{Oliveira2009}{{27}{2.3.3}{subsection.2.3.3}}}
\@writefile{brf}{\backcite{Gaus2011}{{27}{2.3.3}{subsection.2.3.3}}}
\newlabel{Edft}{{2.30}{27}{Density Functional based Tight-Binding Theory}{equation.2.3.30}{}}
\newlabel{Edftb}{{2.31}{28}{Density Functional based Tight-Binding Theory}{equation.2.3.31}{}}
\newlabel{Edftb-long}{{2.32}{28}{Density Functional based Tight-Binding Theory}{equation.2.3.32}{}}
\newlabel{H0}{{2.33}{28}{Density Functional based Tight-Binding Theory}{equation.2.3.33}{}}
\newlabel{Eterms}{{2.34}{28}{Density Functional based Tight-Binding Theory}{equation.2.3.34}{}}
\newlabel{orbitals}{{2.35}{29}{Density Functional based Tight-Binding Theory}{equation.2.3.35}{}}
\newlabel{Eband}{{2.36}{29}{Density Functional based Tight-Binding Theory}{equation.2.3.36}{}}
\newlabel{matrix}{{2.37}{29}{Density Functional based Tight-Binding Theory}{equation.2.3.37}{}}
\newlabel{Vdftb}{{2.38}{29}{Density Functional based Tight-Binding Theory}{equation.2.3.38}{}}
\newlabel{Hamil}{{2.39}{29}{Density Functional based Tight-Binding Theory}{equation.2.3.39}{}}
\newlabel{Hmatrix}{{2.40}{29}{Density Functional based Tight-Binding Theory}{equation.2.3.40}{}}
\citation{Mulliken1955}
\newlabel{Erep-infinity}{{2.41}{30}{Density Functional based Tight-Binding Theory}{equation.2.3.41}{}}
\newlabel{Erep-right}{{2.42}{30}{Density Functional based Tight-Binding Theory}{equation.2.3.42}{}}
\newlabel{Erep-final}{{2.43}{30}{Density Functional based Tight-Binding Theory}{equation.2.3.43}{}}
\newlabel{relative_p}{{2.44}{30}{Density Functional based Tight-Binding Theory}{equation.2.3.44}{}}
\newlabel{relative_pa}{{2.45}{30}{Density Functional based Tight-Binding Theory}{equation.2.3.45}{}}
\citation{Mulliken1955}
\@writefile{brf}{\backcite{Mulliken1955}{{31}{2.3.3}{equation.2.3.45}}}
\newlabel{E2nd}{{2.47}{31}{Density Functional based Tight-Binding Theory}{equation.2.3.47}{}}
\newlabel{E2ndsimple}{{2.48}{31}{Density Functional based Tight-Binding Theory}{equation.2.3.48}{}}
\@writefile{brf}{\backcite{Mulliken1955}{{31}{2.3.3}{equation.2.3.48}}}
\newlabel{Mulliken}{{2.49}{31}{Density Functional based Tight-Binding Theory}{equation.2.3.49}{}}
\citation{Bader1985,Bader1990,Glendening1998,Glendening2012}
\citation{Singh1984,Besler1990}
\citation{Li1998,Kalinowski2004,Kelly2005,Rapacioli2009corr}
\newlabel{Escc}{{2.50}{32}{Density Functional based Tight-Binding Theory}{equation.2.3.50}{}}
\newlabel{secular-eq}{{2.51}{32}{Density Functional based Tight-Binding Theory}{equation.2.3.51}{}}
\newlabel{Huv}{{2.52}{32}{Density Functional based Tight-Binding Theory}{equation.2.3.52}{}}
\@writefile{brf}{\backcite{Bader1985}{{32}{2.3.3}{equation.2.3.52}}}
\citation{Mayer1983,Cances1997,Lu2012}
\citation{Lewis1995,Gianturco1999,Elstner2001,Wu2002,Grimme2004,Zimmerli2004,Neumann2005,Goursot2007}
\citation{Frenkel2001}
\@writefile{brf}{\backcite{Bader1990}{{33}{2.3.3}{equation.2.3.52}}}
\@writefile{brf}{\backcite{Glendening1998}{{33}{2.3.3}{equation.2.3.52}}}
\@writefile{brf}{\backcite{Glendening2012}{{33}{2.3.3}{equation.2.3.52}}}
\@writefile{brf}{\backcite{Singh1984}{{33}{2.3.3}{equation.2.3.52}}}
\@writefile{brf}{\backcite{Besler1990}{{33}{2.3.3}{equation.2.3.52}}}
\@writefile{brf}{\backcite{Li1998}{{33}{2.3.3}{equation.2.3.52}}}
\@writefile{brf}{\backcite{Kalinowski2004}{{33}{2.3.3}{equation.2.3.52}}}
\@writefile{brf}{\backcite{Kelly2005}{{33}{2.3.3}{equation.2.3.52}}}
\@writefile{brf}{\backcite{Rapacioli2009corr}{{33}{2.3.3}{equation.2.3.52}}}
\newlabel{CM3}{{2.53}{33}{Density Functional based Tight-Binding Theory}{equation.2.3.53}{}}
\@writefile{brf}{\backcite{Mayer1983}{{33}{2.3.3}{equation.2.3.53}}}
\@writefile{brf}{\backcite{Cances1997}{{33}{2.3.3}{equation.2.3.53}}}
\@writefile{brf}{\backcite{Lu2012}{{33}{2.3.3}{equation.2.3.53}}}
\newlabel{CM3-classical}{{2.54}{33}{Density Functional based Tight-Binding Theory}{equation.2.3.54}{}}
\@writefile{brf}{\backcite{Lewis1995}{{33}{2.3.3}{equation.2.3.54}}}
\@writefile{brf}{\backcite{Gianturco1999}{{33}{2.3.3}{equation.2.3.54}}}
\@writefile{brf}{\backcite{Elstner2001}{{33}{2.3.3}{equation.2.3.54}}}
\@writefile{brf}{\backcite{Wu2002}{{33}{2.3.3}{equation.2.3.54}}}
\@writefile{brf}{\backcite{Grimme2004}{{33}{2.3.3}{equation.2.3.54}}}
\@writefile{brf}{\backcite{Zimmerli2004}{{33}{2.3.3}{equation.2.3.54}}}
\@writefile{brf}{\backcite{Neumann2005}{{33}{2.3.3}{equation.2.3.54}}}
\@writefile{brf}{\backcite{Goursot2007}{{33}{2.3.3}{equation.2.3.54}}}
\newlabel{dispersionE}{{2.55}{33}{Density Functional based Tight-Binding Theory}{equation.2.3.55}{}}
\citation{Jones1924,Lennard1924,Morse1929,Born1932,Stillinger1985,Kaplan2006}
\citation{Bahar1997}
\citation{Morse1929,Girifalco1959}
\citation{Jones1924,Lennard1924}
\citation{Lennard1931}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.4}Force Field Methods}{34}{subsection.2.3.4}}
\@writefile{brf}{\backcite{Frenkel2001}{{34}{2.3.4}{subsection.2.3.4}}}
\@writefile{brf}{\backcite{Jones1924}{{34}{2.3.4}{subsection.2.3.4}}}
\@writefile{brf}{\backcite{Lennard1924}{{34}{2.3.4}{subsection.2.3.4}}}
\@writefile{brf}{\backcite{Morse1929}{{34}{2.3.4}{subsection.2.3.4}}}
\@writefile{brf}{\backcite{Born1932}{{34}{2.3.4}{subsection.2.3.4}}}
\@writefile{brf}{\backcite{Stillinger1985}{{34}{2.3.4}{subsection.2.3.4}}}
\@writefile{brf}{\backcite{Kaplan2006}{{34}{2.3.4}{subsection.2.3.4}}}
\@writefile{brf}{\backcite{Bahar1997}{{34}{2.3.4}{subsection.2.3.4}}}
\newlabel{harmonic}{{2.56}{34}{Force Field Methods}{equation.2.3.56}{}}
\@writefile{brf}{\backcite{Morse1929}{{34}{2.3.4}{equation.2.3.56}}}
\@writefile{brf}{\backcite{Girifalco1959}{{34}{2.3.4}{equation.2.3.56}}}
\newlabel{Morse}{{2.57}{34}{Force Field Methods}{equation.2.3.57}{}}
\@writefile{brf}{\backcite{Jones1924}{{34}{2.3.4}{equation.2.3.57}}}
\@writefile{brf}{\backcite{Lennard1924}{{34}{2.3.4}{equation.2.3.57}}}
\citation{Monticelli2013}
\@writefile{brf}{\backcite{Lennard1931}{{35}{2.3.4}{equation.2.3.57}}}
\newlabel{LennarsJones}{{2.58}{35}{Force Field Methods}{equation.2.3.58}{}}
\@writefile{brf}{\backcite{Monticelli2013}{{35}{2.3.4}{equation.2.3.58}}}
\newlabel{potential}{{2.59}{35}{Force Field Methods}{equation.2.3.59}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2.4}Exploration of PES}{36}{section.2.4}}
\@writefile{lof}{\contentsline {figure}{\numberline {2.3}{\ignorespaces Schematic representation of some key points on a model potential energy surface.}}{36}{figure.caption.7}}
\newlabel{PES}{{2.3}{36}{Schematic representation of some key points on a model potential energy surface}{figure.caption.7}{}}
\citation{Metropolis1987}
\citation{Metropolis1949}
\citation{Kroese2014}
\citation{Rosenbluth1955,Binder1993,Baeurle2009}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.1}Monte Carlo Simulations}{37}{subsection.2.4.1}}
\@writefile{brf}{\backcite{Metropolis1987}{{37}{2.4.1}{subsection.2.4.1}}}
\@writefile{brf}{\backcite{Metropolis1949}{{37}{2.4.1}{subsection.2.4.1}}}
\@writefile{brf}{\backcite{Kroese2014}{{37}{2.4.1}{subsection.2.4.1}}}
\@writefile{brf}{\backcite{Rosenbluth1955}{{38}{2.4.1}{subsection.2.4.1}}}
\@writefile{brf}{\backcite{Binder1993}{{38}{2.4.1}{subsection.2.4.1}}}
\@writefile{brf}{\backcite{Baeurle2009}{{38}{2.4.1}{subsection.2.4.1}}}
\newlabel{thermalAverage}{{2.60}{38}{Monte Carlo Simulations}{equation.2.4.60}{}}
\newlabel{SingleIntegral}{{2.61}{39}{Monte Carlo Simulations}{equation.2.4.61}{}}
\newlabel{SingleAverage}{{2.62}{39}{Monte Carlo Simulations}{equation.2.4.62}{}}
\newlabel{limI}{{2.63}{39}{Monte Carlo Simulations}{equation.2.4.63}{}}
\newlabel{IntegralPx}{{2.64}{39}{Monte Carlo Simulations}{equation.2.4.64}{}}
\newlabel{INp}{{2.65}{39}{Monte Carlo Simulations}{equation.2.4.65}{}}
\citation{Alder1957}
\citation{Gibson1960,Rahman1964}
\citation{Allen2017,Cicccotti1987,Van1990,Berne1998,Tuckerman2000,Frenkel2001,Karplus2002,Rapaport2004,Tavan2005,Van2006}
\citation{Parrinello1980,Ballone1988,Gutierrez1996,Karplus2002}
\citation{Briant1975,Postma1982,Honeycutt1987,Dang1997,Coveney2016}
\citation{Charati1998,Yeh2004,Braga2014,Pranami2015}
\citation{Mondello1997,Hess2002,Yeh2004,Zhang2015}
\citation{Aragon1976,Vuilleumier1999,Pavone2006,Brancato2006}
\newlabel{averaA}{{2.66}{40}{Monte Carlo Simulations}{equation.2.4.66}{}}
\newlabel{Markov1}{{2.67}{40}{Monte Carlo Simulations}{equation.2.4.67}{}}
\newlabel{Markov2}{{2.68}{40}{Monte Carlo Simulations}{equation.2.4.68}{}}
\newlabel{balanceEq}{{2.69}{40}{Monte Carlo Simulations}{equation.2.4.69}{}}
\newlabel{assess}{{2.70}{40}{Monte Carlo Simulations}{equation.2.4.70}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.2}Classical Molecular Dynamics}{40}{subsection.2.4.2}}
\citation{Beck2000,Wang2003}
\citation{Wei1994,Light2000}
\@writefile{brf}{\backcite{Alder1957}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Gibson1960}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Rahman1964}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Frenkel2001}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Allen2017}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Cicccotti1987}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Van1990}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Berne1998}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Tuckerman2000}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Karplus2002}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Rapaport2004}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Tavan2005}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Van2006}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Karplus2002}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Parrinello1980}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Ballone1988}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Gutierrez1996}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Briant1975}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Postma1982}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Honeycutt1987}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Dang1997}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Coveney2016}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Charati1998}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Yeh2004}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Braga2014}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Pranami2015}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Yeh2004}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Mondello1997}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Hess2002}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Zhang2015}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Aragon1976}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Vuilleumier1999}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Pavone2006}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Brancato2006}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Beck2000}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Wang2003}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Wei1994}{{41}{2.4.2}{subsection.2.4.2}}}
\@writefile{brf}{\backcite{Light2000}{{41}{2.4.2}{subsection.2.4.2}}}
\citation{Batina1991,Butcher2008}
\citation{Gear1966,Diethelm2002}
\citation{Runge1895,Kutta1901,Butcher1996,Butcher2015}
\citation{Verlet1967}
\citation{Fraige2004}
\citation{Swope1982}
\newlabel{Newton}{{2.71}{42}{Classical Molecular Dynamics}{equation.2.4.71}{}}
\newlabel{Force}{{2.72}{42}{Classical Molecular Dynamics}{equation.2.4.72}{}}
\@writefile{brf}{\backcite{Batina1991}{{42}{2.4.2}{equation.2.4.72}}}
\@writefile{brf}{\backcite{Butcher2008}{{42}{2.4.2}{equation.2.4.72}}}
\@writefile{brf}{\backcite{Gear1966}{{42}{2.4.2}{equation.2.4.72}}}
\@writefile{brf}{\backcite{Diethelm2002}{{42}{2.4.2}{equation.2.4.72}}}
\@writefile{brf}{\backcite{Runge1895}{{42}{2.4.2}{equation.2.4.72}}}
\@writefile{brf}{\backcite{Kutta1901}{{42}{2.4.2}{equation.2.4.72}}}
\@writefile{brf}{\backcite{Butcher1996}{{42}{2.4.2}{equation.2.4.72}}}
\@writefile{brf}{\backcite{Butcher2015}{{42}{2.4.2}{equation.2.4.72}}}
\@writefile{brf}{\backcite{Verlet1967}{{42}{2.4.2}{equation.2.4.72}}}
\@writefile{brf}{\backcite{Fraige2004}{{42}{2.4.2}{equation.2.4.72}}}
\@writefile{brf}{\backcite{Swope1982}{{42}{2.4.2}{equation.2.4.72}}}
\newlabel{DiscretisationError1}{{2.73}{43}{Classical Molecular Dynamics}{equation.2.4.73}{}}
\newlabel{DiscretisationError2}{{2.74}{43}{Classical Molecular Dynamics}{equation.2.4.74}{}}
\newlabel{Verlet}{{2.75}{43}{Classical Molecular Dynamics}{equation.2.4.75}{}}
\newlabel{Velo}{{2.76}{43}{Classical Molecular Dynamics}{equation.2.4.76}{}}
\newlabel{VV}{{2.78}{43}{Classical Molecular Dynamics}{equation.2.4.78}{}}
\citation{Ray1981,Ray1999}
\citation{Nose1984,Nose1984M,Hoover1985,Hunenberger2005}
\citation{Torrie1977,Hansmann1993,Marchi1999,Bartels2000,Darve2001}
\citation{Laio2002,Iannuzzi2003,Barducci2011}
\citation{Kirkpatrick1983,Van1987}
\newlabel{VV1}{{2.79}{44}{Classical Molecular Dynamics}{equation.2.4.79}{}}
\newlabel{VV2}{{2.80}{44}{Classical Molecular Dynamics}{equation.2.4.80}{}}
\newlabel{VV3}{{2.81}{44}{Classical Molecular Dynamics}{equation.2.4.81}{}}
\@writefile{brf}{\backcite{Ray1981}{{44}{2.4.2}{equation.2.4.81}}}
\@writefile{brf}{\backcite{Ray1999}{{44}{2.4.2}{equation.2.4.81}}}
\@writefile{brf}{\backcite{Nose1984}{{44}{2.4.2}{equation.2.4.81}}}
\@writefile{brf}{\backcite{Nose1984M}{{44}{2.4.2}{equation.2.4.81}}}
\@writefile{brf}{\backcite{Hoover1985}{{44}{2.4.2}{equation.2.4.81}}}
\@writefile{brf}{\backcite{Hunenberger2005}{{44}{2.4.2}{equation.2.4.81}}}
\citation{Swendsen1986}
\citation{Geyer1991}
\citation{Hukushima1996}
\citation{Falcioni1999}
\citation{Earl2005}
\citation{Sugita1999}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.3}Parallel-Tempering Molecular Dynamics}{45}{subsection.2.4.3}}
\newlabel{sec:PTMD}{{2.4.3}{45}{Parallel-Tempering Molecular Dynamics}{subsection.2.4.3}{}}
\@writefile{brf}{\backcite{Torrie1977}{{45}{2.4.3}{subsection.2.4.3}}}
\@writefile{brf}{\backcite{Hansmann1993}{{45}{2.4.3}{subsection.2.4.3}}}
\@writefile{brf}{\backcite{Marchi1999}{{45}{2.4.3}{subsection.2.4.3}}}
\@writefile{brf}{\backcite{Bartels2000}{{45}{2.4.3}{subsection.2.4.3}}}
\@writefile{brf}{\backcite{Darve2001}{{45}{2.4.3}{subsection.2.4.3}}}
\@writefile{brf}{\backcite{Laio2002}{{45}{2.4.3}{subsection.2.4.3}}}
\@writefile{brf}{\backcite{Iannuzzi2003}{{45}{2.4.3}{subsection.2.4.3}}}
\@writefile{brf}{\backcite{Barducci2011}{{45}{2.4.3}{subsection.2.4.3}}}
\@writefile{brf}{\backcite{Kirkpatrick1983}{{45}{2.4.3}{subsection.2.4.3}}}
\@writefile{brf}{\backcite{Van1987}{{45}{2.4.3}{subsection.2.4.3}}}
\@writefile{brf}{\backcite{Swendsen1986}{{45}{2.4.3}{subsection.2.4.3}}}
\@writefile{brf}{\backcite{Geyer1991}{{45}{2.4.3}{subsection.2.4.3}}}
\@writefile{brf}{\backcite{Hukushima1996}{{45}{2.4.3}{subsection.2.4.3}}}
\@writefile{brf}{\backcite{Falcioni1999}{{45}{2.4.3}{subsection.2.4.3}}}
\@writefile{brf}{\backcite{Earl2005}{{45}{2.4.3}{subsection.2.4.3}}}
\@writefile{brf}{\backcite{Sugita1999}{{45}{2.4.3}{subsection.2.4.3}}}
\@writefile{lof}{\contentsline {figure}{\numberline {2.4}{\ignorespaces Schematics of the PTMD algorithm in its synchronous version. Replicas of the same system, numbered from $C_1$ to $C_N$, are simulated subject to different temperatures (from T$_1$ to T$_N$). Once $X$ MD steps (straight solid arrows) have been performed by each replica, configuration exchanges are attempted between neighbouring simulations according to the Metropolis criterion. Some of them undergo successful swapping (solid curved arrows) while other not (dashed curved arrows). MD simulations then proceed for $X$ additional MD steps before new attempts of exchange.\relax }}{46}{figure.caption.8}}
\newlabel{ptmd_s}{{2.4}{46}{Schematics of the PTMD algorithm in its synchronous version. Replicas of the same system, numbered from $C_1$ to $C_N$, are simulated subject to different temperatures (from T$_1$ to T$_N$). Once $X$ MD steps (straight solid arrows) have been performed by each replica, configuration exchanges are attempted between neighbouring simulations according to the Metropolis criterion. Some of them undergo successful swapping (solid curved arrows) while other not (dashed curved arrows). MD simulations then proceed for $X$ additional MD steps before new attempts of exchange.\relax }{figure.caption.8}{}}
\citation{Wales1997,Wales1999}
\citation{Hartke1993,Unger1993,Sivanandam2008,Toledo2014}
\newlabel{Metropolis}{{2.82}{47}{Parallel-Tempering Molecular Dynamics}{equation.2.4.82}{}}
\newlabel{newVelo}{{2.83}{47}{Parallel-Tempering Molecular Dynamics}{equation.2.4.83}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.4}Global Optimization}{47}{subsection.2.4.4}}
\@writefile{brf}{\backcite{Wales1997}{{47}{2.4.4}{subsection.2.4.4}}}
\@writefile{brf}{\backcite{Wales1999}{{47}{2.4.4}{subsection.2.4.4}}}
\@writefile{brf}{\backcite{Hartke1993}{{47}{2.4.4}{subsection.2.4.4}}}
\@writefile{brf}{\backcite{Unger1993}{{47}{2.4.4}{subsection.2.4.4}}}
\@writefile{brf}{\backcite{Sivanandam2008}{{47}{2.4.4}{subsection.2.4.4}}}
\@writefile{brf}{\backcite{Toledo2014}{{47}{2.4.4}{subsection.2.4.4}}}
\FN@pp@footnotehinttrue
\@setckpt{2_Introduction/introduction}{
\setcounter{page}{49}
\setcounter{equation}{83}
\setcounter{enumi}{5}
\setcounter{enumii}{0}
\setcounter{enumiii}{0}
\setcounter{enumiv}{0}
\setcounter{footnote}{0}
\setcounter{mpfootnote}{0}
\setcounter{part}{0}
\setcounter{chapter}{2}
\setcounter{section}{4}
\setcounter{subsection}{4}
\setcounter{subsubsection}{0}
\setcounter{paragraph}{0}
\setcounter{subparagraph}{0}
\setcounter{figure}{4}
\setcounter{table}{0}
\setcounter{ContinuedFloat}{0}
\setcounter{pp@next@reset}{1}
\setcounter{@fnserial}{0}
\setcounter{NAT@ctr}{0}
\setcounter{Item}{5}
\setcounter{Hfootnote}{0}
\setcounter{bookmark@seq@number}{15}
\setcounter{parentequation}{0}
\setcounter{section@level}{2}
}

0
thesis/2_Introduction/introduction.bbl Normal file
View File

51
thesis/2_Introduction/introduction.blg Normal file
View File

@ -0,0 +1,51 @@
This is BibTeX, Version 0.99d (TeX Live 2019)
Capacity: max_strings=100000, hash_size=100000, hash_prime=85009
The top-level auxiliary file: general_introduction.aux
White space in argument---line 104 of file general_introduction.aux
: \citation{F\unhbox
: \voidb@x \bgroup \accent 127a\penalty \@M \hskip \z@skip \egroup ssler2004}
I'm skipping whatever remains of this command
I found no \bibdata command---while reading file general_introduction.aux
I found no \bibstyle command---while reading file general_introduction.aux
You've used 91 entries,
0 wiz_defined-function locations,
261 strings with 2339 characters,
and the built_in function-call counts, 0 in all, are:
= -- 0
> -- 0
< -- 0
+ -- 0
- -- 0
* -- 0
:= -- 0
add.period$ -- 0
call.type$ -- 0
change.case$ -- 0
chr.to.int$ -- 0
cite$ -- 0
duplicate$ -- 0
empty$ -- 0
format.name$ -- 0
if$ -- 0
int.to.chr$ -- 0
int.to.str$ -- 0
missing$ -- 0
newline$ -- 0
num.names$ -- 0
pop$ -- 0
preamble$ -- 0
purify$ -- 0
quote$ -- 0
skip$ -- 0
stack$ -- 0
substring$ -- 0
swap$ -- 0
text.length$ -- 0
text.prefix$ -- 0
top$ -- 0
type$ -- 0
warning$ -- 0
while$ -- 0
width$ -- 0
write$ -- 0
(There were 3 error messages)

BIN
thesis/2_Introduction/introduction.dvi Normal file
View File

Binary file not shown.

70988
thesis/2_Introduction/introduction.log Normal file
View File

File diff suppressed because it is too large Load Diff

1521
thesis/2_Introduction/introduction.tex Normal file
View File

File diff suppressed because it is too large Load Diff

BIN
thesis/3/.DS_Store vendored Normal file
View File

Binary file not shown.

BIN
thesis/3/figures/.DS_Store vendored Normal file
View File

Binary file not shown.

BIN
thesis/3/figures/11a-f.pdf Normal file
View File

Binary file not shown.

BIN
thesis/3/figures/12a-f.pdf Normal file
View File

Binary file not shown.

BIN
thesis/3/figures/1a-f-b3lyp.pdf Normal file
View File

Binary file not shown.

BIN
thesis/3/figures/1a-f.pdf Normal file
View File

Binary file not shown.

BIN
thesis/3/figures/2a-f.pdf Normal file
View File

Binary file not shown.

BIN
thesis/3/figures/3a-f.pdf Normal file
View File

Binary file not shown.

BIN
thesis/3/figures/4a-f.pdf Normal file
View File

Binary file not shown.

BIN
thesis/3/figures/5a-f.pdf Normal file
View File

Binary file not shown.

BIN
thesis/3/figures/6a-f.pdf Normal file
View File

Binary file not shown.

BIN
thesis/3/figures/7a-f.pdf Normal file
View File

Binary file not shown.

BIN
thesis/3/figures/E-distance-nh3-w.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 351 KiB

BIN
thesis/3/figures/E-distance-nh4-w.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 320 KiB

BIN
thesis/3/figures/Uloss.pdf Normal file
View File

Binary file not shown.

BIN
thesis/3/figures/a-b.pdf Normal file
View File

Binary file not shown.

BIN
thesis/3/figures/dimers.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 107 KiB

BIN
thesis/3/figures/fragcrosssec.pdf Normal file
View File

Binary file not shown.

BIN
thesis/3/figures/fragcrosssec_error.pdf Normal file
View File

Binary file not shown.

BIN
thesis/3/figures/mass7w.pdf Normal file
View File

Binary file not shown.

BIN
thesis/3/figures/nh3-4-7w.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 719 KiB

BIN
thesis/3/figures/nh3-8-10w.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 756 KiB

BIN
thesis/3/figures/nh3-nh4-1w.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 161 KiB

BIN
thesis/3/figures/nh3-nh4-20w.jpeg Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 82 KiB

BIN
thesis/3/figures/nh3-nh4-2w.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 256 KiB

BIN
thesis/3/figures/nh3-nh4-3w.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 514 KiB

BIN
thesis/3/figures/nh4-4-6w.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 735 KiB

BIN
thesis/3/figures/nh4-7-10w.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 944 KiB

BIN
thesis/3/figures/protonAffinity.pdf Normal file
View File

Binary file not shown.

BIN
thesis/3/figures/uracil.pdf Normal file
View File

Binary file not shown.

345
thesis/3/structure_stability.aux Normal file
View File

@ -0,0 +1,345 @@
\relax
\providecommand\hyper@newdestlabel[2]{}
\citation{deMonNano2009}
\citation{Elstner1998}
\citation{Gaus2013para}
\citation{Li1998,Thompson2003,Rapacioli2009corr}
\citation{Rapacioli2009corr,Elstner2001,Zhechkov2005}
\citation{Simon2012,Odutola1980}
\FN@pp@footnotehinttrue
\@writefile{toc}{\contentsline {chapter}{\numberline {3}Exploration of Structural and Energetic Properties}{49}{chapter.3}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{chap:structure}{{3}{49}{Exploration of Structural and Energetic Properties}{chapter.3}{}}
\citation{Sugita1999,Sugita2000,Earl2005}
\citation{Elstner1998}
\citation{Nose1984M,Hoover1985}
\citation{Douady2009}
\@writefile{toc}{\contentsline {section}{\numberline {3.1}Computational Details}{50}{section.3.1}}
\newlabel{sec:structure-methods}{{3.1}{50}{Computational Details}{section.3.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.1}SCC-DFTB Potential}{50}{subsection.3.1.1}}
\@writefile{brf}{\backcite{deMonNano2009}{{50}{3.1.1}{subsection.3.1.1}}}
\@writefile{brf}{\backcite{Elstner1998}{{50}{3.1.1}{subsection.3.1.1}}}
\@writefile{brf}{\backcite{Gaus2013para}{{50}{3.1.1}{subsection.3.1.1}}}
\@writefile{brf}{\backcite{Li1998}{{50}{3.1.1}{subsection.3.1.1}}}
\@writefile{brf}{\backcite{Rapacioli2009corr}{{50}{3.1.1}{subsection.3.1.1}}}
\@writefile{brf}{\backcite{Thompson2003}{{50}{3.1.1}{subsection.3.1.1}}}
\@writefile{brf}{\backcite{Rapacioli2009corr}{{50}{3.1.1}{subsection.3.1.1}}}
\@writefile{brf}{\backcite{Elstner2001}{{50}{3.1.1}{subsection.3.1.1}}}
\@writefile{brf}{\backcite{Zhechkov2005}{{50}{3.1.1}{subsection.3.1.1}}}
\@writefile{brf}{\backcite{Simon2012}{{50}{3.1.1}{subsection.3.1.1}}}
\@writefile{brf}{\backcite{Odutola1980}{{50}{3.1.1}{subsection.3.1.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.2}SCC-DFTB Exploration of PES}{50}{subsection.3.1.2}}
\@writefile{brf}{\backcite{Earl2005}{{50}{3.1.2}{subsection.3.1.2}}}
\@writefile{brf}{\backcite{Sugita1999}{{50}{3.1.2}{subsection.3.1.2}}}
\@writefile{brf}{\backcite{Sugita2000}{{50}{3.1.2}{subsection.3.1.2}}}
\@writefile{brf}{\backcite{Elstner1998}{{50}{3.1.2}{subsection.3.1.2}}}
\citation{Nose1984M,Hoover1985}
\citation{Wolken2000,Pedersen2014}
\citation{Weigend2005,Weigend2006}
\citation{GaussianCode}
\citation{Boys2002}
\@writefile{brf}{\backcite{Nose1984M}{{51}{3.1.2}{subsection.3.1.2}}}
\@writefile{brf}{\backcite{Hoover1985}{{51}{3.1.2}{subsection.3.1.2}}}
\@writefile{brf}{\backcite{Douady2009}{{51}{3.1.2}{subsection.3.1.2}}}
\@writefile{brf}{\backcite{Nose1984M}{{51}{3.1.2}{subsection.3.1.2}}}
\@writefile{brf}{\backcite{Hoover1985}{{51}{3.1.2}{subsection.3.1.2}}}
\@writefile{brf}{\backcite{Wolken2000}{{51}{3.1.2}{subsection.3.1.2}}}
\@writefile{brf}{\backcite{Pedersen2014}{{51}{3.1.2}{subsection.3.1.2}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.3}MP2 Geometry Optimizations, Relative and Binding Energies}{51}{subsection.3.1.3}}
\@writefile{brf}{\backcite{Weigend2005}{{51}{3.1.3}{subsection.3.1.3}}}
\@writefile{brf}{\backcite{Weigend2006}{{51}{3.1.3}{subsection.3.1.3}}}
\@writefile{brf}{\backcite{GaussianCode}{{51}{3.1.3}{subsection.3.1.3}}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.1}{\ignorespaces Structures of the two protonated uracil isomers, u178 (keto-enol form) and u138 (di-keto form), used as initial conditions in the PTMD simulations.\relax }}{52}{figure.caption.9}}
\newlabel{uracil_s}{{3.1}{52}{Structures of the two protonated uracil isomers, u178 (keto-enol form) and u138 (di-keto form), used as initial conditions in the PTMD simulations.\relax }{figure.caption.9}{}}
\@writefile{brf}{\backcite{Boys2002}{{52}{3.1.3}{subsection.3.1.3}}}
\citation{Keesee1989,Gilligan2000,Sennikov2005,Cabellos2016,Orabi2013,Bommer2016,Rodgers2003,Van2004,Gibb2004,Tielens2005,Parise2005,Boogert2015,Dulieu2010,Michoulier2018}
\citation{Kulmala2004}
\citation{Ziereis1986}
\citation{Perkins1984,Arnold1997}
\citation{Dunne2016}
\citation{Kirkby2011}
\citation{Perkins1984,Herbine1985,Stockman1992,Hulthe1997,Wang1998,Chang1998,Jiang1999,Hvelplund2010,Douady2009,Douady2008,Morrell2010,Bacelo2002,Galashev2013}
\citation{Perkins1984}
\citation{Hulthe1997}
\citation{Hvelplund2010}
\citation{Lee1996,Chang1998,Skurski1998,Jiang1999,Donaldson1999,Sadlej1999,Hvelplund2010,Bacelo2002,Galashev2013}
\citation{Lee1996}
\citation{Bacelo2002}
\citation{Douady2008,Kozack1992polar}
\citation{Morrell2010}
\citation{Pei2015}
\citation{Walters2018}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.4}Structure Classification}{53}{subsection.3.1.4}}
\@writefile{toc}{\contentsline {section}{\numberline {3.2}Structural and Energetic Properties of Ammonium/Ammonia including Water Clusters}{53}{section.3.2}}
\newlabel{sec:ammoniumwater}{{3.2}{53}{Structural and Energetic Properties of Ammonium/Ammonia including Water Clusters}{section.3.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2.1}General introduction}{53}{subsection.3.2.1}}
\@writefile{brf}{\backcite{Tielens2005}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Keesee1989}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Gilligan2000}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Sennikov2005}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Cabellos2016}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Orabi2013}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Bommer2016}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Rodgers2003}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Van2004}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Gibb2004}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Parise2005}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Boogert2015}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Dulieu2010}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Michoulier2018}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Kulmala2004}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Ziereis1986}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Perkins1984}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Arnold1997}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Dunne2016}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Kirkby2011}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Douady2009}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Perkins1984}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Herbine1985}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Stockman1992}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Hulthe1997}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Wang1998}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Chang1998}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Jiang1999}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Hvelplund2010}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Douady2008}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Morrell2010}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Bacelo2002}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Galashev2013}{{53}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Perkins1984}{{53}{3.2.1}{subsection.3.2.1}}}
\citation{Choi2010,Choi2013,Korchagina2017,Simon2019}
\citation{Simon2012,Simon2013water}
\citation{Korchagina2016}
\citation{Simon2017formation}
\citation{Winget2003}
\citation{Gaus2013para}
\@writefile{brf}{\backcite{Hulthe1997}{{54}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Hvelplund2010}{{54}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Chang1998}{{54}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Jiang1999}{{54}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Hvelplund2010}{{54}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Bacelo2002}{{54}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Galashev2013}{{54}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Lee1996}{{54}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Skurski1998}{{54}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Donaldson1999}{{54}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Sadlej1999}{{54}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Lee1996}{{54}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Bacelo2002}{{54}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Douady2008}{{54}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Kozack1992polar}{{54}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Morrell2010}{{54}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Pei2015}{{54}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Walters2018}{{54}{3.2.1}{subsection.3.2.1}}}
\citation{Thompson2003,Rapacioli2009}
\citation{Simon2019}
\@writefile{brf}{\backcite{Korchagina2017}{{55}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Choi2010}{{55}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Choi2013}{{55}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Simon2019}{{55}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Simon2012}{{55}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Simon2013water}{{55}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Korchagina2016}{{55}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Simon2017formation}{{55}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Winget2003}{{55}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Gaus2013para}{{55}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Rapacioli2009}{{55}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Thompson2003}{{55}{3.2.1}{subsection.3.2.1}}}
\@writefile{brf}{\backcite{Simon2019}{{55}{3.2.1}{subsection.3.2.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2.2}Results and Discussion}{55}{subsection.3.2.2}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.2.1}Dissociation Curves and SCC-DFTB Potential}{55}{subsubsection.3.2.2.1}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.2}{\ignorespaces Binding energies of (H$_2$O){NH$_4$}$^+$ as a function of the N---O distance at MP2/Def2TZVP (plain black), MP2/Def2TZVP with BSSE correction (dotted black), original SCC-DFTB (plain red), SCC-DFTB (0.14/1.28) (dotted red) and SCC-DFTB (0.12/1.16) (dashed red) levels of theory.\relax }}{56}{figure.caption.10}}
\newlabel{fig:E_nh4}{{3.2}{56}{Binding energies of (H$_2$O){NH$_4$}$^+$ as a function of the N---O distance at MP2/Def2TZVP (plain black), MP2/Def2TZVP with BSSE correction (dotted black), original SCC-DFTB (plain red), SCC-DFTB (0.14/1.28) (dotted red) and SCC-DFTB (0.12/1.16) (dashed red) levels of theory.\relax }{figure.caption.10}{}}
\citation{Winget2003,Gaus2013para}
\@writefile{lof}{\contentsline {figure}{\numberline {3.3}{\ignorespaces Binding energies of (H$_2$O){NH$_3$} as a function of the N---O distance at MP2/Def2TZVP (plain black), MP2/Def2TZVP with BSSE correction (dotted black), original SCC-DFTB (plain red), SCC-DFTB (0.14/1.28) (dotted red) and SCC-DFTB (0.12/1.16) (dashed red) levels of theory.\relax }}{57}{figure.caption.11}}
\newlabel{fig:E_nh3}{{3.3}{57}{Binding energies of (H$_2$O){NH$_3$} as a function of the N---O distance at MP2/Def2TZVP (plain black), MP2/Def2TZVP with BSSE correction (dotted black), original SCC-DFTB (plain red), SCC-DFTB (0.14/1.28) (dotted red) and SCC-DFTB (0.12/1.16) (dashed red) levels of theory.\relax }{figure.caption.11}{}}
\citation{Maclot2011,Domaracka2012,Markush2016,Castrovilli2017}
\@writefile{lof}{\contentsline {figure}{\numberline {3.4}{\ignorespaces Structure of (H$_2$O){NH$_4$}$^+$ obtained from geometry optimization at the SCC-DFTB 0.14/1.28 (right) and original SCC-DFTB (left) levels.\relax }}{58}{figure.caption.12}}
\newlabel{dimers}{{3.4}{58}{Structure of (H$_2$O){NH$_4$}$^+$ obtained from geometry optimization at the SCC-DFTB 0.14/1.28 (right) and original SCC-DFTB (left) levels.\relax }{figure.caption.12}{}}
\@writefile{brf}{\backcite{Gaus2013para}{{58}{3.2.2.1}{figure.caption.11}}}
\@writefile{brf}{\backcite{Winget2003}{{58}{3.2.2.1}{figure.caption.11}}}
\citation{Wincel2009}
\citation{Boudaiffa2000}
\citation{Smyth2011,Siefermann2011,Alizadeh2013}
\citation{Rasmussen2010}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.2.2}Small Species: (H$_2$O)$_{1-3}${NH$_4$}$^+$ and (H$_2$O)$_{1-3}${NH$_3$}}{59}{subsubsection.3.2.2.2}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.2.3}Properties of (H$_2$O)$_{4-10}${NH$_4$}$^+$ Clusters}{59}{subsubsection.3.2.2.3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2.3}Conclusions for Ammonium/Ammonia Including Water Clusters}{59}{subsection.3.2.3}}
\@writefile{toc}{\contentsline {section}{\numberline {3.3}Structural and Energetic Properties of Protonated Uracil Water Clusters}{59}{section.3.3}}
\newlabel{structureUH}{{3.3}{59}{Structural and Energetic Properties of Protonated Uracil Water Clusters}{section.3.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3.1}General introduction}{59}{subsection.3.3.1}}
\@writefile{brf}{\backcite{Castrovilli2017}{{59}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Maclot2011}{{59}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Domaracka2012}{{59}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Markush2016}{{59}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Wincel2009}{{59}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Boudaiffa2000}{{59}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Smyth2011}{{59}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Siefermann2011}{{59}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Alizadeh2013}{{59}{3.3.1}{subsection.3.3.1}}}
\citation{Coates2018}
\citation{Nelson1994,Sadr2014,Molina2016}
\citation{Bakker2008}
\citation{Shishkin2000,Gadre2000,Van2001diffu,Gaigeot2001,Danilov2006,Bacchus2015}
\citation{Gadre2000,Van2001diffu,Gaigeot2001,Danilov2006,Bacchus2015}
\citation{Gaigeot2001}
\citation{Shishkin2000}
\citation{Bacchus2015}
\citation{Danilov2006}
\citation{Bacchus2015}
\citation{Gadre2000}
\citation{Danilov2006,Bacchus2015}
\citation{Braud2019}
\@writefile{brf}{\backcite{Rasmussen2010}{{60}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Coates2018}{{60}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Nelson1994}{{60}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Sadr2014}{{60}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Molina2016}{{60}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Bakker2008}{{60}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Shishkin2000}{{60}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Gadre2000}{{60}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Van2001diffu}{{60}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Gaigeot2001}{{60}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Danilov2006}{{60}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Bacchus2015}{{60}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Gadre2000}{{60}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Van2001diffu}{{60}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Gaigeot2001}{{60}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Danilov2006}{{60}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Bacchus2015}{{60}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Gaigeot2001}{{60}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Shishkin2000}{{60}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Bacchus2015}{{60}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Danilov2006}{{60}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Bacchus2015}{{60}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Gadre2000}{{60}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Danilov2006}{{61}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Bacchus2015}{{61}{3.3.1}{subsection.3.3.1}}}
\@writefile{brf}{\backcite{Braud2019}{{61}{3.3.1}{subsection.3.3.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3.2}Results and Discussion}{61}{subsection.3.3.2}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.3.2.1}Experimental Results}{61}{subsubsection.3.3.2.1}}
\newlabel{exp_ur}{{3.3.2.1}{61}{Experimental Results}{subsubsection.3.3.2.1}{}}
\citation{Dalleska1993}
\citation{Zamith2012}
\citation{Myers2007}
\@writefile{lof}{\contentsline {figure}{\numberline {3.5}{\ignorespaces Time of flight of mass spectrum obtained by colliding (H$_2$O)$_{7}$UH$^+$ with Ne at 7.2 eV center of mass collision energy (93.5 eV in the laboratory frame).}}{62}{figure.caption.13}}
\newlabel{mass7w}{{3.5}{62}{Time of flight of mass spectrum obtained by colliding (H$_2$O)$_{7}$UH$^+$ with Ne at 7.2 eV center of mass collision energy (93.5 eV in the laboratory frame)}{figure.caption.13}{}}
\@writefile{brf}{\backcite{Dalleska1993}{{62}{3.3.2.1}{figure.caption.13}}}
\@writefile{brf}{\backcite{Zamith2012}{{62}{3.3.2.1}{figure.caption.13}}}
\newlabel{cross-section-geo}{{3.3}{62}{Experimental Results}{equation.3.3.3}{}}
\citation{Zamith2012}
\citation{Dalleska1993}
\citation{Dalleska1993,Hansen2009}
\citation{Wincel2009}
\citation{Bakker2008}
\citation{Dalleska1993,Hansen2009}
\citation{Wincel2009}
\citation{Dalleska1993}
\citation{Zamith2012}
\citation{Dalleska1993}
\citation{Zamith2012}
\@writefile{brf}{\backcite{Myers2007}{{63}{3.3.2.1}{equation.3.3.3}}}
\@writefile{brf}{\backcite{Zamith2012}{{63}{3.3.2.1}{equation.3.3.3}}}
\@writefile{brf}{\backcite{Dalleska1993}{{63}{3.3.2.1}{equation.3.3.3}}}
\@writefile{brf}{\backcite{Dalleska1993}{{63}{3.3.2.1}{equation.3.3.3}}}
\@writefile{brf}{\backcite{Hansen2009}{{63}{3.3.2.1}{equation.3.3.3}}}
\@writefile{brf}{\backcite{Wincel2009}{{63}{3.3.2.1}{equation.3.3.3}}}
\@writefile{brf}{\backcite{Bakker2008}{{63}{3.3.2.1}{equation.3.3.3}}}
\@writefile{brf}{\backcite{Dalleska1993}{{63}{3.3.2.1}{equation.3.3.3}}}
\@writefile{brf}{\backcite{Hansen2009}{{63}{3.3.2.1}{equation.3.3.3}}}
\@writefile{brf}{\backcite{Wincel2009}{{63}{3.3.2.1}{equation.3.3.3}}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.6}{\ignorespaces Fragmentation cross sections of clusters (H$_2$O)$_{n-1}$UH$^+$ at a collision energy of 7.2 eV plotted as a function of the total number n of molecules in the clusters. The experimental results and geometrical cross sections are shown for collision with H$_2$O and Ne. The results from Dalleska et al.\cite {Dalleska1993} using Xe as target atoms on pure protonated water clusters (H$_2$O)$_{2-6}$H$^+$ and from Zamith \textit {et al.} \cite {Zamith2012} using water as target molecules on deuterated water clusters (D$_2$O)$_{n=5,10}$H$^+$ are also shown. The geometrical collision cross sections of water clusters in collision with Xe atoms and water molecules are also plotted. Error bars represent one standard deviation.}}{64}{figure.caption.14}}
\@writefile{brf}{\backcite{Dalleska1993}{{64}{3.6}{figure.caption.14}}}
\@writefile{brf}{\backcite{Zamith2012}{{64}{3.6}{figure.caption.14}}}
\newlabel{fragcrosssec}{{3.6}{64}{Fragmentation cross sections of clusters (H$_2$O)$_{n-1}$UH$^+$ at a collision energy of 7.2 eV plotted as a function of the total number n of molecules in the clusters. The experimental results and geometrical cross sections are shown for collision with H$_2$O and Ne. The results from Dalleska et al.\cite {Dalleska1993} using Xe as target atoms on pure protonated water clusters (H$_2$O)$_{2-6}$H$^+$ and from Zamith \textit {et al.} \cite {Zamith2012} using water as target molecules on deuterated water clusters (D$_2$O)$_{n=5,10}$H$^+$ are also shown. The geometrical collision cross sections of water clusters in collision with Xe atoms and water molecules are also plotted. Error bars represent one standard deviation}{figure.caption.14}{}}
\citation{Kurinovich2002}
\citation{Magnera1991}
\citation{Cheng1998}
\citation{Cheng1998}
\citation{Magnera1991}
\citation{Cheng1998}
\citation{Kurinovich2002}
\citation{Magnera1991}
\citation{Cheng1998}
\citation{Kurinovich2002}
\citation{Bakker2008}
\@writefile{lof}{\contentsline {figure}{\numberline {3.7}{\ignorespaces Proportion of neutral uracil molecule loss plotted as a function of the number of water molecules n in the parent cluster (H$_2$O)$_{n}$UH$^+$. Results obtained for collisions with Ne atoms at 7.2 eV center of mass collision energy.}}{65}{figure.caption.15}}
\newlabel{Uloss}{{3.7}{65}{Proportion of neutral uracil molecule loss plotted as a function of the number of water molecules n in the parent cluster (H$_2$O)$_{n}$UH$^+$. Results obtained for collisions with Ne atoms at 7.2 eV center of mass collision energy}{figure.caption.15}{}}
\@writefile{brf}{\backcite{Kurinovich2002}{{65}{3.3.2.1}{figure.caption.15}}}
\@writefile{brf}{\backcite{Magnera1991}{{65}{3.3.2.1}{figure.caption.15}}}
\@writefile{brf}{\backcite{Cheng1998}{{65}{3.3.2.1}{figure.caption.15}}}
\@writefile{brf}{\backcite{Cheng1998}{{65}{3.3.2.1}{figure.caption.15}}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.8}{\ignorespaces The proton affinities of water clusters as a function of the number of water molecules n, which are taken from the work of Magnera (black circles) \cite {Magnera1991} and from the work of Cheng (blue squares).\cite {Cheng1998} The value of the proton affinity of uracil (red dotted dashed line) is also plotted.\cite {Kurinovich2002}}}{66}{figure.caption.16}}
\@writefile{brf}{\backcite{Magnera1991}{{66}{3.8}{figure.caption.16}}}
\@writefile{brf}{\backcite{Cheng1998}{{66}{3.8}{figure.caption.16}}}
\@writefile{brf}{\backcite{Kurinovich2002}{{66}{3.8}{figure.caption.16}}}
\newlabel{protonAffinity}{{3.8}{66}{The proton affinities of water clusters as a function of the number of water molecules n, which are taken from the work of Magnera (black circles) \cite {Magnera1991} and from the work of Cheng (blue squares).\cite {Cheng1998} The value of the proton affinity of uracil (red dotted dashed line) is also plotted.\cite {Kurinovich2002}}{figure.caption.16}{}}
\@writefile{brf}{\backcite{Bakker2008}{{66}{3.3.2.1}{figure.caption.16}}}
\citation{Wolken2000}
\citation{Pedersen2014}
\citation{Pedersen2014}
\citation{Bakker2008}
\@writefile{lot}{\contentsline {table}{\numberline {3.1}{\ignorespaces Binding energy of two (H$_2$O)U isomers at MP2/Def2TZVP and SCC-DFTB levels of theory.\relax }}{67}{table.caption.17}}
\newlabel{tab:DNH}{{3.1}{67}{Binding energy of two (H$_2$O)U isomers at MP2/Def2TZVP and SCC-DFTB levels of theory.\relax }{table.caption.17}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.3.2.2}Calculated Structures of Protonated Uracil Water Clusters}{67}{subsubsection.3.3.2.2}}
\newlabel{calcul_ur}{{3.3.2.2}{67}{Calculated Structures of Protonated Uracil Water Clusters}{subsubsection.3.3.2.2}{}}
\@writefile{brf}{\backcite{Wolken2000}{{68}{3.3.2.2}{table.caption.17}}}
\@writefile{brf}{\backcite{Pedersen2014}{{68}{3.3.2.2}{table.caption.17}}}
\@writefile{brf}{\backcite{Pedersen2014}{{68}{3.3.2.2}{table.caption.17}}}
\@writefile{brf}{\backcite{Bakker2008}{{68}{3.3.2.2}{table.caption.17}}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.9}{\ignorespaces Lowest-energy structures of (H$_2$O)UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \r A.}}{69}{figure.caption.18}}
\newlabel{1a-f}{{3.9}{69}{Lowest-energy structures of (H$_2$O)UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA }{figure.caption.18}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.10}{\ignorespaces Lowest-energy structures of (H$_2$O)UH$^+$ obtained at the B3LYP/6-311++G(3df,2p) level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. The corresponding values with ZPVE corrections are provided in brackets. Important hydrogen-bond distances are indicated in bold and are given in \r A.}}{70}{figure.caption.19}}
\newlabel{1a-f-b3lyp}{{3.10}{70}{Lowest-energy structures of (H$_2$O)UH$^+$ obtained at the B3LYP/6-311++G(3df,2p) level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. The corresponding values with ZPVE corrections are provided in brackets. Important hydrogen-bond distances are indicated in bold and are given in \AA }{figure.caption.19}{}}
\citation{Zundel1968}
\@writefile{lof}{\contentsline {figure}{\numberline {3.11}{\ignorespaces Lowest-energy structures of (H$_2$O)$_2$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \r A.}}{71}{figure.caption.20}}
\newlabel{2a-f}{{3.11}{71}{Lowest-energy structures of (H$_2$O)$_2$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA }{figure.caption.20}{}}
\@writefile{brf}{\backcite{Zundel1968}{{71}{3.3.2.2}{figure.caption.23}}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.12}{\ignorespaces (H$_2$O)$_3$UH$^+$ lowest-energy structures obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \r A.}}{72}{figure.caption.21}}
\newlabel{3a-f}{{3.12}{72}{(H$_2$O)$_3$UH$^+$ lowest-energy structures obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA }{figure.caption.21}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.13}{\ignorespaces Lowest-energy structures of (H$_2$O)$_4$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \r A.}}{73}{figure.caption.22}}
\newlabel{4a-f}{{3.13}{73}{Lowest-energy structures of (H$_2$O)$_4$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA }{figure.caption.22}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.14}{\ignorespaces Lowest-energy structures of (H$_2$O)$_5$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \r A.}}{74}{figure.caption.23}}
\newlabel{5a-f}{{3.14}{74}{Lowest-energy structures of (H$_2$O)$_5$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA }{figure.caption.23}{}}
\citation{Molina2015,Molina2016}
\@writefile{lof}{\contentsline {figure}{\numberline {3.15}{\ignorespaces Lowest-energy structures of (H$_2$O)$_6$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \r A.}}{75}{figure.caption.24}}
\newlabel{6a-f}{{3.15}{75}{Lowest-energy structures of (H$_2$O)$_6$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA }{figure.caption.24}{}}
\@writefile{brf}{\backcite{Molina2015}{{76}{3.3.2.2}{figure.caption.27}}}
\@writefile{brf}{\backcite{Molina2016}{{76}{3.3.2.2}{figure.caption.27}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3.3}Conclusions on (H$_2$O)$_{n}$UH$^+$ clusters}{76}{subsection.3.3.3}}
\FN@pp@footnotehinttrue
\@writefile{lof}{\contentsline {figure}{\numberline {3.16}{\ignorespaces Lowest-energy structures of (H$_2$O)$_7$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \r A.}}{77}{figure.caption.25}}
\newlabel{7a-f}{{3.16}{77}{Lowest-energy structures of (H$_2$O)$_7$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA }{figure.caption.25}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.17}{\ignorespaces Lowest-energy structures of (H$_2$O)$_{11}$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \r A.}}{78}{figure.caption.26}}
\newlabel{11a-f}{{3.17}{78}{Lowest-energy structures of (H$_2$O)$_{11}$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA }{figure.caption.26}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.18}{\ignorespaces Lowest-energy structures of (H$_2$O)$_{12}$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \r A.}}{79}{figure.caption.27}}
\newlabel{12a-f}{{3.18}{79}{Lowest-energy structures of (H$_2$O)$_{12}$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA }{figure.caption.27}{}}
\@setckpt{3/structure_stability}{
\setcounter{page}{80}
\setcounter{equation}{3}
\setcounter{enumi}{5}
\setcounter{enumii}{0}
\setcounter{enumiii}{0}
\setcounter{enumiv}{0}
\setcounter{footnote}{0}
\setcounter{mpfootnote}{0}
\setcounter{part}{0}
\setcounter{chapter}{3}
\setcounter{section}{3}
\setcounter{subsection}{3}
\setcounter{subsubsection}{0}
\setcounter{paragraph}{0}
\setcounter{subparagraph}{0}
\setcounter{figure}{18}
\setcounter{table}{1}
\setcounter{ContinuedFloat}{0}
\setcounter{pp@next@reset}{1}
\setcounter{@fnserial}{0}
\setcounter{NAT@ctr}{0}
\setcounter{Item}{5}
\setcounter{Hfootnote}{0}
\setcounter{bookmark@seq@number}{34}
\setcounter{parentequation}{0}
\setcounter{section@level}{2}
}

52825
thesis/3/structure_stability.log Normal file
View File

File diff suppressed because it is too large Load Diff

476
thesis/3/structure_stability.tex Normal file
View File

@ -0,0 +1,476 @@
% this file is c\emph{•}alled up by thesis.tex
% content in this file will be fed into the main document
%%\chapter{Aims of the project} % top level followed by section, subsection
\raggedbottom
\ifpdf
\graphicspath{{3/figures/PNG/}{3/figures/PDF/}{3/figures/}}
\else
\graphicspath{{3/figures/EPS/}{3/figures/}}
\fi
\chapter{Exploration of Structural and Energetic Properties} \label{chap:structure}
This \textbf{third chapter} of my thesis merges two independent studies dealing with the determination of the low-energy isomers of
ammonium/ammonia water clusters, (H$_2$O)$_{n}${NH$_4$}$^+$ and (H$_2$O)$_{n}$NH$_3$, and protonated uracil water clusters, (H$_2$O)$_{n}$UH$^+$.
As highlighted in the general introduction of this thesis and in chapter~\ref{chap:comput_method}, performing global optimization of
molecular clusters is not straightforward. The two studies presented in this chapter thus share a main common methodology which is the
combination of the \textbf{self-consistent-charge density functional based tight-binding} (SCC-DFTB) method for the efficient calculation of the potential
energy surfaces (PES) and the \textbf{parallel-tempering molecular dynamics} (PTMD) approach for their exploration. All low-energy isomers
reported in this chapter are discussed in terms of structure, relative energy and binding energy which are compared to the literature
when available. Calculations at higher level of theory are also performed to refine the results obtained at the SCC-DFTB level or to
validate the results it provides. In particular, in this chapter, we propose an improve set of parameters to describe sp$^3$ nitrogen
containing compounds at the SCC-DFTB level. Our results are also used to complement collision-induced dissociation experiments
performed by S. Zamith and J.-M. l'Hermite at the \textit{Laboratoire Collisions Agr\'egats R\'eactivit\'e} (LCAR).
%The background of the systems studied in this thesis and theoretical methods related to the projects of this thesis have been introduced in chapter \ref{chap:general_intro} and chapter \ref{chap:comput_method}. Then the two kinds of projects investigated in my Phd will be shown in the following chapter \ref{chap:structure} and chpater \ref{chap:collision}.
%For the topics about ammonium/ammonia water clusters and protonated uracil water clusters, both of the two studies are about the structural and energetic properties. For instance, some lowest-energy isomers were obtained and the relative binding energies of the lowest-energy isomers were calculated. So the work of these two topics are put in the same chapter. These two studies demonstrates the accuracy of SCC-DFTB to describe ammonium/ammonia water clusters and protonated uracil water clusters. The calculation methods for the topics about ammonium/ammonia water clusters and protonated uracil water clusters are almost the same, therefore, the methods of these two topics will be described together. But their introduction, results, and conclusion will be shown independently (in different subsections). For the topic about ammonium/ammonia water clusters, it is a pure theoretical calculation while for the topic about protonated uracil water clusters, it is collaborated with the experiment and some experimental results will be displayed.
\section{Computational Details} \label{sec:structure-methods}
\subsection{SCC-DFTB Potential}
SCC-DFTB electronic structure calculations presented in this chapter were all performed with the deMonNano code.\cite{deMonNano2009} The details
of the method are presented in section~\ref{sec:DFTB} of chapter~\ref{chap:comput_method}.
%DFTB is an approximated DFT scheme whose computational efficiency depends on the use of parameterized integrals.\cite{Elstner2014, Elstner1998, dftb1, dftb2}
The mio-set for the Slater-Koster tables of integrals was used.\cite{Elstner1998} However, it has been shown that these integrals do not properly described
sp$^3$ hybridized nitrogen, in particular, proton affinity.\cite{Gaus2013para} Consequently, in order to avoid spurious deprotonation of the sp$^3$ hybridized
nitrogen in NH$_4^+$ and to correctly reproduce binding energies calculated at the MP2/Def2TZVP level, we propose to modify the original mio-set for
Slater-Koster tables of N-H integrals by applying them a multiplying factor. Several of them were tested and we present here the results
we obtained for two of them: 1.16 and 1.28. For the sp$^2$ nitrogen of uracil, the original integrals of the mio-set were used. To improve
description of the intermolecular interactions, the original Mulliken charges were replaced by the CM3 charges,\cite{Li1998, Thompson2003, Rapacioli2009corr}
(see equation~\ref{CM3} in section~\ref{sec:DFTB}) and an empirical correction term (see equation~\ref{dispersionE} in section~\ref{sec:DFTB}) was used
to describe dispersion interactions.\cite{Rapacioli2009corr, Elstner2001, Zhechkov2005} Simon \textit{et al.} developed a SCC-DFTB potential that leads
to geometries, frequencies, and relative energies close to the corresponding experimental and CCSD(T)/aug-cc-pVTZ results.\cite{Simon2012, Odutola1980}
The corresponding $D_{OH}$ parameter, \textit{i.e.} 0.129, is retained in the studies presented in thus chapter. $D_{NH}$ is tested in the study of
ammonium/ammonia water clusters and two values were retained and thoroughly tested: 0.12 and 0.14. D$_{NO}$ is set to zero.
\subsection{SCC-DFTB Exploration of PES}
To determine the lowest-energy isomers of (H$_2$O)$_{1-10,20}${NH$_4$}$^+$, (H$_2$O)$_{1-10}$NH$_3$
and (H$_2$O)$_{1-7,11,12}$UH$^+$ clusters, we thoroughly explore their PES using PTMD \cite{Sugita1999, Sugita2000, Earl2005}
simulations combined with a SCC-DFTB \cite{Elstner1998} description of the energies and gradients. I describe
below the \textbf{detailed parameters used for all the simulations conducted within this chapter}.
\textbf{Detailed parameters for PTMD simulations of (H$_2$O)$_{1-10,20}${NH$_4$}$^+$ and (H$_2$O)$_{1-10}$NH$_3$ clusters} are as follows.
For (H$_2$O)$_{1-3}${NH$_4$}$^+$ and (H$_2$O)$_{1-3}${NH$_3$} clusters, 16 replicas were used
with a linear distribution of temperatures with a 15~K step ranging from 10 to 250 K. 40 replicas with a 6~K step ranging from 10 to 250~K were
considered for (H$_2$O)$_{4-10,20}${NH$_4$}$^+$ and (H$_2$O)$_{4-10}${NH$_3$} species. All trajectories were 5~ns long and a time step
of 0.5 fs was used to integrate the equations of motion. A Nos{\'e}-Hoover chain of 5 thermostats was employed for all the simulations to achieve
simulatons in the canonical ensemble.\cite{Nose1984M, Hoover1985} Thermostat frequencies were fixed at 400 cm$^{-1}$.
To identify low-energy isomers of (H$_2$O)$_{1-3}${NH$_4$}$^+$ and (H$_2$O)$_{1-3}${NH$_3$} clusters, 303 geometries were periodically
selected from each replicas and further optimized at the SCC-DFTB level, which produced 4848 optimized geometries per cluster. For
(H$_2$O)$_{4-10,20}${NH$_4$}$^+$ and (H$_2$O)$_{4-10}${NH$_3$} clusters, 500 geometries were periodically selected from each
replicas leading to 20000 optimized geometries per cluster. For (H$_2$O)$_{20}${NH$_4$}$^+$, the initial structure used for the global
optimization process was the lowest-energy structure reported by Douady \textit{et al.}.\cite{Douady2009} The five lowest-energy
isomers among the 4848 or 20000 optimized geometries were further optimized using the MP2/Def2TZVP method. See below for the
details on MP2/Def2TZVP calculations.
\textbf{Detailed parameters for PTMD simulations of (H$_2$O)$_{1-7,11,12}$UH$^+$ clusters} are as follows.
40 replicas with temperatures rnaging linearly from 50 to 350 K were used. Each trajectory was 4 ns long, and the integration time step was 0.5 fs.
A reasonable time interval for the PT exchanges was 2.5 ps. A Nos{\'e}-Hoover chain of five thermostats with frequencies of 800 cm$^{-1}$ was
applied to achieve an exploration in the canonical ensemble.\cite{Nose1984M, Hoover1985} To avoid any spurious influence of the initial
geometry on the PES exploration, three distinct PTMD simulations were carried out with distinct initial proton location: on the uracil in two cases
and on a water molecule in the other one. In the former cases, we used two isomers u178 and u138 of UH$^+$ shown in Figure~\ref{uracil_s} as
the initial geometries.\cite{Wolken2000, Pedersen2014} 600 geometries per temperature were linearly selected along each PTMD simulation
for subsequent geometry optimization leading to 72000 structures optimized at SCC-DFTB level. These structures were sorted in ascending
energy order and checked for redundancy. 9, 23, 46, 31, 38, 45, 63, 20, and 29 structures were then selected for (H$_2$O)UH$^+$,
(H$_2$O)$_{2}$UH$^+$, (H$_2$O)$_{3}$UH$^+$, (H$_2$O)$_{4}$UH$^+$, (H$_2$O)$_{5}$UH$^+$, (H$_2$O)$_{6}$UH$^+$,
(H$_2$O)$_{7}$UH$^+$, (H$_2$O)$_{11}$UH$^+$ and (H$_2$O)$_{12}$UH$^+$ respectively, to perform geometry optimizations at the MP2/Def2TZVP
level. See below for the details on MP2/Def2TZVP calculations.
%\figuremacro{uracil}{Structures of the two protonated uracil isomers, u178 (keto-enol form) and u138 (di-keto form), used as initial conditions in the PTMD simulations.}
\begin{figure}[h!]
\includegraphics[width=0.5\linewidth]{a-b.pdf}
\centering
\caption{Structures of the two protonated uracil isomers, u178 (keto-enol form) and u138 (di-keto form), used as initial conditions in the PTMD simulations.}
\label{uracil_s}
\end{figure}
\subsection{MP2 Geometry Optimizations, Relative and Binding Energies}
Some low-energy isomers obtained at the SCC-DFTB level were further optimized at the MP2 level of theory in combination
with an all electron Def2TZVP basis-set.\cite{Weigend2005, Weigend2006} All calculations used a a tight criteria for geometry
convergence and an ultrafine grid for the numerical integration. All MP2 calculations were performed with the Gaussian 09
package.\cite{GaussianCode}
\textbf{Detailed parameters for (H$_2$O)$_{1-10,20}${NH$_4$}$^+$ and (H$_2$O)$_{1-10}$NH$_3$ clusters.}
Following SCC-DFTB optimizations, the five lowest-energy isomers of (H$_2$O)$_{1-10}${NH$_4$}$^+$ and
(H$_2$O)$_{1-10}${NH$_3$} clusters were further optimized at the MP2/Def2TZVP level of theory.
In section~\ref{sec:ammoniumwater}, relatives energies with respect to the lowest-energy isomer of each
cluster are reported. Impact of zero-point vibrational energy (ZPVE) corrections on relative
energies were evaluated at MP2/Def2TZVP level. To evaluate the strength of water-ammonium and water-ammonia
interactions and to assess the accuracy of the SCC-DFTB method, we also report binding energies.
Two distinct approaches were used to calculate binding energies. The first one considers only the binding
energy between the water cluster as a whole and the impurity, {NH$_4$}$^+$ or NH$_3$, while the second one
considers the binding energy between all the molecules of the cluster. In both cases, the geometry of the molecules
is the one found in the optimized cluster. Using these two methods, relative binding energies (E$_{bind.}$(SCC-DFTB)-E$_{bind.}$(MP2/Def2TZVP))
$\Delta E_{bind.}^{whole}$ and $\Delta E_{bind.}^{sep.}$ were obtained. For all binding energies of
(H$_2$O)$_{1-10}${NH$_4$}$^+$ and (H$_2$O)$_{1-10}${NH$_3$} clusters calculated at MP2/Def2TZVP level,
basis set superposition errors (BSSE) correction was considered by using the counterpoise method of Boys and
Bernardi.\cite{Boys2002}
\textbf{Detailed parameters for (H$_2$O)$_{1-7, 11, 12}$UH$^+$ clusters.}
Following SCC-DFTB optimizations, the six lowest-energy isomers of
(H$_2$O)$_{1-7, 11, 12}$UH$^+$ clusters were further optimized at the MP2/Def2TZVP level of theory.
The binding and relative energies calculated at MP2/Def2TZVP level without BSSE correction
of clusters (H$_2$O)$_{2-7, 11, 12}$UH$^+$ are discussed in section~\ref{structureUH}.
\subsection{Structure Classification}
For clusters (H$_2$O)$_{1-10}${NH$_4$}$^+$ and (H$_2$O)$_{1-10}${NH$_3$},
\textquotedblleft n-x\textquotedblright and \textquotedblleft n$^\prime$-x\textquotedblright labels are used to distinguish between the
(H$_2$O)$_{n}${NH$_4$}$^+$ and (H$_2$O)$_{n}${NH$_3$} reported isomers, respectively, obtained at the SCC-DFTB level. For comparison,
\textquotedblleft n-x\textquotedblright and \textquotedblleft n$^\prime$-x\textquotedblright isomers are also optimized at the MP2/Def2TZVP
level. In that case, the resulting structures are referred to as \textquotedblleft n-x$^*$\textquotedblright and
\textquotedblleft n$^\prime$-x$^*$\textquotedblright~ to distinguish them more easily although they display the same general topology as
\textquotedblleft n-x\textquotedblright and \textquotedblleft n$^\prime$-x\textquotedblright isomers.
In these notations, n and n$^\prime$ denote the number of water molecules in the ammonium and ammonia water clusters, respectively.
x is an alphabetic character going from a to e that differentiates between the five low-energy isomers reported for each cluster in ascending
energy order, \textit{i.e.} a designates the lowest-energy isomer.
%\section{\label{sec:ammoniumwater}The structure and energetics properties study of ammonium or ammonia including water clusters}
\section{Structural and Energetic Properties of Ammonium/Ammonia including Water Clusters} \label{sec:ammoniumwater}
\subsection{General introduction}
%Ionic clusters (typically made up of a core ion surrounded by one or more solvating molecules) are known to be involved in the chemistry of the upper and mid atmosphere [6].《Ion rearrangement at the beginning of cluster formation: isomerization pathways and dissociation kinetics for the ionized dimethylamine dimer》
Water clusters play an important role in various areas such as atmospheric and astrochemical science, chemistry and biology.\cite{Keesee1989, Gilligan2000,
Sennikov2005, Cabellos2016, Orabi2013, Bommer2016, Rodgers2003, Van2004, Gibb2004, Tielens2005, Parise2005, Boogert2015, Dulieu2010, Michoulier2018}
They are involved into the critical stages of nucleation and growth of water-containing droplets in the atmosphere thus contributing to the physical and
chemical properties of this medium.\cite{Kulmala2004}
%For instance, water clusters are able to absorb a significant amount of radiant energy thus decreasing the greenhouse effect.\cite{Galashev2010}
In many cases, the presence of chemical impurities interacting with water aggregates strongly affect their properties.
For instance, ammonia is an important compound commonly found in the atmosphere and which displays a key role in aerosol chemistry.\cite{Ziereis1986} Its high
basicity makes it a potential proton sink that can form a ionic center for nucleation.\cite{Perkins1984, Arnold1997} E. Dunne and co-workers also reported that most nucleation occurring in the atmosphere involves ammonia or biogenic organic compounds, in addition to sulfuric acid.\cite{Dunne2016} J. Kirkby \textit{et al.}
also found that even a small amount of atmospherically relevant ammonia can increase the nucleation rate of sulphuric acid particles by several orders of magnitude.\cite{Kirkby2011}
The significance of ammonium and ammonia water clusters have thus motivated a large amount of experimental and theoretical studies during the past decades.\cite{Perkins1984, Herbine1985, Stockman1992, Hulthe1997, Wang1998, Chang1998, Jiang1999, Hvelplund2010, Douady2009, Douady2008, Morrell2010, Bacelo2002, Galashev2013}
As a few examples, in 1984, (H$_2$O)$_{2}${NH$_4$}$^+$ was identified using mass spectrometry by Perkin \textit{et al.}\cite{Perkins1984} In 1997, Stenhagen
and co-workers studied the {(H$_2$O)$_{20}$H$_3$O}$^+$ and (H$_2$O)$_{20}${NH$_4$}$^+$ clusters and found that both species display a similar
structure.\cite{Hulthe1997} Hvelplund \textit{et al.} later reported a combined experimental and theoretical study devoted to protonated mixed ammonia/water
which highlighted the idea that small protonated mixed clusters of water and ammonia contain a central {NH$_4$}$^+$ core.\cite{Hvelplund2010}
%The (H$_2$O)NH$_3$ complex has been experimentally investigated via radio frequency and microwave spectra by Herbine \textit{et al.}, and via microwave and tunable far-infrared spectroscopy by Stockman and co-workers.\cite{Herbine1985, Stockman1992}
Theoretical calculations devoted to ammonium and ammonia water clusters have also been extensively conducted.\cite{Lee1996, Chang1998,
Skurski1998, Jiang1999, Donaldson1999, Sadlej1999, Hvelplund2010, Bacelo2002, Galashev2013} Among them, Novoa \textit{et al.} studied the (H$_2$O)$_4$NH$_3$
aggregate and found the existence of a minimum in its potential energy surface corresponding to a (H$_2$O)$_{3}$···{NH$_4$}$^+$···OH$^-$ structure, resulting from
one proton transfer from a water molecule to the ammonia molecule.\cite{Lee1996} Bacelo later reported a number of low-energy minima for (H$_2$O)$_{3-4}$NH$_3$
clusters obtained from \textit{ab initio} calculation and a Monte Carlo exploration of the potential energy surface (PES).\cite{Bacelo2002} More recently, Douady \textit{et al.}
performed a global optimization of (H$_2$O)$_{n}${NH$_4$}$^+$ (n = 1-24) clusters again using a Monte Carlo procedure in combination with a Kozack and Jordan
empirical force field.\cite{Douady2008, Kozack1992polar}
In this study, the finite temperature properties as well as vibrational signature of several clusters thus highlighting the key contribution of simulations in understanding such species. Morrell and Shields also studied the
(H$_2$O)$_{n}${NH$_4$}$^+$ (n = 1-10) aggregates \textit{via} a mixed molecular dynamics and quantum mechanics methodology to calculate energies and free energies
of formations which were in good agreement with previous experimental and theoretical results.\cite{Morrell2010}
More recently, Pei \textit{et al.} determined that (H$_2$O)$_{n}$NH$_4^+$ clusters start to adopt a closed-cage geometry at $n$=8.\cite{Pei2015}
Finally, Walters and collaborators determined the geometry of (H$_2$O)$_{16}$NH$_3$ and (H$_2$O)$_{16}$NH$_4^+$ at the HF/6-31G(d) level,
and observed strong hydrogen bonding between water and the lone pair of NH$_3$ and bewteen NH$_4^+$ and the four adjacent water molecules.\cite{Walters2018}
As for the study of other molecular clusters, the range of applicability of theoretical simulations to describe ammonium and ammonia water clusters is dictated
by the balance between accuracy, transferability and computational efficiency. While \textit{ab-initio} methods can accurately model small aggregates, their
application to large species is more difficult, in particular when an exhaustive exploration of the PES is required. In contrast, force-field
potentials are computationally extremely efficient and can be coupled to global optimization methods but their transferability is limited.
The SCC-DFTB approach can be seen as an intermediate approach which combines the strengths of both \textit{ab-initio} and force-field methods.
Indeed, it can be as accurate as DFT while computationally more efficient and is more transferable than force fields (see Chapter~2)
In the recent years, SCC-DFTB has been successfully applied to the study of various molecular clusters: pure, protonated, and de-protonated water
clusters,\cite{Choi2010, Choi2013, Korchagina2017, Simon2019} water clusters on polycyclic aromatic hydrocarbons,\cite{Simon2012, Simon2013water}
sulfate-containing water clusters,\cite{Korchagina2016} water clusters in an argon matrix,\cite{Simon2017formation} whether it is for global optimization or
for the study of finite-temperature properties. However, in its original formulation, SCC-DFTB does not provide good results for the description of ammonia
and ammonium as nitrogen hybridization seems to be a problem for minimal basis-set methods like SCC-DFTB.\cite{Winget2003} Elstner and coworkers found
consistent errors (about 14.0 kcal.mol$^{-1}$) for deprotonation energies of sp$^3$ hybridized nitrogen containing systems, whereas sp$^1$ and sp$^2$ systems
display much smaller errors.\cite{Gaus2013para}
In the present section, we first propose an improvement of the SCC-DFTB scheme to describe ammonium and ammonia water clusters by modifying
both Hamiltonian and overlap N-H integrals and introducing optimized atomic charges.\cite{Thompson2003, Rapacioli2009} By combining this
improved SCC-DFTB scheme with PTMD simulations, global optimization of the (H$_2$O)$_{1-10}${NH$_4$}$^+$ and (H$_2$O)$_{1-10}${NH$_3$}
clusters is then performed which allows to report a number of low-energy isomers for these species. Among them, a selected number of structures
are further optimized at the MP2/Def2TZVP level of theory to confirm they are low-energy structures of the PES and to rationalize the difference in
relative energy between both methods. A detailed description of the reported low-energy isomers is then provided as well as comparisons with the
literature. The heat capacity curve of (H$_2$O)$_{20}${NH$_4$}$^+$ is also obtained at the SCC-DFTB level and compared to previously published
simulations. Some conclusions are finally presented. A very small part of this work has been published in 2019 in a review in\textit{Molecular Simulation}.\cite{Simon2019}
A full paper devoted to this work is in preparation.
\subsection{Results and Discussion}
\subsubsection{Dissociation Curves and SCC-DFTB Potential}
In order to define the best SCC-DFTB parameter to model ammonia and ammonium water clusters, we have tested various sets of corrections.
Each correction involves two modifications of the potential, the first one is the CM3 charge parameter D$_{NH}$ and the second one is the
multiplying factor, noted $xNH$, applied to the NH integrals in the Slater-Koster tables. So a given set is noted D$_{NH}$/$xNH$. Two sets of
corrections have provided satisfactory results, 0.12/1.16 and 0.14/1.28. Figure~\ref{fig:E_nh4} and ~\ref{fig:E_nh3} present dissociation
curves obtained at the MP2/Def2TZVP, MP2/Def2TZVP with BSSE correction, original SCC-DFTB, SCC-DFTB 0.14/1.28 and SCC-DFTB
0.12/1.16 levels of theory. These curves are obtained using the same set of geometries regardless of the method applied to calculate
the binding energies. They are obtained from the MP2/Def2TZVP optimized structures in which the distance between the water and the
ammonium/ammonia was shifted along the N--O vector, all other geometrical parameters being kept fixed.
\begin{figure}[h!]
\includegraphics[width=0.6\linewidth]{E-distance-nh4-w.png}
\centering
\caption{Binding energies of (H$_2$O){NH$_4$}$^+$ as a function of the N---O distance at MP2/Def2TZVP (plain black), MP2/Def2TZVP with BSSE correction (dotted black),
original SCC-DFTB (plain red), SCC-DFTB (0.14/1.28) (dotted red) and SCC-DFTB (0.12/1.16) (dashed red) levels of theory.}
\label{fig:E_nh4}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=0.6\linewidth]{E-distance-nh3-w.png}
\centering
\caption{Binding energies of (H$_2$O){NH$_3$} as a function of the N---O distance at MP2/Def2TZVP (plain black), MP2/Def2TZVP with BSSE correction (dotted black),
original SCC-DFTB (plain red), SCC-DFTB (0.14/1.28) (dotted red) and SCC-DFTB (0.12/1.16) (dashed red) levels of theory.}
\label{fig:E_nh3}
\end{figure}
From Figure~\ref{fig:E_nh4}, the five curves display the same trends with a minimum located at almost the same N---O distance. At the curve minimum,
binding energies vary between XX and XX~kcal.mol$^{-1}$ at the original SCC-DFTB and SCC-DFTB 0.14/1.28 levels, respectively. The binding energy
obtained at the SCC-DFTB 0.12/1.16 level is the closest to that obtained at MP2/Def2TZVP level with BSSE correction with a binding energy difference of
only XX~kcal.mol$^{-1}$. The SCC-DFTB 0.14/1.28 curve is also very close with a difference in binding energy only XX~kcal.mol$^{-1}$ higher. It is
worth mentioning that both sets of corrections lead to improved results as compared to the original SCC-DFTB parameters which leads to a too low
binding energy as compared to MP2/Def2TZVP level with BSSE correction. Also the position of the minimum is more shifted at the original SCC-DFTB
level than with corrections. So from structural and energetic point of views, both sets of corrections are satisfactory.
From Figure~\ref{fig:E_nh3}, the five curves display significant differences. This effect is accentuated by smaller binding energy values: they
vary from XX to XX~kcal.mol$^{-1}$ at the original SCC-DFTB and MP2/Def2TZVP levels, respectively, at the minimum of the curves. The binding
energy obtained at the SCC-DFTB 0.14/1.28 level is the closest to that obtained at MP2/Def2TZVP level with BSSE correction with a binding energy
difference of only XX~kcal.mol$^{-1}$. The SCC-DFTB 0.12/1.16 curve is also rather close with a difference in binding energy only XX~kcal.mol$^{-1}$
higher. Here also, both sets of corrections lead to improved results as compared to the original SCC-DFTB parameters. The position of the minimum
is also better reproduced by the the corrected potentials than by the original SCC-DFTB. It is worth mentioning that the rather difference in binding
energy between (H$_2$O){NH$_4$}$^+$ and (H$_2$O)NH$_3$ was expected owing to a stronger electrostatic contribution of {NH$_4$}$^+$ to the
binding energy.
Another very important point when comparing the original SCC-DFTB potential and the corrected potentials, is the structure obtained for the
(H$_2$O){NH$_4$}$^+$ dimer. Figure~\ref{dimers} compares the structure obtained from geometry optimization at the SCC-DFTB 0.14/1.28
and original SCC-DFTB levels. The N-H covalent bond involved in the hydrogen bond is significantly longer with the original potential while
the N---O distance is XXX. This is reminiscent of the too low proton affinity of {NH$_4$}$^+$ predicted by the original SCC-DFTB potential.
This discrepancy has been previously highlighted in other studies,\cite{Winget2003,Gaus2013para} and makes this potential unusable in any
realistic molecular dynamics simulation as it leads to a spurious deprotonation. Both sets of corrections are free of this error. \red{An additional
proof of this assertion is presented in Figure~\ref{XX} that displays the energy barrier for the proton transfer at constant N---O distance obtained
from different methods.}
%\begin{figure}[H]
\begin{figure}
\includegraphics[width=0.3\linewidth]{dimers.png}
\centering
\caption{Structure of (H$_2$O){NH$_4$}$^+$ obtained from geometry optimization at the SCC-DFTB 0.14/1.28 (right) and original SCC-DFTB (left) levels.}
\label{dimers}
\end{figure}
Figures~\ref{fig:E_nh4} and ~\ref{fig:E_nh3} show that SCC-DFTB 0.14/1.28 better describe (H$_2$O){NH$_3$} dissociation curve while SCC-DFTB 0.12/1.16
better describe (H$_2$O){NH$_4$}$^+$. As one looks for a unique potential to describe both ammonium and ammonia water clusters, we choose SCC-DFTB
0.14/1.28 for the present study. Indeed, as (H$_2$O){NH$_3$} is characterized by a much lower binding energy than (H$_2$O){NH$_4$}$^+$, an error of
the of order of XX~kcal.mol$^{-1}$ is more likely to play a significant role for ammonia than ammonium containing species. All the following discussion therefore
involve the SCC-DFTB 0.14/1.28 potential.
\subsubsection{Small Species: (H$_2$O)$_{1-3}${NH$_4$}$^+$ and (H$_2$O)$_{1-3}${NH$_3$}}
\subsubsection{Properties of (H$_2$O)$_{4-10}${NH$_4$}$^+$ Clusters}
\subsection{Conclusions for Ammonium/Ammonia Including Water Clusters}
\section{Structural and Energetic Properties of Protonated Uracil Water Clusters} \label{structureUH}
\subsection{General introduction}
Gas phase investigations of molecules help to understand the intrinsic properties of molecules that are free from the effects of solvents.
The gas phase study needs to be extended towards more realistic biomolecular systems, to reveal how the intrinsic molecular properties are affected by the surrounding medium when the biomolecules are in a natural environment.\cite{Maclot2011, Domaracka2012, Markush2016, Castrovilli2017} The hydration study of biomolecules is of paramount importance to get insights into their behavior in aqueous medium, especially the effects on their structure, stability and dynamics.
The nucleobases in DNA and RNA play a significant role in the encoding and expression of genetic information in living systems while water is a natural medium of many reactions in living organisms. The study of the interaction between nucleobase molecules and aqueous environment has attracted a lot of interests among biologists and chemists. Exploring the clusters composed of nucleobase molecules with water is a good workbench to observe how the properties of nucleobase molecules change when going from isolated gas-phase to hydrated species.
The radiation can cause damages on RNA and DNA molecules, which is proficiently applied in radiotherapy for cancer treatment. The major drawback in radiotherapy is the unselective damage in both healthy and tumor cells, which has a big side effect. This makes it particularly important to explore the radiation fragments.
Uracil (U), C$_4$H$_4$N$_2$O$_2$, is one of the four nucleobases of RNA, has been paid attention concerning radiation damage. Protonated uracil UH$^+$ can be generated by radiation damages.\cite{Wincel2009}
The reasons for such degradation can be due to the interaction with slow electrons, as shown by the work of Boudaiffa \textit{et al.} \cite{Boudaiffa2000}
Several studies have been devoted to the effect of hydration on the electron affinity of DNA nucleobases. \cite{Smyth2011, Siefermann2011, Alizadeh2013} For instance, Rasmussen \textit{et al.} found that a water molecule is more likely to interact with a charged species than with a neutral one though the study of hydration effects on the lowest triplet states of cytosine, uracil, and thymine by including one or two water molecules explicitly, \cite{Rasmussen2010}
However, a lot of work is still needed to be performed to understand the role of aqueous environment on charged nucleobases of DNA and RNA.
Collision experiments is a useful tool that can be applied to understand the reactivity of molecules and provide access to structural information.\cite{Coates2018}
Fragmentation of the bare protonated U has already been performed under collision-induced dissociation (CID) with tandem mass spectrometry,\cite{Nelson1994, Sadr2014, Molina2016}
however, there are only few studies available concerning the effect of hydration on such process. Infrared photodissociation spectroscopy of singly
hydrated protonated uracil shows that the most stable tautomeric form of the neutral uracil (diketo) differs from the most stable one for bare
protonated uracil (keto-enol).\cite{Bakker2008}
%Some theoretical studies reported the structures taken by neutral microhydrated uracil, containing up to 15 water molecules.\cite{Shishkin2000, Gadre2000, Gaigeot2001, Danilov2006, Bacchus2015}
However, fragmentation studies of such species under CID conditions have not been performed. \textbf{S. Zamith and J.-M. l'Hermite conducted such CID
experiments on protonated uracil water species (H$_2$O)$_{1-15}$UH$^+$ during my thesis and I collaborated with them in order to provide a theoretical
support to their measurements}.
%The dissociation of mass selected (H$_2$O)$_{1-15}$UH$^+$ clusters is induced by collisions with target rare gas atoms (Ne, Ar) or water molecules (H$_2$O, D$_2$O) at a controlled center of mass collision energy 7.2 eV which is chosen high enough so that a large number of fragmentation channels are explored. After the collisions, the remaining charged species, which have lost one or several neutral subunits, are detected. We find essentially the same results whatever the nature of target atoms of molecules is. The resulting inter-molecular dissociation patterns of the (H$_2$O)$_{1-15}$UH$^+$ clusters show that below n = 5 only water molecules are evaporated whereas, for n $\geq$ 5, a new fragmentation channel appears that corresponds to the loss of neutral uracil.
Theoretical studies have already been devoted to mixed uracil-water clusters and intended to describe the lowest energy structures. However,
only neutral species ((H$_2$O)$_{n}$U) were considered.\cite{Shishkin2000, Gadre2000, Van2001diffu, Gaigeot2001, Danilov2006, Bacchus2015}
Those studies showed that for sizes up to with $n$ = 3, the water molecules arrange in monomers or dimers in the plane of the uracil molecule
\cite{Gadre2000, Van2001diffu, Gaigeot2001, Danilov2006, Bacchus2015} with no trimer formation. But for $n$ \textgreater~3, very different structures
were predicted depending on the considered study. For instance, Ghomi predicted that for $n$ = 7,\cite{Gaigeot2001} water molecules arrang
in dimers and trimers in the plane of the uracil molecule, whereas for n = 11, water molecules form locked chains.\cite{Shishkin2000} 3D configurations were also proposed. For instance, all water molecules lie above the uracil plane for $n$ = 4, 5 reported by Calvo \textit{et al.}.\cite{Bacchus2015} Similarly, for $n$ = 11, Danilov \textit{et al.} also obtained a
structure that consists of a water cluster above the uracil molecule.\cite{Danilov2006} Such structures are predicted to start with 4 water molecules
reported by Calvo and collaborator \cite{Bacchus2015} or with 6 water molecules (though 5 have not been calculated) reported by Gadre \textit{et al.}.\cite{Gadre2000}
Those studies may suggest that for few water molecules (up to two), the proton should be located on the uracil molecule, whereas when a large number
of water molecules surround the uracil, the charge is expected to be located on the water molecules. Of course, the excess proton is expected to strongly
influence the structure of the lowest energy isomers of each species, as observed for pure water clusters, so the size at which the proton is transferred
from uracil to water cannot be deduced from the aforementioned studies. Moreover, all those theoretical studies do not lead to the same low-energy
structures as highlighted by Danilov and Calvo.\cite{Danilov2006, Bacchus2015} Consequently, although it is instructive from a qualitative point
of view, the analysis of the experimental data by S. Zamith and J.-M. l'Hermite cannot be based on those studies. We have therefore undertaken a
theoretical simulation of hydrated protonated uracil clusters (H$_2$O)$_{1-7, 11, 12}$UH$^+$ to determine their lowest-energy structures to
complete the experiments by S. Zamith and J.-M. l'Hermite at the \textit{Laboratoire Collisions Agr\'egats R\'eactivit\'e }(LCAR). This work has
been published in 2019 in the \textit{The Journal of Chemical Physics}.\cite{Braud2019}
\subsection{Results and Discussion}
In the following section, section~\ref{exp_ur}, I present in details the results obtained from the CID experiments of S. Zamith and J.-M. l'Hermite
and the main concepts used to interpret the data. The following section, section~\ref{calcul_ur}, is devoted to the theoretical determination of
the low-energy isomers of the (H$_2$O)$_{1-7,11,12}$UH$^+$ clusters. A more detailed presentation of CID experiments is also provided in
section~\ref{exp_cid} of chapter~4, where these details are important to explicitly model CID experiments.
\subsubsection{Experimental Results} \label{exp_ur}
\textbf{Time of flight of mass spectrum(TOFMS) .}
A typical fragmentation mass spectrum obtained by colliding (H$_2$O)$_{7}$UH$^+$ with neon at a center of mass collision energy of 7.2 eV is shown in Figure \ref{mass7w}. The more intense peak on the right comes from the parent cluster (H$_2$O)$_{7}$UH$^+$, the next 7 peaks at the left of the parent peak correspond to the loss of 1-7 water molecules of parent cluster, and the next 5 peaks to the left results from the evaporation of the uracil molecule and several water molecules from parent cluster. This mass spectrum is obtained at the highest pressure explored in the present experiments. This is still true for the largest size investigated here, namely, (H$_2$O)$_{15}$UH$^+$. From the result of the fragmentation mass spectrum displayed in Figure \ref{mass7w}, it indicates multiple collisions are possible, which allows the evaporation of all water molecules. Moreover, the intensity of evaporation of water molecules is bigger than the one of evaporation of U.
In our study, we are interested in two specific channels. Channel 1 corresponds to the loss of only neutral water molecules, whereas channel 2 corresponds to the loss of neutral uracil and one or several water molecules,
\begin{align}
\mathrm{Channel~1, ~(H_2O)_nUH^+} & \rightarrow ~ \mathrm{(H_2O)_{n-x}UH^+ + xH_2O } \\
\mathrm{Channel~2, ~(H_2O)_nUH^+} & \rightarrow ~ \mathrm{ (H_2O)_{n-x}H^+ + xH_2O + U}
\end{align}
\figuremacro{mass7w}{Time of flight of mass spectrum obtained by colliding (H$_2$O)$_{7}$UH$^+$ with Ne
at 7.2 eV center of mass collision energy (93.5 eV in the laboratory frame).}
\textbf{Fragmentation cross section.}
The total fragmentation cross sections of clusters
(H$_2$O)$_{n-1}$UH$^+$, pure water clusters \newline (H$_2$O)$_{n=2-6}$H$^+$,\cite{Dalleska1993} and deuterated water clusters (D$_2$O)$_{n=5, 10}$H$^+$ \cite{Zamith2012} are plotted in Figure \ref{fragcrosssec} as a function of the cluster size n. Here n stands for the total number of molecules when the cluster includes uracil molecule. Different target atoms and molecules were used in these experiments: Water molecules or neon atoms in our experiments, xenon atoms in Dalleska’s experiments. These experimental data are compared to the geometrical (\textit{i.e.}, hard sphere) cross sections given by:
\begin{align}
\label{cross-section-geo}
\sigma_{geo} = \pi \left(\left[n_w\times r_w^3 + n_Ur_U^3\right]^{1/3} + r_T \right)^2
\end{align}
where $n_w$ is the number of water molecules, and $n_U$ is the number of uracil molecules ($n_U$ = 0 or 1 in the present study). $r_w$, $r_U$, and $r_T$ refer to the molecular radii of water, uracil, and the target atom or molecule, respectively. The molecular radii are deduced from macroscopic densities that gives $r_U$ = 3.2 \AA \cite{Myers2007} and $r_w$ = 1.98 \AA. The radii of rare gas target atoms are taken as their Van der Waals radii $r_{Ne}$ = 1.54 \AA and $r_{Xe}$ = 2.16 \AA.
The main differences between the curves in Figure \ref{fragcrosssec} can be rationalized as follows: The larger the size of the target atom (or molecule) is, the bigger the fragmentation cross section will be. The experimental fragmentation cross sections of clusters (H$_2$O)$_{n-1}$H$^+$ colliding with water molecules are larger than the values obtained for collisions with Ne atoms. In the same vein, for a given number of molecules in the cluster, the cross section is larger for clusters containing uracil. The overall trend of all curves in Figure \ref{fragcrosssec} is the same: The
fragmentation cross sections increase with the size and seem to tend toward the geometrical one.
The cross sections measured for clusters containing uracil colliding with water molecules (black squares) are of the same magnitude as the ones previously obtained for deuterated pure water clusters (green full circles) at a similar collision energy.\cite{Zamith2012} For clusters containing uracil, fragmentation cross sections are systematically larger than the one for pure water clusters by an amount of the same magnitude as the one predicted by the geometrical cross sections. For instance, the difference between red squares and blue stars, and the difference between red full line and blue dashed line has the same magnitude.
The fragmentation cross sections obtained by Dalleska
and coworkers \cite{Dalleska1993} for protonated water clusters are within our error bars for n = 5, 6 and about a factor of 2 lower for n = 3, 4. However their cross section is notably lower for (H$_2$O)$_2$H$^+$ as compared to our measurement for (H$_2$O)UH$^+$. This difference may be explained by the fact that UH$^+$ forms a weaker bond with water than H$_2$OH$^+$ does. Indeed the dissociation energy D[H$_2$OH$^+$–H$_2$O] is 1.35 eV \cite{Dalleska1993, Hansen2009} whereas the value for D[UH$^+$–H$_2$O] is estimated between 0.54 \cite{Wincel2009} and 0.73 eV. \cite{Bakker2008} The same behavior is observed for n = 3, and the dissociation energy D[(H$_2$O)$_2$H$^+$–H$_2$O] = 0.86 eV \cite{Dalleska1993, Hansen2009} is greater than the dissociation energy D[U(H$_2$O)H$^+$–H$_2$O] = 0.49 eV.\cite{Wincel2009} Hence the dissociation of water molecules is more favored in the protonated uracil cluster than in the pure water clusters.
\figuremacro{fragcrosssec}{Fragmentation cross sections of clusters (H$_2$O)$_{n-1}$UH$^+$ at a collision energy of 7.2 eV plotted as a function of the total number n of molecules in the clusters. The experimental results and geometrical cross sections are shown for collision with H$_2$O and Ne. The results from Dalleska et al.\cite{Dalleska1993} using Xe as target atoms on pure protonated water clusters (H$_2$O)$_{2-6}$H$^+$ and from Zamith \textit{et al.} \cite{Zamith2012} using water as target molecules on deuterated water clusters (D$_2$O)$_{n=5,10}$H$^+$ are also shown. The geometrical collision cross sections of water clusters in collision with Xe atoms and water molecules are also plotted. Error bars represent one standard deviation.}
\textbf{Intermolecular fragmentation.}
Figure \ref{Uloss} displays the percentage of the fragments that have lost a neutral uracil molecule over all the fragments, plotted as a function of the number of water molecules in the parent cluster (H$_2$O)$_{n}$UH$^+$. It shows that for the cluster (H$_2$O)$_{n}$UH$^+$ with a small number of water molecules, almost no neutral uracil is evaporated. From n = 5 and more clearly from n = 6, the loss of neutral uracil molecule increases up to about 20\% for (H$_2$O)$_{9}$UH$^+$.
\figuremacro{Uloss}{Proportion of neutral uracil molecule loss plotted as a function of the number of water molecules n in the parent cluster (H$_2$O)$_{n}$UH$^+$. Results obtained for collisions with Ne atoms at 7.2 eV center of mass collision energy.}
The fragmentation can arise from two distinct mechanisms (direct and statistical fragmentation processes) depending on the life time of the collision complex. On the one hand, if the fragmentation occurs in a very short time after collision, the dissociation is impulsive (direct). In this case, we thus assume that the nature of the collision products is partly determined by the nature of the lowest-energy isomers of parent clusters and especially by the location of the excess proton in the structure. In other words, the lowest-energy isomer of the parent cluster obviously plays a major role in determining the fragmentation channels. On the other hand, in the case of long-lived collision complexes, collision energy is transferred to the parent cluster and is redistributed among all degrees of freedom. This is a slow process, and the structures involved during the fragmentation are no longer the lowest-energy isomer, \textit{i.e.}, the structure of the cluster can undergo structural reorganizations before evaporation. Furthermore, the excess proton can also diffuse in the structure and for instance, recombine with the uracil. Then the role of the initial structure of the parent clusters is strongly reduced in determining the fragmentation channels.
In Figure \ref{Uloss}, we focus on the loss of the neutral uracil molecule in the detected fragments since it indicates where the proton lies after collision, namely, on the uracil or on a water cluster. A transition in the nature of fragmentation product is clearly seen from n = 5-6. To account for this transition, we consider that evaporation originates from a direct fragmentation process. A short discussion about the implications of possible structural rearrangement prior to dissociation, which occurs in a statistical process, will be provided in section~\ref{calcul_ur}.
The relative proton affinities of each component of the
mixed clusters gives a first estimate of which molecule, uracil or water, is more likely to carry the positive charge prior to collisions. Experimentally, the gas phase proton affinity of uracil is bracketed to 9 $\pm$ 0.12 eV.\cite{Kurinovich2002} For the proton affinity of water molecule, an experimental value is reported at 7.31 eV \cite{Magnera1991} and a theoretical one at 7.5 eV.\cite{Cheng1998} In the work of Cheng, it shows that the proton affinity of water clusters increases with their size.\cite{Cheng1998} The proton affinities extracted from the different studies for the uracil molecule and for water clusters as a function of the number of water molecules are displayed in Figure~\ref{protonAffinity}.
\figuremacro{protonAffinity}{The proton affinities of water clusters as a function of the number of water
molecules n, which are taken from the work of Magnera (black circles) \cite{Magnera1991} and from the work of Cheng (blue squares).\cite{Cheng1998} The value of the proton affinity of uracil (red dotted dashed line) is also plotted.\cite{Kurinovich2002}}
It clearly shows that the proton affinity of uracil, PA[U], is larger than the one of water monomer PA[H$_2$O]. Thus, for the mono-hydrated uracil, from the energetic point of view, the proton is on the uracil molecule and the only observed fragments are indeed protonated uracil molecules. Moreover, an experimental work \cite{Bakker2008} confirms that there is no proton transfer from the uracil to the water molecule in mono-hydrated clusters. Proton affinity of the uracil molecule is also larger than that of the water dimer, or even the trimer: PA[U] $>$ PA[(H$_2O$)$_n$], n = 2 or 3 depending on the considered data for water. This is still consistent with our experimental observation of no neutral uracil molecule loss for n = 2 and 3. However from the PA values, one would predict that the appearance of neutral uracil should occur for n $\approx$ 3-4. For instance, for n = 4, assuming a statistical fragmentation for which the energies of final products are expected to be of relevance, the channel U + (H$_2$O)$_4$H$^+$ is energetically favorable. If one now assumes a direct dissociation, where the parent protonation state remains unchanged, one also expects that neutral uracil evaporates. However, experimentally, for n = 4, no neutral uracil evaporation is observed. The loss of neutral uracil starts at n = 5 and becomes significant only at n = 6.
This analysis based on PA is however quite crude. Indeed, it assumes that the protonated uracil cluster would be composed of a uracil molecule attached to an intact water cluster. However, one expects that the hydration of uracil may be more complicated than this simple picture. Therefore, the uracil hydration is explored theoretically in the next Section, Section~\ref{calcul_ur}, in order to determine the proton location more realistically.
\subsubsection{Calculated Structures of Protonated Uracil Water Clusters} \label{calcul_ur}
As discussed in section~\ref{sec:ammoniumwater}, we have proposed a modified set of NH parameters to describe sp$^3$ nitrogen atoms. For,
sp$^2$ nitrogen atoms there is no need to modified the integral parameters as SCC-DFTB describe them rather correctly. Consequently, only the
$D_{NH}$ parameter needs to be defined for the present calculations. Table~\ref{tab:DNH} present the binding energy of the two
(H$_2$O)U isomers represented in Figure~\ref{uracil_s} at MP2/Def2TZVP and SCC-DFTB levels of theory. Both $D_\textrm{NH}$ = 0.12 and
$D_\textrm{NH}$ = 0.14 lead to consistent binding energies. So, to be consistent with the work performed in the previous section, we
have used $D_\textrm{NH}$ = 0.14 in the following.
\begin{table}
%\footnotesize
\begin{center}
%\begin{adjustbox}{width=1\textwidth}
% \small
\caption{Binding energy of two (H$_2$O)U isomers at MP2/Def2TZVP and SCC-DFTB levels of theory.}
\label{tab:DNH}
\resizebox{1.0\textwidth}{!}{
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
\textbf{isomer} & \boldm{$E_{bind_{MP2}}$} & \boldm{$E_{bind_{DFTB}}$}
& \boldm{$E_{Re}$} &\boldm{$E_{bind_{DFTB}}$}
& \boldm{$E_{Re}$}
&\boldm{$E_{bind_{DFTB}}$}
& \boldm{$E_{Re}$} \\
& & \boldm{$D_{{NH}_{0.0}}$} & \boldm{$D_{{NH}_{0.0}}$} & \boldm{$D_{{NH}_{0.12}}$} & \boldm{$D_{{NH}_{0.12}}$} & \boldm{$D_{{NH}_{0.14}}$} &\boldm{$D_{{NH}_{0.14}}$} \\
\hline
\bf{a} & -8.3 & -8.6 & -0.3 & -9.8 &-1.5 & -10.0 &-1.7 \\
\hline
\bf{b} & -6.9 & -6.6 & 0.3 & -6.9 & 0.0 & -6.9 & 0.0 \\
\hline
\end{tabular}}
% \end{adjustbox}
\end{center}
\end{table}
%\figuremacro{a-b}{The structure of isomer a and b of cluster (H$_2$O)U.}
The lowest-energy isomers determined theoretically for
hydrated uracil protonated clusters (H$_2$O)$_{n=1-7, 11, 12}$UH$^+$ are shown in Figures \ref{1a-f}-\ref{12a-f}. In the experiments, clusters are produced at a temperature of about 25 K, so only a very few isomers are likely to be populated. Indeed, the clusters are produced in the canonical ensemble at the temperature $T_\mathrm c \approx$ 25 K, so only isomers for which the Boltzmann factor exp(-$\Delta E k_\mathrm{B} T_\mathrm{c}$) is larger than 10$^{-7}$ are considered here. In this formula, $\Delta E$ represents the relative energy of a considered isomer with respect to the lowest-energy one. Thus for each isomer, only the first six lowest-energy structures of U(H$_2$O)$_{n=1-7, 11, 12}$UH$^+$ obtained from the PES exploration will be discussed.
Figure \ref{1a-f} displays the six lowest-energy isomers obtained for (H$_2$O)UH$^+$. Two (1a and 1b) of them contain the u138-like isomer of U (each one with a different orientation of the hydroxyl hydrogen). Three of them (1c, 1d, and 1e) contain the u178 isomer and 1f contains the u137\cite{Wolken2000} isomer with a reverse orientation of the hydroxyl hydrogen. From those isomers, different sites are possible for the water molecule attachment which leads to variety of isomers even for such small size system. To the best of our knowledge, (H$_2$O)UH$^+$ is the most studied protonated uracil water cluster and our results are consistent with previous
published studies. Indeed, Pedersen and co-workers \cite{Pedersen2014} conducted ultraviolet action spectroscopy on (H$_2$O)UH$^+$ and discussed their measurements in the light of theoretical calculations performed on two isomers: ur138w8 (1a in the present study) and ur178w7 (1c).\cite{Pedersen2014} Their energy ordering at 0 K is the same whatever the computational method they used: B3LYP/6-311++G(3df,2p), M06-2X/6-311++G(3df,2p), MP2/6-311++G(3df,2p), CCSD(T)/6-311++G(3df,2p), and CCSD(T)/augcc-pVTZ and is similar to what we obtain. Similarly, Bakker and co-workers\cite{Bakker2008} considered three isomers: U(DK)H$^+_W$ (1a), U(KE)H$^+_{Wa}$ (1c), and U(KE)H$^+_{Wb}$ (1e) at the B3LYP/6-311++G(3df,2p) level of theory and obtained the same energy ordering as we do. Our methodology has thus allowed us to retrieve those isomers and to locate two new low-energy structures (1b and 1d). 1f is too high in energy to be considered in low-temperature experiments that are in the same range of relative energies but have never been discussed. To ensure that they are not artificially favored in our computational method, calculations were also performed at the B3LYP/6-311++G(3df,2p) level of theory. The results are presented in Figure \ref{1a-f-b3lyp}, which are consistent with the MP2/Def2TZVP ones. This makes us confident in the ability of the present methodology to locate meaningful low energy structures. Importantly, no isomer with the proton on the water molecule was obtained, neither at the DFTB or MP2 levels.
\figuremacrob{1a-f}{Lowest-energy structures of (H$_2$O)UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm{rel}$) and binding energies ($E_\textrm{bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA.}
\figuremacrob{1a-f-b3lyp}{Lowest-energy structures of (H$_2$O)UH$^+$ obtained at the B3LYP/6-311++G(3df,2p) level of theory. Relative ($E_\textrm{rel}$) and binding energies ($E_\textrm{bind}$) are given in kcal.mol$^{-1}$. The corresponding values with ZPVE corrections are provided in brackets. Important hydrogen-bond distances are indicated in bold and are given in \AA.}
Figures \ref{2a-f} and \ref{3a-f} display the first six lowest-energy isomers obtained for (H$_2$O)$_2$UH$^+$ and (H$_2$O)$_3$UH$^+$, respectively. For (H$_2$O)$_2$UH$^+$, the lowest energy structure, 2a contains the u138 isomer of uracil. 2b, 2d, and 2e contain u178 and 2c contains u138 with reverse orientation of the hydroxyl hydrogen. 2f contains u178 with reverse orientation of the hydroxyl hydrogen. This demonstrates that, similarly to (H$_2$O)UH$^+$, a diversity of uracil isomers are present in the low-energy structures of (H$_2$O)$_2$UH$^+$ which makes an exhaustive exploration of its PES more difficult. The same behavior is observed for (H$_2$O)$_3$UH$^+$. The configuration of u138 does not allow for the formation of a water dimer which leads to two unbound water molecules in 2a. By contrast, a water-water hydrogen bond is observed for 2b and 2c. The existence of a water dimer was not encountered in the low-energy isomers of the unprotonated (H$_2$O)$_2$U species due to the absence of the hydroxyl group on U. It is worth pointing out that 2a, 2b, 2c, and 2d are very close in energy which makes their exact energy ordering difficult to determine. However, no isomer displaying an unprotonated uracil in the low-energy isomers of (H$_2$O)$_2$UH$^+$ was located. The lowest-energy structure of (H$_2$O)$_3$UH$^+$, 3a, is characterized by two water-water hydrogen bond that forms a linear water trimer. Higher energy isomers display only one (3b, 3d, and 3e) or zero (3c and 3f) water-water bond (see Figure \ref{3a-f}). Similarly to (H$_2$O)$_2$UH$^+$, no isomer displaying an unprotonated uracil was located for (H$_2$O)$_3$UH$^+$.
\figuremacrob{2a-f}{Lowest-energy structures of (H$_2$O)$_2$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm{rel}$) and binding energies ($E_\textrm{bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA.}
\figuremacrob{3a-f}{(H$_2$O)$_3$UH$^+$ lowest-energy structures obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm{rel}$) and binding energies ($E_\textrm{bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA.}
The first six lowest-energy isomers obtained for (H$_2$O)$_4$UH$^+$ and (H$_2$O)$_5$UH$^+$ are displayed in Figures \ref{4a-f} and \ref{5a-f}, which constitute a transition in the behavior of the proton. Indeed, in (H$_2$O)$_4$UH$^+$, two kind of low-lying energy structures appear: (i) structures composed of UH$^+$, one water trimer, and one isolated water molecule (4b, 4d, 4e, and 4f); (ii) structures composed of U and a protonated water tetramer (4a and 4c). In the latter case, the hydronium ion is always bounded to an uracil oxygen atom. The U–H$_2$OH$^+$ bond is always rather strong as compared to U–H$_2$O bonds as highlighted by the corresponding short oxygen-hydrogen distance. Furthermore, speaking of distances, the difference between the U–H$_2$OH$^+$ and UH$^+$–H$_2$O forms is rather fuzzy and might be sensitive to computational parameters and also to quantum fluctuations of the hydrogen. This suggests that collision with (H$_2$O)$_4$UH$^+$ is more likely to induce evaporation of H$_2$O rather than H$_2$OH$^+$ or a protonated water cluster. The picture is significantly different in (H$_2$O)$_5$UH$^+$ where the lowest-energy structure displays a hydronium ion separated by one water molecule from U. Such structures do not appear in (H$_2$O)$_4$UH$^+$ due to the limited number of water molecules available to separate H$_2$OH$^+$ from U. Such separation suggests that, if considering a direct dissociation process, evaporation of neutral uracil can now occurs in agreement with the experimental observations (see discussion above). One can see that 5b, which is only 0.3 kcal.mol$^{-1}$ higher in energy than 5a, still displays a U–H$_2$OH$^+$ link. This is in line with the low amount of neutral uracil that is evaporated in the experiment (see Figure \ref{Uloss}).
\figuremacrob{4a-f}{Lowest-energy structures of (H$_2$O)$_4$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm{rel}$) and binding energies ($E_\textrm{bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA.}
\figuremacrob{5a-f}{Lowest-energy structures of (H$_2$O)$_5$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm{rel}$) and binding energies ($E_\textrm{bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA.}
Figures \ref{6a-f} and \ref{7a-f} display the first six lowest-energy isomers obtained for (H$_2$O)$_6$UH$^+$ and (H$_2$O)$_7$UH$^+$. Similarly to (H$_2$O)$_5$UH$^+$, the first lowest-energy structure, 6a and 7a, we located for both species (H$_2$O)$_6$UH$^+$ and (H$_2$O)$_7$UH$^+$ has the excess proton on a water molecule that is separated by one water molecule from the uracil. This appears to be common to the clusters with at least 5 water molecules. This is also observed for higher-energy isomers (6c, 6d, 7c, 7e, and 7f). Other characteristics of the proton are also observed: proton in a similar Zundel form \cite{Zundel1968} bounded to the uracil (6b, 6e, and 7d) or H$_2$OH$^+$ still bounded to uracil (6f and 7b).
Finally, due to the neutral uracil loss proportion starts to decrease from n=9 (see Figure \ref{Uloss}), which attracted us to perform the optimization of big cluster (H$_2$O)$_{11, 12}$UH$^+$ as examples to explore why it has this change. The first six low-lying energy isomers obtained for cluster (H$_2$O)$_{11, 12}$UH$^+$ are shown in Figures \ref{11a-f} and \ref{12a-f}.
In all isomers (11a to 11f) of cluster (H$_2$O)$_{11}$UH$^+$, the excess is on the water cluster and was separated by water molecule from uracil.
For 12a, 12b, 12c, and 12d, it is obvious that the excess proton is not directly bounded to the uracil. The uracil in 12a and 12d belongs to the di-keto form (there is a hydrogen atom on each nitrogen of uracil), and the excess proton was separated by one water molecule from uracil, additionally, the uracil is surrounded by the water cluster, all of these may lead the excess proton to go to the near oxygen atom of uracil. For 12b, the excess proton is on the water cluster and is very far from the uracil. For 12c, the excess proton was separately by one water molecule from uracil. For isomers 12e and 12f, the excess proton is between the uracil and a water molecule. The uracil is surrounded by the water cluster in 12e but it is not in 12f. Of course, for (H$_2$O)$_{11}$UH$^+$, (H$_2$O)$_{12}$UH$^+$, (H$_2$O)$_6$UH$^+$ and (H$_2$O)$_7$UH$^+$ and also (H$_2$O)$_4$UH$^+$ and (H$_2$O)$_5$UH$^+$, the amount of low-energy isomers is expected to be very large and we do not intended to find them all. Furthermore, due to the limited number of MP2 geometry optimization we performed, there is few chances that we located the global energy minima for (H$_2$O)$_6$UH$^+$, (H$_2$O)$_7$UH$^+$, (H$_2$O)$_{11}$UH$^+$ and (H$_2$O)$_{12}$UH$^+$. However, the general picture we are able to draw from the present discussed structures fully supports the experimental results: from (H$_2$O)$_5$UH$^+$, it exists low-energy structures populated at very low temperature in which the excess proton is not directly bound to the uracil molecule. Upon fragmentation, this allows the proton to remain bounded to the water molecules.
\figuremacrob{6a-f}{Lowest-energy structures of (H$_2$O)$_6$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm{rel}$) and binding energies ($E_\textrm{bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA.}
\figuremacrob{7a-f}{Lowest-energy structures of (H$_2$O)$_7$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm{rel}$) and binding energies ($E_\textrm{bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA.}
\figuremacrob{11a-f}{Lowest-energy structures of (H$_2$O)$_{11}$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm{rel}$) and binding energies ($E_\textrm{bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA.} \\
\figuremacrob{12a-f}{Lowest-energy structures of (H$_2$O)$_{12}$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm{rel}$) and binding energies ($E_\textrm{bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA.}
All the aforementioned low-lying energy structures are relevant to describe the \newline (H$_2$O)$_{n=1-7, 11, 12}$UH$^+$ species at low temperature and to understand the relation between the parent cluster size and the amount of evaporated neutral uracil in the case of direct dissociation. However, as already stated, one has to keep in mind that upon collision statistical dissociation can also occur. In that case, structural rearrangements are expected to occur which are important to understand each individual mass spectra of the (H$_2$O)$_{n=1-15}$UH$^+$ clusters and the origin of each collision product. For instance, the fragment UH$^+$ is detected for all cluster sizes in experiment. This means that for the largest sizes, for which we have shown from the calculation that the proton is located away from the uracil, proton transfer does occur prior to dissociation. One possible scenario is that after collision, water molecules sequentially evaporates. When the number of water molecules is small enough, the proton affinity of uracil gets larger than the one of the remaining attached water cluster. Proton transfer is then likely and therefore protonated uracil can be obtained at the end.
If one turns to the neutral uracil evaporation channel, it appears that the smaller clusters H$_2$OH$^+$ and (H$_2$O)$_2$H$^+$ are not present in the time of flight mass spectra. This absence might have two origins. First, the dissociation energies of the protonated water monomers and dimers are substantially higher than larger sizes, and they are therefore less prone to evaporation. Second, as already mentioned, for such small sizes, the proton affinity of uracil gets larger than the one of the water dimer or trimer and proton transfer to the uracil is likely to occur.
In order to confirm the above scenarios, simulations
and/or evaporation rate calculation would have to be conducted to describe the fragmentation channels in details. MD simulations of protonated uracil have already been performed by Spezia and co-workers to understand the collision-induced dissociation.\cite{Molina2015, Molina2016} Although, in the present case, the initial position of the excess proton appears as a key parameter to explain the evaporation of neutral uracil, such MD simulations could be additionally conducted to provide a clearer picture on the various evaporation pathways, which will be shown in section \ref{sec:collisionwUH}.
\subsection{Conclusions on (H$_2$O)$_{n}$UH$^+$ clusters}
The work in this section presents the collision-induced dissociation of hydrated protonated uracil (H$_2$O)$_{n=1-15}$UH$^+$ clusters and their experimental
absolute fragmentation cross sections. The experiments demonstrate that the evaporation channels evolve with size: Below n = 5, the observed charged fragments
always contain the uracil molecule, whereas from n = 5, the loss of a neutral uracil molecule becomes significant. To understand this transition, I conducted an
exhaustive exploration of the potential energy surface of (H$_2$O)$_{n=1-7, 11, 12}$UH$^+$ clusters combining a rough exploration at the SCC-DFTB level with
fine geometry optimizations at the MP2 level of theory. Those calculations show that below n = 5, the excess proton is either on the uracil or on a water molecule
directly bound to uracil, \textit{i.e.}, forming a strongly bound U–H$_2$OH$^+$ complex. From n = 5 and above, clusters contain enough water molecules to allow
for a net separation between uracil and the excess proton: The latter is often found bound to a water molecule which is separated from uracil by at least one other
water molecule. Upon direct dissociation, the excess proton and the uracil can thus belong to different fragments. This study demonstrates that combination of
collision-induced dissociation experiments and theoretical calculation allows to probe the solvation and protonation properties of organic molecules such as nucleobases.
This is a step toward a better understanding of the role of water in the chemistry of in vivo DNA and RNA bases. However, the knowledge of the lowest-energy isomers
of the species involved in CID experiments is not enough to understand all the collision process. To get a deeper understanding of the collision mechanism, an explicit
modelling of the collision is needed?. This question is addressed in the next chapter of this thesis.
% ---------------------------------------------------------------------------

BIN
thesis/4/.DS_Store vendored Normal file
View File

Binary file not shown.

411
thesis/4/collision.aux Normal file
View File

@ -0,0 +1,411 @@
\relax
\providecommand\hyper@newdestlabel[2]{}
\FN@pp@footnotehinttrue
\citation{Brechignac1989,Brechignac1994}
\citation{Wong2004,Bush2008}
\citation{Holm2010,Gatchell2014,Gatchell2017}
\citation{Boering1992,Wells2005,Zamith2019thermal}
\@writefile{toc}{\contentsline {chapter}{\numberline {4}Dynamical Simulation of Collision-Induced Dissociation}{81}{chapter.4}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{chap:collision}{{4}{81}{Dynamical Simulation of Collision-Induced Dissociation}{chapter.4}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4.1}Experimental Methods}{81}{section.4.1}}
\newlabel{exp_cid}{{4.1}{81}{Experimental Methods}{section.4.1}{}}
\@writefile{brf}{\backcite{Brechignac1989}{{81}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Brechignac1994}{{81}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Wong2004}{{81}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Bush2008}{{81}{4.1}{section.4.1}}}
\citation{Ma1997,Chowdhury2009}
\citation{Nelson1994,Molina2015}
\citation{Carl2007}
\citation{Sleno2004ion,Wells2005}
\citation{Cody1982}
\citation{Olsen2007higher,Hart2011}
\citation{Gauthier1991,Laskin2005}
\citation{Mcquinn2009,Carl2013,Hofstetter2013,Coates2017,Coates2018}
\citation{Graul1989,Wei1991,Goebbert2006,Haag2009}
\citation{Liu2006,Nguyen2011,Shuck2014}
\citation{Castrovilli2017,Bera2018}
\citation{Li1992,Bobbert2002,Liu2006,Bakker2008,Markush2016,Castrovilli2017}
\citation{Carl2013,Hofstetter2013,Coates2018}
\citation{Dawson1982,Bakker2008,Mcquinn2009,Zamith2012}
\citation{Liu2006}
\citation{Carl2013,Hofstetter2013,Coates2018}
\@writefile{brf}{\backcite{Holm2010}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Gatchell2017}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Gatchell2014}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Zamith2019thermal}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Boering1992}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Wells2005}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Ma1997}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Chowdhury2009}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Nelson1994}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Molina2015}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Carl2007}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Wells2005}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Sleno2004ion}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Cody1982}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Olsen2007higher}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Hart2011}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Gauthier1991}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Laskin2005}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Coates2018}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Mcquinn2009}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Carl2013}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Hofstetter2013}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Coates2017}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Graul1989}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Wei1991}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Goebbert2006}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Haag2009}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Liu2006}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Nguyen2011}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Shuck2014}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Castrovilli2017}{{82}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Bera2018}{{82}{4.1}{section.4.1}}}
\citation{Spasov2000,Armentrout2008}
\citation{Braud2019}
\citation{Zamith2020threshold}
\citation{Klippenstein1992,Baer1996}
\citation{Armentrout2008}
\@writefile{brf}{\backcite{Liu2006}{{83}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Castrovilli2017}{{83}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Markush2016}{{83}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Bakker2008}{{83}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Li1992}{{83}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Bobbert2002}{{83}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Coates2018}{{83}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Carl2013}{{83}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Hofstetter2013}{{83}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Dawson1982}{{83}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Bakker2008}{{83}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Zamith2012}{{83}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Mcquinn2009}{{83}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Liu2006}{{83}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Coates2018}{{83}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Carl2013}{{83}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Hofstetter2013}{{83}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Spasov2000}{{83}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Armentrout2008}{{83}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Braud2019}{{83}{4.1}{section.4.1}}}
\@writefile{brf}{\backcite{Zamith2020threshold}{{83}{4.1}{section.4.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1.1}Principle of TCID}{83}{subsection.4.1.1}}
\newlabel{principleTCID}{{4.1.1}{83}{Principle of TCID}{subsection.4.1.1}{}}
\@writefile{brf}{\backcite{Klippenstein1992}{{83}{4.1.1}{subsection.4.1.1}}}
\@writefile{brf}{\backcite{Baer1996}{{83}{4.1.1}{subsection.4.1.1}}}
\citation{Rodgers1998,Armentrout2007}
\citation{Braud2017}
\@writefile{brf}{\backcite{Armentrout2008}{{84}{4.1.1}{subsection.4.1.1}}}
\newlabel{CIDcross}{{4.1}{84}{Principle of TCID}{equation.4.1.1}{}}
\@writefile{brf}{\backcite{Rodgers1998}{{84}{4.1.1}{equation.4.1.1}}}
\@writefile{brf}{\backcite{Armentrout2007}{{84}{4.1.1}{equation.4.1.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1.2}Experimental Setup}{84}{subsection.4.1.2}}
\newlabel{EXPsetup}{{4.1.2}{84}{Experimental Setup}{subsection.4.1.2}{}}
\@writefile{brf}{\backcite{Braud2017}{{84}{4.1.2}{figure.caption.28}}}
\citation{Chirot2006new}
\@writefile{lof}{\contentsline {figure}{\numberline {4.1}{\ignorespaces Schematic view of the experimental setup. (a) Cluster gas aggregation source. (b) Thermalization chamber. (c) First Wiley\IeC {\textendash }McLaren acceleration stage. (d) Massfilter. (e) Energy focusing. (f) Deceleration. (g) Collision cell. (h) Second Wiley\IeC {\textendash }McLaren acceleration stage. (i) Reflectron. (j) Micro-channel plate detector.}}{85}{figure.caption.28}}
\newlabel{experiment-setup}{{4.1}{85}{Schematic view of the experimental setup. (a) Cluster gas aggregation source. (b) Thermalization chamber. (c) First Wiley–McLaren acceleration stage. (d) Massfilter. (e) Energy focusing. (f) Deceleration. (g) Collision cell. (h) Second Wiley–McLaren acceleration stage. (i) Reflectron. (j) Micro-channel plate detector}{figure.caption.28}{}}
\citation{Elstner1998,Porezag1995,Seifert1996,Frenzel2004,Elstner2014,Spiegelman2020}
\citation{Simon2017,Korchagina2017,Rapacioli2018,Simon2018}
\citation{Warshel1976}
\citation{Cui2001,Iftner2014}
\citation{Kukk2015}
\citation{Kukk2015}
\citation{Simon2017}
\citation{Simon2017,Simon2018,Rapacioli2018atomic}
\@writefile{brf}{\backcite{Chirot2006new}{{86}{4.1.2}{figure.caption.28}}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.2}{\ignorespaces Schematic of the simplified experimental setup.}}{86}{figure.caption.29}}
\newlabel{exp-setup}{{4.2}{86}{Schematic of the simplified experimental setup}{figure.caption.29}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4.2}Computational Details}{86}{section.4.2}}
\newlabel{Comput_meth}{{4.2}{86}{Computational Details}{section.4.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.1}SCC-DFTB Potential}{86}{subsection.4.2.1}}
\newlabel{DFTBpotential}{{4.2.1}{86}{SCC-DFTB Potential}{subsection.4.2.1}{}}
\@writefile{brf}{\backcite{Elstner1998}{{86}{4.2.1}{subsection.4.2.1}}}
\@writefile{brf}{\backcite{Elstner2014}{{86}{4.2.1}{subsection.4.2.1}}}
\@writefile{brf}{\backcite{Porezag1995}{{86}{4.2.1}{subsection.4.2.1}}}
\@writefile{brf}{\backcite{Seifert1996}{{86}{4.2.1}{subsection.4.2.1}}}
\@writefile{brf}{\backcite{Frenzel2004}{{86}{4.2.1}{subsection.4.2.1}}}
\@writefile{brf}{\backcite{Spiegelman2020}{{86}{4.2.1}{subsection.4.2.1}}}
\@writefile{brf}{\backcite{Korchagina2017}{{86}{4.2.1}{subsection.4.2.1}}}
\@writefile{brf}{\backcite{Simon2017}{{86}{4.2.1}{subsection.4.2.1}}}
\@writefile{brf}{\backcite{Rapacioli2018}{{86}{4.2.1}{subsection.4.2.1}}}
\@writefile{brf}{\backcite{Simon2018}{{86}{4.2.1}{subsection.4.2.1}}}
\@writefile{brf}{\backcite{Warshel1976}{{86}{4.2.1}{subsection.4.2.1}}}
\@writefile{brf}{\backcite{Cui2001}{{86}{4.2.1}{subsection.4.2.1}}}
\@writefile{brf}{\backcite{Iftner2014}{{86}{4.2.1}{subsection.4.2.1}}}
\@writefile{brf}{\backcite{Kukk2015}{{86}{4.2.1}{subsection.4.2.1}}}
\citation{Dontot2019}
\citation{Nose1984,Hoover1985}
\@writefile{brf}{\backcite{Kukk2015}{{87}{4.2.1}{subsection.4.2.1}}}
\@writefile{brf}{\backcite{Simon2017}{{87}{4.2.1}{subsection.4.2.1}}}
\@writefile{brf}{\backcite{Simon2017}{{87}{4.2.1}{subsection.4.2.1}}}
\@writefile{brf}{\backcite{Simon2018}{{87}{4.2.1}{subsection.4.2.1}}}
\@writefile{brf}{\backcite{Rapacioli2018atomic}{{87}{4.2.1}{subsection.4.2.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.2}Collision Trajectories}{87}{subsection.4.2.2}}
\newlabel{makingtrajectories}{{4.2.2}{87}{Collision Trajectories}{subsection.4.2.2}{}}
\@writefile{brf}{\backcite{Dontot2019}{{87}{4.2.2}{subsection.4.2.2}}}
\@writefile{brf}{\backcite{Nose1984}{{87}{4.2.2}{subsection.4.2.2}}}
\@writefile{brf}{\backcite{Hoover1985}{{87}{4.2.2}{subsection.4.2.2}}}
\newlabel{vectorq}{{4.2}{88}{Collision Trajectories}{equation.4.2.2}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.3}{\ignorespaces Schematic of the generation of the initial inputs.}}{88}{figure.caption.30}}
\newlabel{howinputs}{{4.3}{88}{Schematic of the generation of the initial inputs}{figure.caption.30}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.3}Trajectory Analysis}{88}{subsection.4.2.3}}
\newlabel{trajecanylysis}{{4.2.3}{88}{Trajectory Analysis}{subsection.4.2.3}{}}
\citation{Braud2019}
\newlabel{integ}{{4.3}{89}{Trajectory Analysis}{equation.4.2.3}{}}
\newlabel{sec:collisionwUH}{{4.3}{89}{Dynamical Simulation of Collision-Induced Dissociation of Protonated Uracil Water Clusters}{section.4.3}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4.3}Dynamical Simulation of Collision-Induced Dissociation of Protonated Uracil Water Clusters}{89}{section.4.3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.3.1}Introduction}{89}{subsection.4.3.1}}
\@writefile{brf}{\backcite{Braud2019}{{89}{4.3.1}{subsection.4.3.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.3.2}Results and Discussion}{90}{subsection.4.3.2}}
\newlabel{resul_disc}{{4.3.2}{90}{Results and Discussion}{subsection.4.3.2}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.3.2.1}Statistical Convergence}{90}{subsubsection.4.3.2.1}}
\newlabel{convergence}{{4.3.2.1}{90}{Statistical Convergence}{subsubsection.4.3.2.1}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.4}{\ignorespaces Schematic representation of random argon orientations for the collision with the second lowest-energy isomer of cluster (H$_2$O)$_3$UH$^+$. 200 (a), 400 (b) and 600 (c) random argon orientations are generated with impact parameter being 0. ~200 orientations are generated with impact parameter being 0 and 6 (d), respectively.}}{91}{figure.caption.31}}
\newlabel{3b-sphere}{{4.4}{91}{Schematic representation of random argon orientations for the collision with the second lowest-energy isomer of cluster (H$_2$O)$_3$UH$^+$. 200 (a), 400 (b) and 600 (c) random argon orientations are generated with impact parameter being 0. ~200 orientations are generated with impact parameter being 0 and 6 (d), respectively}{figure.caption.31}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.5}{\ignorespaces Schematic representation of random argon orientations for the collision with the second lowest-energy isomer of cluster (H$_2$O)$_{12}$UH$^+$. 200 (a), 400 (b) and 600 (c) random argon orientations are generated with impact parameter being 0. ~200 orientations are generated with impact parameter value being 0 and 7 (d), respectively.}}{92}{figure.caption.32}}
\newlabel{12f-sphere}{{4.5}{92}{Schematic representation of random argon orientations for the collision with the second lowest-energy isomer of cluster (H$_2$O)$_{12}$UH$^+$. 200 (a), 400 (b) and 600 (c) random argon orientations are generated with impact parameter being 0. ~200 orientations are generated with impact parameter value being 0 and 7 (d), respectively}{figure.caption.32}{}}
\newlabel{PNUL}{{4.4}{92}{Statistical Convergence}{equation.4.3.4}{}}
\citation{Braud2019}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.3.3}Time-Dependent Proportion of Fragments}{93}{subsection.4.3.3}}
\newlabel{time}{{4.3.3}{93}{Time-Dependent Proportion of Fragments}{subsection.4.3.3}{}}
\@writefile{brf}{\backcite{Braud2019}{{93}{4.3.3}{subsection.4.3.3}}}
\@writefile{lot}{\contentsline {table}{\numberline {4.1}{\ignorespaces The proportions of $P_{NUL}$ and $\sigma _{frag}$ of first lowest-energy isomer and the isomer whose $P_{NUL}$ fits the experiment (in bold) of (H$_2$O)$_{1-5}$UH$^+$ with simulations of 200, 400, and 600 as initial conditions.\relax }}{94}{table.caption.33}}
\newlabel{tab:converge-1w-5w}{{4.1}{94}{The proportions of $P_{NUL}$ and $\sigma _{frag}$ of first lowest-energy isomer and the isomer whose $P_{NUL}$ fits the experiment (in bold) of (H$_2$O)$_{1-5}$UH$^+$ with simulations of 200, 400, and 600 as initial conditions.\relax }{table.caption.33}{}}
\@writefile{lot}{\contentsline {table}{\numberline {4.2}{\ignorespaces The proportions of $P_{NUL}$ and $\sigma _{frag}$ of first lowest-energy isomer and the isomer whose $P_{NUL}$ fits the experiment (in bold) of (H$_2$O)$_{6, 7, 11, 12}$UH$^+$ with simulations of 200, 400, and 600 as initial conditions.\relax }}{95}{table.caption.34}}
\newlabel{tab:converge-6w-12w}{{4.2}{95}{The proportions of $P_{NUL}$ and $\sigma _{frag}$ of first lowest-energy isomer and the isomer whose $P_{NUL}$ fits the experiment (in bold) of (H$_2$O)$_{6, 7, 11, 12}$UH$^+$ with simulations of 200, 400, and 600 as initial conditions.\relax }{table.caption.34}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.6}{\ignorespaces Time-dependent proportions of the main fragments obtained from the dissociation of the lowest-energy isomers of (H$_2$O)$_1$UH$^+$ (left) and (H$_2$O)$_{2}$UH$^+$ (right).}}{96}{figure.caption.35}}
\newlabel{proporEachFrag-1a2a}{{4.6}{96}{Time-dependent proportions of the main fragments obtained from the dissociation of the lowest-energy isomers of (H$_2$O)$_1$UH$^+$ (left) and (H$_2$O)$_{2}$UH$^+$ (right)}{figure.caption.35}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.3.4}Proportion of Neutral Uracil Loss and Total Fragmentation Cross Sections for Small Clusters}{96}{subsection.4.3.4}}
\newlabel{small}{{4.3.4}{96}{Proportion of Neutral Uracil Loss and Total Fragmentation Cross Sections for Small Clusters}{subsection.4.3.4}{}}
\citation{Braud2019}
\@writefile{lof}{\contentsline {figure}{\numberline {4.7}{\ignorespaces Time-dependent proportions of the main fragments obtained from the dissociation of the lowest-energy isomers of (H$_2$O)$_3$UH$^+$ (left) and (H$_2$O)$_{4}$UH$^+$ (right). Bottom panels correspond to a zoom over the lower proportions.}}{97}{figure.caption.36}}
\newlabel{proporEachFrag-3a4a-zoom}{{4.7}{97}{Time-dependent proportions of the main fragments obtained from the dissociation of the lowest-energy isomers of (H$_2$O)$_3$UH$^+$ (left) and (H$_2$O)$_{4}$UH$^+$ (right). Bottom panels correspond to a zoom over the lower proportions}{figure.caption.36}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.8}{\ignorespaces Time-dependent proportions of the main fragments obtained from the dissociation of the lowest-energy isomers of (H$_2$O)$_5$UH$^+$ (left) and (H$_2$O)$_{6}$UH$^+$ (right). Bottom panels correspond to a zoom over the lower proportions.}}{98}{figure.caption.37}}
\newlabel{proporEachFrag-5a6a-zoom}{{4.8}{98}{Time-dependent proportions of the main fragments obtained from the dissociation of the lowest-energy isomers of (H$_2$O)$_5$UH$^+$ (left) and (H$_2$O)$_{6}$UH$^+$ (right). Bottom panels correspond to a zoom over the lower proportions}{figure.caption.37}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.9}{\ignorespaces Time-dependent proportions of the main fragments obtained from the dissociation of the lowest-energy isomer of (H$_2$O)$_{11}$UH$^+$. Right panel corresponds to a zoom over the lower proportions.}}{98}{figure.caption.38}}
\newlabel{proporEachFrag-11a-zoom}{{4.9}{98}{Time-dependent proportions of the main fragments obtained from the dissociation of the lowest-energy isomer of (H$_2$O)$_{11}$UH$^+$. Right panel corresponds to a zoom over the lower proportions}{figure.caption.38}{}}
\@writefile{lot}{\contentsline {table}{\numberline {4.3}{\ignorespaces Relative energy $E_{rel.}$ (in kcal.mol$^{-1}$) at the MP2/Def2TZVP level, LEP, $P_{PU}$ (in \%), $P_{NUL}$ (in \%), $\sigma _{frag}$ (in \r A$^2$) of the considered low-energy isomers of (H$_2$O)$_{1-7, 11, 12}$UH$^+$ clusters. Isomers which $P_{NUL}$ fit best to the experimental value are indicated in bold. $P_{{NUL}_{exp}}$ and $\sigma _{{frag}_{exp}}$ are the experimental values for $P_{NUL}$ and $\sigma _{frag}$, respectively. For (H$_2$O)$_{12}$UH$^+$, experimental values were obtained for collision with Ne, whereas all other theoretical and experimental data are for collision with Ar.\relax }}{99}{table.caption.41}}
\newlabel{tab:full}{{4.3}{99}{Relative energy $E_{rel.}$ (in kcal.mol$^{-1}$) at the MP2/Def2TZVP level, LEP, $P_{PU}$ (in \%), $P_{NUL}$ (in \%), $\sigma _{frag}$ (in \AA $^2$) of the considered low-energy isomers of (H$_2$O)$_{1-7, 11, 12}$UH$^+$ clusters. Isomers which $P_{NUL}$ fit best to the experimental value are indicated in bold. $P_{{NUL}_{exp}}$ and $\sigma _{{frag}_{exp}}$ are the experimental values for $P_{NUL}$ and $\sigma _{frag}$, respectively. For (H$_2$O)$_{12}$UH$^+$, experimental values were obtained for collision with Ne, whereas all other theoretical and experimental data are for collision with Ar.\relax }{table.caption.41}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.10}{\ignorespaces Time-dependent proportions of the main fragments obtained from the dissociation of the lowest-energy isomers of (H$_2$O)$_7$UH$^+$ (left) and (H$_2$O)$_{12}$UH$^+$ (right). Bottom panels correspond to a zoom over the lower proportions.}}{100}{figure.caption.39}}
\newlabel{proporEachFrag-7a12a-zoom}{{4.10}{100}{Time-dependent proportions of the main fragments obtained from the dissociation of the lowest-energy isomers of (H$_2$O)$_7$UH$^+$ (left) and (H$_2$O)$_{12}$UH$^+$ (right). Bottom panels correspond to a zoom over the lower proportions}{figure.caption.39}{}}
\@writefile{brf}{\backcite{Braud2019}{{100}{4.3.4}{table.caption.41}}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.11}{\ignorespaces Time-dependent proportions of the main fragments obtained from the dissociation of the the third lowest-energy isomer of (H$_2$O)$_7$UH$^+$ (left) and the third lowest-energy isomer (H$_2$O)$_{12}$UH$^+$ (right). Bottom panels correspond to a zoom over the lower proportions.}}{101}{figure.caption.40}}
\newlabel{proporEachFrag-7d12c-zoom}{{4.11}{101}{Time-dependent proportions of the main fragments obtained from the dissociation of the the third lowest-energy isomer of (H$_2$O)$_7$UH$^+$ (left) and the third lowest-energy isomer (H$_2$O)$_{12}$UH$^+$ (right). Bottom panels correspond to a zoom over the lower proportions}{figure.caption.40}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.12}{\ignorespaces Selected low-energy configurations of (H$_2$O)$_{1-3}$UH$^+$. Relative energies at the MP2/Def2TZVP level are in kcal.mol$^{-1}$.}}{102}{figure.caption.42}}
\newlabel{fig-1a-3b}{{4.12}{102}{Selected low-energy configurations of (H$_2$O)$_{1-3}$UH$^+$. Relative energies at the MP2/Def2TZVP level are in kcal.mol$^{-1}$}{figure.caption.42}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.13}{\ignorespaces Selected low-energy configurations of (H$_2$O)$_{4-5}$UH$^+$. Relative energies at the MP2/Def2TZVP level are in kcal.mol$^{-1}$.}}{103}{figure.caption.43}}
\newlabel{fig-4a-5d}{{4.13}{103}{Selected low-energy configurations of (H$_2$O)$_{4-5}$UH$^+$. Relative energies at the MP2/Def2TZVP level are in kcal.mol$^{-1}$}{figure.caption.43}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.14}{\ignorespaces Selected low-energy configurations of (H$_2$O)$_{6}$UH$^+$. Relative energies at the MP2/Def2TZVP level are in kcal.mol$^{-1}$.}}{104}{figure.caption.44}}
\newlabel{fig-6a-6f}{{4.14}{104}{Selected low-energy configurations of (H$_2$O)$_{6}$UH$^+$. Relative energies at the MP2/Def2TZVP level are in kcal.mol$^{-1}$}{figure.caption.44}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.15}{\ignorespaces Selected low-energy configurations of (H$_2$O)$_{7}$UH$^+$. Relative energies at the MP2/Def2TZVP level are in kcal.mol$^{-1}$.}}{105}{figure.caption.45}}
\newlabel{fig-7a-7d}{{4.15}{105}{Selected low-energy configurations of (H$_2$O)$_{7}$UH$^+$. Relative energies at the MP2/Def2TZVP level are in kcal.mol$^{-1}$}{figure.caption.45}{}}
\citation{Braud2019}
\@writefile{lof}{\contentsline {figure}{\numberline {4.16}{\ignorespaces Theoretical (green and blue lines) and experimental (red line) $P_{NUL}$ values for the (H$_2$O)$_{1-7, 11, 12}$UH$^+$ clusters. Theory 1 (green line) is obtained from the isomers which $P_{NUL}$ matches best to the experimental data while Theory 2 (blue line) is obtained from lowest-energy isomers.}}{106}{figure.caption.46}}
\newlabel{neutralUloss-Ne-Ar}{{4.16}{106}{Theoretical (green and blue lines) and experimental (red line) $P_{NUL}$ values for the (H$_2$O)$_{1-7, 11, 12}$UH$^+$ clusters. Theory 1 (green line) is obtained from the isomers which $P_{NUL}$ matches best to the experimental data while Theory 2 (blue line) is obtained from lowest-energy isomers}{figure.caption.46}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.3.5}Behaviour at Larger Sizes, the Cases of (H$_2$O)$_{11, 12}$UH$^+$}{106}{subsection.4.3.5}}
\newlabel{large}{{4.3.5}{106}{Behaviour at Larger Sizes, the Cases of (H$_2$O)$_{11, 12}$UH$^+$}{subsection.4.3.5}{}}
\@writefile{brf}{\backcite{Braud2019}{{106}{4.3.5}{subsection.4.3.5}}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.17}{\ignorespaces Theoretical (green and blue lines) and experimental (red line) $\sigma _{frag}$ values for the (H$_2$O)$_{1-7, 11, 12}$UH$^+$ clusters. Theory 1 (green line) is obtained from the isomers which $P_{NUL}$ matches best to the experimental data while Theory 2 (blue line) is obtained from lowest-energy isomers.}}{107}{figure.caption.47}}
\newlabel{cross-section-Ne-Ar}{{4.17}{107}{Theoretical (green and blue lines) and experimental (red line) $\sigma _{frag}$ values for the (H$_2$O)$_{1-7, 11, 12}$UH$^+$ clusters. Theory 1 (green line) is obtained from the isomers which $P_{NUL}$ matches best to the experimental data while Theory 2 (blue line) is obtained from lowest-energy isomers}{figure.caption.47}{}}
\citation{Braud2019}
\@writefile{lof}{\contentsline {figure}{\numberline {4.18}{\ignorespaces Selected low-energy configurations of (H$_2$O)$_{11}$UH$^+$. Relative energies at the MP2/Def2TZVP level are in kcal.mol$^{-1}$.}}{109}{figure.caption.48}}
\newlabel{fig-11a-f}{{4.18}{109}{Selected low-energy configurations of (H$_2$O)$_{11}$UH$^+$. Relative energies at the MP2/Def2TZVP level are in kcal.mol$^{-1}$}{figure.caption.48}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.19}{\ignorespaces Selected low-energy configurations of (H$_2$O)$_{12}$UH$^+$. Relative energies at the MP2/Def2TZVP level are in kcal.mol$^{-1}$.}}{109}{figure.caption.49}}
\newlabel{fig-12a-f}{{4.19}{109}{Selected low-energy configurations of (H$_2$O)$_{12}$UH$^+$. Relative energies at the MP2/Def2TZVP level are in kcal.mol$^{-1}$}{figure.caption.49}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.3.6}Mass Spectra of Fragments with Excess Proton}{110}{subsection.4.3.6}}
\newlabel{mass-spectra}{{4.3.6}{110}{Mass Spectra of Fragments with Excess Proton}{subsection.4.3.6}{}}
\@writefile{brf}{\backcite{Braud2019}{{110}{4.3.6}{subsection.4.3.6}}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.20}{\ignorespaces Simulated mass spectra (positive area) of the charged fragments after 15~ps simulation time (fragments (H$_2$O)$_n$H$^+$ in red and (H$_2$O)$_n$UH$^+$ in blue for argon; (H$_2$O)$_n$H$^+$ in pink and (H$_2$O)$_n$UH$^+$ in green for neon) from isomers (a) 1a, (b) 2b, (c) 3b, (d) 4b. The counterparts in experiment are plotted (negative area).}}{110}{figure.caption.50}}
\newlabel{MS-BR-1w-4w-Ne-Ar-branch}{{4.20}{110}{Simulated mass spectra (positive area) of the charged fragments after 15~ps simulation time (fragments (H$_2$O)$_n$H$^+$ in red and (H$_2$O)$_n$UH$^+$ in blue for argon; (H$_2$O)$_n$H$^+$ in pink and (H$_2$O)$_n$UH$^+$ in green for neon) from isomers (a) 1a, (b) 2b, (c) 3b, (d) 4b. The counterparts in experiment are plotted (negative area)}{figure.caption.50}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.21}{\ignorespaces Simulated mass spectra (positive area) of the charged fragments after 15~ps simulation time (fragments (H$_2$O)$_n$H$^+$ in red and (H$_2$O)$_n$UH$^+$ in blue) from isomers (e) 5d, (f) 6f, (g) 7d, and (h) 11d. The counterparts in experiment are plotted (negative area).}}{111}{figure.caption.51}}
\newlabel{MS-BR-5w-11w-Ne-Ar-branch}{{4.21}{111}{Simulated mass spectra (positive area) of the charged fragments after 15~ps simulation time (fragments (H$_2$O)$_n$H$^+$ in red and (H$_2$O)$_n$UH$^+$ in blue) from isomers (e) 5d, (f) 6f, (g) 7d, and (h) 11d. The counterparts in experiment are plotted (negative area)}{figure.caption.51}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.22}{\ignorespaces Simulated mass spectra (positive area) of the charged fragments after 15~ps simulation time (fragments (H$_2$O)$_n$H$^+$ in red and (H$_2$O)$_n$UH$^+$ in blue) from isomers 12c. The counterparts in experiment obtained for collision with neon are plotted in negative area (H$_2$O)$_n$H$^+$ in pink and (H$_2$O)$_n$UH$^+$ in green).}}{112}{figure.caption.52}}
\newlabel{MS-BR-12w-Ne-branch}{{4.22}{112}{Simulated mass spectra (positive area) of the charged fragments after 15~ps simulation time (fragments (H$_2$O)$_n$H$^+$ in red and (H$_2$O)$_n$UH$^+$ in blue) from isomers 12c. The counterparts in experiment obtained for collision with neon are plotted in negative area (H$_2$O)$_n$H$^+$ in pink and (H$_2$O)$_n$UH$^+$ in green)}{figure.caption.52}{}}
\@writefile{lot}{\contentsline {table}{\numberline {4.4}{\ignorespaces Energies of different (H$_2$O)$_6$UH$^+$ fragments selected from the dissociation of 7d at SCC-DFTB level, and the lowest energies (H$_2$O)$_5$UH$^+$ and (H$_2$O) at SCC-DFTB level. The relative energy $\Delta E$ = $E_{(H_2O)_6UH^+}$ -($E_{(H_2O)_5UH^+}$ +$ E_{H_2O}$). All energies here are given in eV.\relax }}{113}{table.caption.53}}
\newlabel{tab:fragenergy}{{4.4}{113}{Energies of different (H$_2$O)$_6$UH$^+$ fragments selected from the dissociation of 7d at SCC-DFTB level, and the lowest energies (H$_2$O)$_5$UH$^+$ and (H$_2$O) at SCC-DFTB level. The relative energy $\Delta E$ = $E_{(H_2O)_6UH^+}$ -($E_{(H_2O)_5UH^+}$ +$ E_{H_2O}$). All energies here are given in eV.\relax }{table.caption.53}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.3.7}Conclusions about CID of (H$_2$O)$_{n}$UH$^+$}{113}{subsection.4.3.7}}
\newlabel{Concl}{{4.3.7}{113}{Conclusions about CID of (H$_2$O)$_{n}$UH$^+$}{subsection.4.3.7}{}}
\citation{Chung2011,Saggese2015,Eaves2015,Mao2017,Wang2018}
\citation{Kyrtopoulos2001,Farmer2003}
\citation{Aumaitre2019}
\citation{Tielens2008}
\citation{Leger1984,Allamandola1985}
\citation{Rapacioli2005,Berne2008}
\citation{Eschenbach1998,Schmidt2006,Goulart2017,Wang2018,Lei2019}
\citation{Joblin2017}
\citation{Roser2015,Lemmens2019}
\citation{Schmidt2006,Holm2010,Gatchell2015,Joblin2017,Gatchell2017,Zamith2019thermal}
\citation{Zamith2019thermal}
\citation{Delaunay2015}
\citation{Zhen2018}
\citation{Chen2018}
\@writefile{toc}{\contentsline {section}{\numberline {4.4}Dynamical Simulation of Collision-Induced Dissociation for Pyrene Dimer Cation}{115}{section.4.4}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.4.1}Introduction}{115}{subsection.4.4.1}}
\@writefile{brf}{\backcite{Eaves2015}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Chung2011}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Saggese2015}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Mao2017}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Wang2018}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Kyrtopoulos2001}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Farmer2003}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Aumaitre2019}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Tielens2008}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Leger1984}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Allamandola1985}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Rapacioli2005}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Berne2008}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Schmidt2006}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Wang2018}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Eschenbach1998}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Goulart2017}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Lei2019}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Joblin2017}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Roser2015}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Lemmens2019}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Joblin2017}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Holm2010}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Schmidt2006}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Gatchell2015}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Gatchell2017}{{115}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Zamith2019thermal}{{115}{4.4.1}{subsection.4.4.1}}}
\citation{Piacenza2005,Birer2015}
\citation{Zhao2008truhlar,Rapacioli2009corr,Mao2017,Bowal2019}
\citation{Ricca2013}
\citation{Grafenstein2009}
\citation{Rapacioli2009}
\citation{Joblin2017}
\citation{Dontot2019}
\citation{Dontot2016}
\citation{Dontot2020}
\citation{Porezag1995,Seifert1996,Elstner1998,Spiegelman2020}
\citation{Rapacioli2011}
\citation{Gatchell2016,Gatchell2016knockout}
\citation{Zamith2020threshold}
\citation{Zamith2019thermal}
\@writefile{brf}{\backcite{Zamith2019thermal}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Delaunay2015}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Zhen2018}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Chen2018}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Piacenza2005}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Birer2015}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Rapacioli2009corr}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Mao2017}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Zhao2008truhlar}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Bowal2019}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Ricca2013}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Grafenstein2009}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Rapacioli2009}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Joblin2017}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Dontot2019}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Dontot2016}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Dontot2020}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Elstner1998}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Porezag1995}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Seifert1996}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Spiegelman2020}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Rapacioli2011}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Gatchell2016}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Gatchell2016knockout}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Zamith2020threshold}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{brf}{\backcite{Zamith2019thermal}{{116}{4.4.1}{subsection.4.4.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.4.2}Calculation of Energies}{117}{subsection.4.4.2}}
\newlabel{Eparti}{{4.5}{117}{Calculation of Energies}{equation.4.4.5}{}}
\newlabel{Eintra}{{4.6}{118}{Calculation of Energies}{equation.4.4.6}{}}
\newlabel{Einter}{{4.7}{118}{Calculation of Energies}{equation.4.4.7}{}}
\newlabel{Erotation}{{4.9}{118}{Calculation of Energies}{equation.4.4.9}{}}
\citation{Zamith2020threshold}
\citation{Levine1987}
\citation{Zamith2020threshold}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.4.3}Simulation of the Experimental TOFMS}{119}{subsection.4.4.3}}
\@writefile{brf}{\backcite{Zamith2020threshold}{{119}{4.4.3}{subsection.4.4.3}}}
\@writefile{brf}{\backcite{Levine1987}{{119}{4.4.3}{subsection.4.4.3}}}
\@writefile{brf}{\backcite{Zamith2020threshold}{{119}{4.4.3}{subsection.4.4.3}}}
\citation{Dontot2019,Zamith2020threshold}
\@writefile{lof}{\contentsline {figure}{\numberline {4.23}{\ignorespaces Principle of MD+PST.}}{120}{figure.caption.54}}
\newlabel{MDPST}{{4.23}{120}{Principle of MD+PST}{figure.caption.54}{}}
\newlabel{sec:results}{{4.4.4}{121}{Results and Discussion}{subsection.4.4.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.4.4}Results and Discussion}{121}{subsection.4.4.4}}
\@writefile{brf}{\backcite{Zamith2020threshold}{{121}{4.4.4}{subsection.4.4.4}}}
\@writefile{brf}{\backcite{Dontot2019}{{121}{4.4.4}{subsection.4.4.4}}}
\newlabel{sec:MS}{{4.4.4.1}{121}{TOFMS Comparison}{subsubsection.4.4.4.1}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.4.4.1}TOFMS Comparison}{121}{subsubsection.4.4.4.1}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.24}{\ignorespaces Normalized time of flight mass spectra of the parent pyrene dimer cation (a), and the pyrene fragment Py$^+$ (b) resulting from the collision of Py$_2^+$ with argon at a center of mass collision energy of 17.5~eV. The black line is for the experimental result whereas red and green curves are the MD+PST and PST model results. The blue curve is the PST subcontribution of the MD+PST model.}}{121}{figure.caption.55}}
\newlabel{expTOF}{{4.24}{121}{Normalized time of flight mass spectra of the parent pyrene dimer cation (a), and the pyrene fragment Py$^+$ (b) resulting from the collision of Py$_2^+$ with argon at a center of mass collision energy of 17.5~eV. The black line is for the experimental result whereas red and green curves are the MD+PST and PST model results. The blue curve is the PST subcontribution of the MD+PST model}{figure.caption.55}{}}
\newlabel{sec:MDanalysis}{{4.4.4.2}{122}{Molecular Dynamics Analysis}{subsubsection.4.4.4.2}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.4.4.2}Molecular Dynamics Analysis}{122}{subsubsection.4.4.4.2}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.25}{\ignorespaces Snapshots for two different molecular dynamics trajectories. Top and bottom: trajectories with impact parameter of 3.5~\r A{} and a collision energy of 17.5~eV, leading to dissociation and non-dissociation (top and bottom, respectively).}}{123}{figure.caption.56}}
\newlabel{collisions}{{4.25}{123}{Snapshots for two different molecular dynamics trajectories. Top and bottom: trajectories with impact parameter of 3.5~\AA {} and a collision energy of 17.5~eV, leading to dissociation and non-dissociation (top and bottom, respectively)}{figure.caption.56}{}}
\citation{Chen2014,Gatchell2016knockout}
\@writefile{lof}{\contentsline {figure}{\numberline {4.26}{\ignorespaces Distribution of transferred energy in rovibrational modes $\Delta E_{int}^{Py_2}$ for trajectories leading to dissociation at the end of MD (center of mass collision energy of 17.5~eV). The dashed line shows the distribution of transferred energy used in the LOC model.}}{125}{figure.caption.57}}
\newlabel{distriPerc-Etf-175eV-d-bin03}{{4.26}{125}{Distribution of transferred energy in rovibrational modes $\Delta E_{int}^{Py_2}$ for trajectories leading to dissociation at the end of MD (center of mass collision energy of 17.5~eV). The dashed line shows the distribution of transferred energy used in the LOC model}{figure.caption.57}{}}
\@writefile{brf}{\backcite{Gatchell2016knockout}{{125}{4.4.4.2}{figure.caption.58}}}
\@writefile{brf}{\backcite{Chen2014}{{125}{4.4.4.2}{figure.caption.58}}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.27}{\ignorespaces Snapshots for molecular dynamics trajectory with impact parameter of 0.5~\r A{} and a collision energy of 27.5 eV leading to intramolecular fragmentation.}}{126}{figure.caption.58}}
\newlabel{fragmentation}{{4.27}{126}{Snapshots for molecular dynamics trajectory with impact parameter of 0.5~\AA {} and a collision energy of 27.5 eV leading to intramolecular fragmentation}{figure.caption.58}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.28}{\ignorespaces Opacity curves as a function of the impact parameter $b$ for several selected center of mass collision energies.}}{126}{figure.caption.59}}
\newlabel{opacitycurves}{{4.28}{126}{Opacity curves as a function of the impact parameter $b$ for several selected center of mass collision energies}{figure.caption.59}{}}
\citation{Zamith2020threshold}
\citation{Dontot2019,Zamith2020threshold}
\@writefile{brf}{\backcite{Zamith2020threshold}{{127}{4.4.4.2}{figure.caption.59}}}
\@writefile{brf}{\backcite{Zamith2020threshold}{{127}{4.4.4.2}{equation.4.4.12}}}
\@writefile{brf}{\backcite{Dontot2019}{{127}{4.4.4.2}{equation.4.4.12}}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.29}{\ignorespaces Dissociation cross sections of Py$_2^+$ after collision with argon as a function of center of mass collision energy for the short (MD), experimental (MD+PST) and infinite timescales. Cross sections resulting from the LOC model are also plotted. $\sigma _\mathrm {MD}$ (0.1) denotes the dissociation cross section for short (MD) timescale with a time step of 0.1 fs.}}{128}{figure.caption.60}}
\newlabel{cross-section}{{4.29}{128}{Dissociation cross sections of Py$_2^+$ after collision with argon as a function of center of mass collision energy for the short (MD), experimental (MD+PST) and infinite timescales. Cross sections resulting from the LOC model are also plotted. $\sigma _\mathrm {MD}$ (0.1) denotes the dissociation cross section for short (MD) timescale with a time step of 0.1 fs}{figure.caption.60}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.30}{\ignorespaces At the end of the MD collision simulations with a time step of 0.1 and 0.5 fs, the total transferred energy $\Delta E_{int}^{Py_2}$ to the rovibrational modes or restricted to the sole dissociated ($\Delta E_{int-d}^{Py_2}$) or undissociated ($\Delta E_{int-ud}^{Py_2}$) pyrene dimers as a function of collision energy. The transeferred energy to the monomers rovibrational modes for the dissociated dimers $\Delta E_{int-d}^{Py^1+Py^2}$ is also plotted.}}{129}{figure.caption.61}}
\newlabel{transferredE-Ar-300}{{4.30}{129}{At the end of the MD collision simulations with a time step of 0.1 and 0.5 fs, the total transferred energy $\Delta E_{int}^{Py_2}$ to the rovibrational modes or restricted to the sole dissociated ($\Delta E_{int-d}^{Py_2}$) or undissociated ($\Delta E_{int-ud}^{Py_2}$) pyrene dimers as a function of collision energy. The transeferred energy to the monomers rovibrational modes for the dissociated dimers $\Delta E_{int-d}^{Py^1+Py^2}$ is also plotted}{figure.caption.61}{}}
\@writefile{lot}{\contentsline {table}{\numberline {4.5}{\ignorespaces The kinetic energy partition after the collision of pyrene dimer with argon at different collision energies $E_{col}$. All energies are in eV.\relax }}{130}{table.caption.62}}
\newlabel{tab:table1}{{4.5}{130}{The kinetic energy partition after the collision of pyrene dimer with argon at different collision energies $E_{col}$. All energies are in eV.\relax }{table.caption.62}{}}
\newlabel{separately}{{4.13}{130}{Molecular Dynamics Analysis}{equation.4.4.13}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.31}{\ignorespaces Mean kinetic energy partition at the end of the MD simulations.}}{131}{figure.caption.63}}
\newlabel{Epartition-Ar-300-SP}{{4.31}{131}{Mean kinetic energy partition at the end of the MD simulations}{figure.caption.63}{}}
\@writefile{lot}{\contentsline {table}{\numberline {4.6}{\ignorespaces The kinetic energy partition and cross section at the end of MD simulations with time step being 0.1 and 0.5 at different collision energies of 20 and 25. All energies are in eV. Time step ($Tstep$) is in fs. Cross section $\sigma _{_{MD}}$ is in ~\r A.\relax }}{132}{table.caption.64}}
\newlabel{tab:table2}{{4.6}{132}{The kinetic energy partition and cross section at the end of MD simulations with time step being 0.1 and 0.5 at different collision energies of 20 and 25. All energies are in eV. Time step ($Tstep$) is in fs. Cross section $\sigma _{_{MD}}$ is in ~\AA .\relax }{table.caption.64}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.32}{\ignorespaces Mean kinetic energy partition at the end of the MD simulations with time step being 0.5 fs at the center of mass collision energy from 2.5 to 25 eV. The mean kinetic energy partition with time step being 0.1 fs at center of mass collision energies of 20 and 25 eV are plotted with filled round circles.}}{132}{figure.caption.65}}
\newlabel{Epartition-Ar-300-Tstep-01}{{4.32}{132}{Mean kinetic energy partition at the end of the MD simulations with time step being 0.5 fs at the center of mass collision energy from 2.5 to 25 eV. The mean kinetic energy partition with time step being 0.1 fs at center of mass collision energies of 20 and 25 eV are plotted with filled round circles}{figure.caption.65}{}}
\citation{Dontot2020}
\@writefile{lof}{\contentsline {figure}{\numberline {4.33}{\ignorespaces Kinetic energy proportion after collision of Py$_2^+$ with argon as a function of collision energy.}}{133}{figure.caption.66}}
\newlabel{prot-Ar-300}{{4.33}{133}{Kinetic energy proportion after collision of Py$_2^+$ with argon as a function of collision energy}{figure.caption.66}{}}
\@writefile{brf}{\backcite{Dontot2020}{{133}{4.4.4.2}{figure.caption.67}}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.34}{\ignorespaces Kinetic energy partition for dissociated (-d) and undissociated (-ud) trajectories at the end of the MD simulation as a function of collision energy.}}{134}{figure.caption.67}}
\newlabel{Epartition-Ar-300-d-ud}{{4.34}{134}{Kinetic energy partition for dissociated (-d) and undissociated (-ud) trajectories at the end of the MD simulation as a function of collision energy}{figure.caption.67}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.35}{\ignorespaces Timescales, as a function of center of mass collision energy, for argon to travel across some typical distances: a carbon-carbon bond (green), a carbon-hydrogen bond (purple) or the largest axis of the pyrene molecule (blue).}}{135}{figure.caption.68}}
\newlabel{figuretimescale}{{4.35}{135}{Timescales, as a function of center of mass collision energy, for argon to travel across some typical distances: a carbon-carbon bond (green), a carbon-hydrogen bond (purple) or the largest axis of the pyrene molecule (blue)}{figure.caption.68}{}}
\newlabel{kineticT}{{4.14}{135}{Molecular Dynamics Analysis}{equation.4.4.14}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.36}{\ignorespaces Instantaneous kinetic temperatures as a function of time for intra and intermolecular modes of the pyrene dimer at a collision energy of 22.5~eV. Impact parameters $b$ are (a) 2, (b) 3, (c) 0, (d) 2.5, (e) 2, and (f) 2~\r A{}. In cases (a) and (b) dissociation takes place whereas in the other cases the dimer remains undissociated at the end of the MD simulation. In (c) to (f) the lower panel is a vertical zoom of the corresponding intramolecular parts in upper panel.}}{136}{figure.caption.69}}
\newlabel{T-time-zoom_abcdef}{{4.36}{136}{Instantaneous kinetic temperatures as a function of time for intra and intermolecular modes of the pyrene dimer at a collision energy of 22.5~eV. Impact parameters $b$ are (a) 2, (b) 3, (c) 0, (d) 2.5, (e) 2, and (f) 2~\AA {}. In cases (a) and (b) dissociation takes place whereas in the other cases the dimer remains undissociated at the end of the MD simulation. In (c) to (f) the lower panel is a vertical zoom of the corresponding intramolecular parts in upper panel}{figure.caption.69}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.37}{\ignorespaces Instantaneous kinetic energies as a function of time for intra and intermolecular modes of the pyrene dimer at a collision energy of 22.5 eV. Impact parameters $b$ are (a) 2, (b) 3, (c) 0, (d) 2.5, (e) 2, and (f) 2 \r A{}. In cases (a) and (b), dissociation takes place whereas in the other cases the dimer remains undissociated at the end of the MD simulation.}}{137}{figure.caption.70}}
\newlabel{E-time-abcdef}{{4.37}{137}{Instantaneous kinetic energies as a function of time for intra and intermolecular modes of the pyrene dimer at a collision energy of 22.5 eV. Impact parameters $b$ are (a) 2, (b) 3, (c) 0, (d) 2.5, (e) 2, and (f) 2 \AA {}. In cases (a) and (b), dissociation takes place whereas in the other cases the dimer remains undissociated at the end of the MD simulation}{figure.caption.70}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.4.5}Conclusions about CID of Py$_2^+$}{138}{subsection.4.4.5}}
\citation{Chen2014,Gatchell2016knockout}
\@writefile{brf}{\backcite{Gatchell2016knockout}{{139}{4.4.5}{subsection.4.4.5}}}
\@writefile{brf}{\backcite{Chen2014}{{139}{4.4.5}{subsection.4.4.5}}}
\FN@pp@footnotehinttrue
\@setckpt{4/collision}{
\setcounter{page}{141}
\setcounter{equation}{14}
\setcounter{enumi}{5}
\setcounter{enumii}{0}
\setcounter{enumiii}{0}
\setcounter{enumiv}{0}
\setcounter{footnote}{0}
\setcounter{mpfootnote}{0}
\setcounter{part}{0}
\setcounter{chapter}{4}
\setcounter{section}{4}
\setcounter{subsection}{5}
\setcounter{subsubsection}{0}
\setcounter{paragraph}{0}
\setcounter{subparagraph}{0}
\setcounter{figure}{37}
\setcounter{table}{6}
\setcounter{ContinuedFloat}{0}
\setcounter{pp@next@reset}{1}
\setcounter{@fnserial}{0}
\setcounter{NAT@ctr}{0}
\setcounter{Item}{5}
\setcounter{Hfootnote}{0}
\setcounter{bookmark@seq@number}{59}
\setcounter{parentequation}{0}
\setcounter{section@level}{2}
}

0
thesis/4/collision.bbl Normal file
View File

47
thesis/4/collision.blg Normal file
View File

@ -0,0 +1,47 @@
This is BibTeX, Version 0.99d (TeX Live 2019)
Capacity: max_strings=100000, hash_size=100000, hash_prime=85009
The top-level auxiliary file: collision.aux
I found no \bibdata command---while reading file collision.aux
I found no \bibstyle command---while reading file collision.aux
You've used 141 entries,
0 wiz_defined-function locations,
364 strings with 3525 characters,
and the built_in function-call counts, 0 in all, are:
= -- 0
> -- 0
< -- 0
+ -- 0
- -- 0
* -- 0
:= -- 0
add.period$ -- 0
call.type$ -- 0
change.case$ -- 0
chr.to.int$ -- 0
cite$ -- 0
duplicate$ -- 0
empty$ -- 0
format.name$ -- 0
if$ -- 0
int.to.chr$ -- 0
int.to.str$ -- 0
missing$ -- 0
newline$ -- 0
num.names$ -- 0
pop$ -- 0
preamble$ -- 0
purify$ -- 0
quote$ -- 0
skip$ -- 0
stack$ -- 0
substring$ -- 0
swap$ -- 0
text.length$ -- 0
text.prefix$ -- 0
top$ -- 0
type$ -- 0
warning$ -- 0
while$ -- 0
width$ -- 0
write$ -- 0
(There were 2 error messages)

93130
thesis/4/collision.log Normal file
View File

File diff suppressed because it is too large Load Diff

860
thesis/4/collision.tex Normal file
View File

@ -0,0 +1,860 @@
% this file is called up by thesis.tex
% content in this file will be fed into the main document
%: ----------------------- name of chapter -------------------------
%\newcommand{\boldm}[1] {\mathversion{bold}#1\mathversion{normal}}
\ifpdf
\graphicspath{{4/figures/PNG/}{4/figures/PDF/}{4/figures/}}
\else
\graphicspath{{4/figures/EPS/}{4/figures/}}
\fi
\chapter{Dynamical Simulation of Collision-Induced Dissociation} \label{chap:collision}
This \textbf{fourth chapter of this thesis} merges two independent studies relating to the dynamical simulation of the
collision-induced dissociation of (H$_2$O)$_n$UH$^+$ clusters and pyrene dimer cation Py$_2^+$. The two studies
in this chapter share the same methodology to generate the collision trajectories for the collision of argon with (H$_2$O)$_n$UH$^+$
and Py$_2^+$. The collision process of the two studies involves dynamical simulations carried out at a QM/MM level where argon
is treated as a polarisable MM particle and the lowest-energy targets (H$_2$O)$_n$UH$^+$ and Py$_2^+$ are treated
as SCC-DFTB level. The dynamical simulations performed in these two studies allow to visualise the collision trajectories
from which it is possible to analyse in details a number of properties. The theoretical results are compared with the CID
experimental results conducted on the same systems, \textit{i.e.} (H$_2$O)$_n$UH$^+$ and Py$_2^+$, by S. Zamith and J.-M. l’Hermite,
which facilitates their interpretation and complete the CID experiments.
\section{Experimental Methods} \label{exp_cid}
The stability of cluster can be investigated from dissociation experiments. Clusters can be dissociated in electric field, magnetic field, high pressure environment, or by heating (such as absorption of photons) or colliding with energetic particles and so on.
For instance, the sodium cluster ions and lithium cluster cation were dissociated with a pulsed UV laser source.\cite{Brechignac1989, Brechignac1994}
Gaseous hydrated trivalent metal ions were dissociated using blackbody infrared radiative dissociation (BIRD).\cite{Wong2004, Bush2008}
The collision between cluster and high or low energetic particles at different pressure also have been investigated.
Collisions between the high energetic projectile ions (such as 3 keV Ar$^+$, 22.5 keV He$^{2+}$) and neutral targets were investigated by Gatchell and Holm.\cite{Holm2010, Gatchell2014, Gatchell2017}
Collisions between clusters and projectile have been also explored at low collision energy, which allows for the derivation of dissociation energies and the thermal evaporation and stability of clusters. \cite{Boering1992, Wells2005, Zamith2019thermal}
By colliding a molecule, or a molecular aggregate, with a non-reactive rare gas atom (neon, argon) or a small molecule such as H$_2$O or N$_2$, it is possible to monitor the parent ions and collision products by use, for instance, of tandem mass spectrometry (MS/MS).\cite{Ma1997, Chowdhury2009} The resulting mass spectra provide a wealth of information about the structure of the parent and product ions from which one can infer, for instance, dissociation mechanisms \cite{Nelson1994, Molina2015} or bond and hydration enthalpies \cite{Carl2007}.
The overall process of collisional activation followed by dissociation/fragmentation is commonly referred to as the collision‐induced dissociation (CID) that is also named collisionally activated dissociation (CAD). CID is a mass spectrometry technique to induce dissociation/fragmentation of selected ions in the gas phase, which is one of standard methods for the determination of dissociation/fragmentation pathways. \cite{Sleno2004ion, Wells2005}
The CID technique consists of accelerating a given ion into a collision gas thereby the ion getting energy and inducing fragmentation. The produced ionic fragments are then mass analyzed, yielding essentially a mass spectrum.\cite{Cody1982}
The CID technique has been applied in different context.
Higher-energy C-trap dissociation is a CID technique specific to the orbitrap mass spectrometer in which dissociation/fragmentation occurs outside the trap \cite{Olsen2007higher, Hart2011}
Sustained off-resonance irradiation collision-induced dissociation (SORI-CID) is a CID technique used in Fourier transform ion cyclotron resonance mass spectrometry which involves accelerating the ions in cyclotron motion, in a circle inside of an ion trap, in the presence of a collision gas.\cite{Gauthier1991, Laskin2005}
%Another technique, multiple-collision induced dissociation (MCID), was used for the study of dissociation energies of singly charged silver cluster, Ag$_n^+$ (2 $\leqslant$ n $\leqslant$ 25) by Kr{\"u}ckeberg and collaborators. \cite{Kruckeberg1999}
CID and the dissociated/fragmented ions produced by CID are used for several purposes: First, partial or complete structural determination can be achieved. Second, CID can simply achieve more sensitive and specific detection. By detecting a unique dissociated/fragmented ion, the precursor ion can be detected in the presence of other ions of the same m/z value, mass-to-charge ratio, which reduces the background and increases the limit of detection.
CID has been applied to a variety of systems, in particular hydrated atomic ions \cite{Mcquinn2009, Carl2013, Hofstetter2013, Coates2017, Coates2018} and molecular ions \cite{Graul1989, Wei1991, Goebbert2006, Haag2009}. In the second case, it has been used to understand the impact of high-energy radiations on living cells and DNA or RNA \cite{Liu2006, Nguyen2011, Shuck2014}, as well as low-energy collisions on molecules of biological interest \cite{Castrovilli2017, Bera2018}.
Theoretical and experimental studies devoted to fragmentation of hydrated molecular aggregates are scarce, \cite{Li1992, Bobbert2002, Liu2006, Bakker2008, Markush2016, Castrovilli2017} although CID has been applied to water clusters containing an atomic ion \cite{Carl2013, Hofstetter2013, Coates2018} and on charged water
clusters \cite{Dawson1982, Bakker2008, Mcquinn2009, Zamith2012}. This is a real lack as understanding hydration of molecules and biomolecules is of paramount importance to get insights into their structure, stability, dynamics and reactivity in aqueous medium. In that respect, CID investigations could play an important role in understanding those properties in a
environment free from long-range solvent effects but also for different hydration degrees or protonation states. This can be evidenced by the experimental study of Liu \textit{et al.} on the fragmentation of the singly-charged adenosine 5'-monophosphate (AMP$^-$)
which shows two different fragmentation channel depending on the solvation state of AMP$^-$.\cite{Liu2006} However, to the best of our knowledge, no modelling was performed to complement these experiments except for a few static calculations.\cite{Carl2013, Hofstetter2013, Coates2018}.
%colliding with a high or low energetic particles at high or low pressure,\cite{Kambara1977, Kruckeberg1999, Spasov2000, Holm2010, Gatchell2014, Gatchell2017, Zamith2019thermal} and so on has been explored in experiment.
%magnetic field and electric field are usually used in the experiment setup for the dissociation of clusters.
%Or write heating, colliding with particles, high pressure, electric field, and magnetic field can induce the dissociation of clusters.
%I can not find literature which describe only electric field or magnetic field can lead to dissociation of clusters. You know some ?}
Threshold collision-induced dissociation (TCID) method has also been used, for instance to study the fragmentation patterns and to measure the dissociation energies of clusters.\cite{Spasov2000, Armentrout2008} Zamith \textit{et al.} did a CID study of the mass-selected protonated uracil water clusters with water molecules and noble gases, respectively.\cite{Braud2019}
In addition, they also reported the TCID study of pyrene cluster cations. \cite{Zamith2020threshold}
For these two projects, the single collision event is the predominant process.
In this chapter, MD simulations based on a quantum chemical formalism are able to model such complex dissociation mechanism to provide an atomic-scale description for these collisions to explain and complete these experiments.
%Mass spectrometry has been the workhorse for studies of collisions involving PAHs, fullerenes and their clusters.
%measure the evaporation rates of mass selected pyrene clusters cations as a function of their initial temperature. The dissociation energy of the clusters are extracted from the experimental data using a statistical decay model, namely the Phase Space theory (PST).
%\subsection{Principle of TCID}
\subsection{Principle of TCID} \label{principleTCID}
In usual TCID setups, experiments are done in ion guides, allowing to perform collisions with large mass atoms such as xenon without losing ions by deflection due to the collision. In order to unambiguously determine dissociation energies, one has to take care of a number of experimental parameters. First, the number of collisions should be as low as possible in order to insure single collision conditions. This can be achieved by performing experiments at various pressures and extrapolating results to zero pressure. Second, one has to consider the possible so-called kinetic shifts that can alter the dissociation energy measurement. Indeed, at threshold collision energy, the system under study might not dissociate during the timescale of the experiment. The apparent threshold has, therefore, to be corrected. This is usually done by extrapolating the experimental values using Rice-Ramsperger-Kassel-Marcus (RRKM) dissociation rates.\cite{Klippenstein1992, Baer1996} Third, the initial thermal energy distribution has to be taken into account. Finally, TCID experimental results are usually fitted assuming a given form for the CID cross section, which can be expressed as \cite{Armentrout2008}:
\begin{eqnarray}
\label{CIDcross}
\sigma(E_{col})=(\sigma_{_0} n/E_{col})\sum_{i}{g_{i}} \int_{E_0-E_i}^{E_{col}}[1-e^{-k(\varepsilon + E_i)\tau}] \times (E_{col}-\varepsilon)^{n-1}d\varepsilon
\end{eqnarray}
where $\sigma_{_0}$ is the collision cross section, $n$ is the energy dependence of the reaction cross section, and $E_{col}$ is the collision energy. The populations $g_i$ of rovibrational states with energies $E_i$ are used to carry out the thermal averaging. The dissociation rate $k$ is usually calculated using RRKM type theories, and $\tau$ is the typical experimental time between the collision and detection. For comparison with experimental curves, eq \ref{CIDcross} is further convolved with the kinetic energy distributions of both the ion and neutral reactants. If one needs to incorporate sequential fragmentation and/or competitive channels, these can also be included.\cite{Rodgers1998, Armentrout2007}
In this method, ion guides are not used. Therefore, it needs to simulate the full ion trajectories in order to ensure that ion losses are correctly taken into account. Collisions are, thus, described with a microscopic model rather than with the average curve given by eq \ref{CIDcross}. This approach allows to quite naturally include sequential dissociation and to potentially test energy transfer models. One advantage of the setup resides in the fact that the systems under study are thermalized at low temperature prior to collisions. This implies that averaging over thermal energies of the parent ion plays a minor role, thus leading to minor uncertainties.
%For instance, for the largest size under study, n = 6, the average internal energy is 13 meV at 25 K.
%\subsection{Experimental setup}
\subsection{Experimental Setup} \label{EXPsetup}
The experimental setup of Laboratoire Collisions Agr{\'e}gats R{\'e}activi{\'e} (LCAR) by Zamith {\textit et al.} for the collision of protonated uracil water clusters or pyrene dimer cation with noble gas atoms is set up as follows:
\figuremacrob{experiment-setup}{Schematic view of the experimental setup. (a) Cluster gas aggregation source. (b) Thermalization chamber. (c) First Wiley–McLaren acceleration stage. (d) Massfilter. (e) Energy focusing. (f) Deceleration. (g) Collision cell. (h) Second Wiley–McLaren acceleration stage. (i) Reflectron. (j) Micro-channel plate detector.}
%%%%%%%%%%
%from uracil exp paper:
%Charged clusters are produced in a gas aggregation source.20 A flow of helium carrier gas and water vapor enters the source in a cell where uracil in solid form (Alpha Aesar, 99\%) is heated at 378 K to get a vapor pressure of about 6.6 $\times$ 10$^{-2}$ mbar.21 A miniature electron gun located at the cell exit allows us to ionize the clusters in the source. The typical kinetic energy of the electrons is 100 eV. The clusters formed in the source at the temperature of liquid nitrogen are carried out of the source by the helium gas flow. The produced clusters then enter the thermalization chamber where tens of thousands collisions between the helium gas and the clusters cool them down to the helium gas temperature. A thermalization temperature of 25 K is obtained by cooling the thermalization chamber with a closed cycle helium cryostat. This low temperature reduces the amount of internal energy prior to collision compared to experiments usually performed at room temperature. For instance, using the harmonic frequencies !i calculated for the neutral uracil,22 its internal energy Eint is estimated by:
%%%%%%%%%%%
Clusters are produced in a gas aggregation source \cite{Braud2017}(a) and then thermalized (b) at 25 K through thousands of collisions with helium. The experimental setup can be used in two modes. In the first mode, only the first Wiley-McLaren acceleration stage (c) is used to work together with the reflectron (i). Clusters are detected using dual micro-channel plates (MCPs) (j) biased at-10 kV. This allows to perform regular Time of Flight Mass Spectrometry (TOFMS) and to optimize the cluster production. In this mode, the mass filter (d), the electrodes for energy focusing (e) and deceleration (f), and the second Wiley-McLaren acceleration stage (h), are grounded.
In the second mode, all the electrodes were used to mass-select the clusters. In order to perform collisions between the mass-selected clusters and the rare gas atoms, precisely delayed high voltage pulses were applied to electrodes (c)-(f). Pulsed high voltages applied to the first Wiley–McLaren electrodes (c) accelerate all the clusters, giving them an average kinetic energy of 622 eV. The applied voltages and the spacing between the electrodes of the Wiley-McLaren are chosen such that, 26 cm downstream, there is a linear relation (to first order) between the position of clusters and their kinetic energy. Using a pulsed high voltage, an electric field is created in this region (e) that compensates this linear kinetic energy dispersion, and all clusters finally have the same kinetic energy within a few electron volts. The time at which this pulsed high voltage is applied determines which cluster size is correctly energy focused. After this kinetic energy focusing, ions are decelerated by a potential barrier (f). At the end of the potential barrier, the potential is shut down in a field free zone and the mass-selected clusters then fly freely through the collision cell (g) up to the second Wile-McLaren acceleration stage (h). Clusters are then mass-analyzed using the reflectron (i) and the MCP detector (j). High voltage is applied on the mass filter (d) when the mass of interest enters the cylinder and shut down before it comes out. This allows us to eliminate part of the neighboring masses.
In the experiments of pyrene clusters, the kinetic energy of the clusters in the laboratory frame is varied between 5 eV and 200 eV. For the experiments of protonated uracil water clusters, the kinetic energy of the clusters in the laboratory frame is 100 eV.
Kinetic energies of the ions can be easily deduced from experimental parameters. Indeed, since the distances in the apparatus are well-known, measuring, for instance, the time the ions take to travel from the end of the slowing down stage to the second acceleration stage gives the speed of the ions. More precise kinetic energy calibration is obtained by recording the signal of the ions as a function of delays and/or voltages. These curves are then reproduced by simulations to obtain the kinetic energy distribution of the ions. \cite{Chirot2006new}
The simplified experiment setup is shown in Figure \ref{exp-setup}.
Clusters are produced in a gas aggregation source and thermalized at a temperature of 25 K. Clusters are then mass-selected with a chosen kinetic energy, which collide with argon atoms in a collision cell. The collision products are then analysed by TOFMS.
%Further details about the experiment can be found elsewhere \cite{zamith_thermal_2019, braud_gas_2017, chirot_new_2006, zamith_CID_2020}.
\figuremacrob{exp-setup}{Schematic of the simplified experimental setup.}
\section{Computational Details} \label{Comput_meth}
\subsection{SCC-DFTB Potential} \label{DFTBpotential}
For the work in this chapter, the SCC-DFTB in combination with the mio-set for the Slater-Koster tables of integrals is applied. \cite{Elstner1998, Porezag1995, Seifert1996, Frenzel2004, Elstner2014, Spiegelman2020} The SCC-DFTB potential for protonated uracil water clusters is shown in section \ref{sec:structure-methods}.
DFTB is an efficient tool to perform MD simulations, in particular addressing the evaporation/dissociation processes in various chemical systems. \cite{Simon2017, Korchagina2017, Rapacioli2018, Simon2018}
The dynamics simulations of the collision process were performed with a QM/MM scheme \cite{Warshel1976} whose details can be found in the original paper\cite{Cui2001, Iftner2014}. The projectile argon is treated as a polarisable MM particle interacting with the target (protonated uracil water cluster or pyrene dimer cation Py$_2^+$), the latter being treated at the DFTB level. The oscillation problem often appears for dissociated or close to dissociation systems. For the collision trajectories described below, a Fermi distribution (Fermi temperature 2000~K) was applied to avoid oscillation issues during the self-consistent procedure.\cite{Kukk2015} The Fermi distribution allows to recover the continuity in energy and gradients in the case of level crossing. \cite{Kukk2015}
It should be mentioned that, in order to keep a low computational cost, no correction has been used to improve the DFTB charge resonance description. However, this charge delocalization issue has been specifically addressed in the case of PAH cation dissociation and it was shown to have a minor effect on the final computed mass spectra \cite{Simon2017}. I also mention that the collision energy is in principle high enough to have electronic excitation in the system, which is taken into account at a crude level by the use of a Fermi temperature. Finally, nuclear quantum effects are not taken into account. Although this may affect the results at very low collision energies, the effect is expected to be small for the experimental collision energies of 7.2 eV and 17.5 eV. Although all these limits should be kept in mind, I would like to emphasize that, recently, the dissociation of PAH molecules has been simulated and a good agreement with experimental results was obtained despite similar crude approximations, namely neglect of non-adiabatic and nuclear quantum effects, improper treatment of charge delocalization and use of a Fermi temperature \cite{Simon2017, Simon2018, Rapacioli2018atomic}.
\subsection{Collision Trajectories} \label{makingtrajectories}
The preparation for the collisional trajectories for the collision of protonated uracil water clusters or Py$_2^+$ with Ar is the same. The schematic example for the collision of Py$_2^+$ with Ar is shown in Figure \ref{howinputs}. Starting from the optimized Py$_2^+$ geometry \cite{Dontot2019}, a preliminary thermalization run of 200 fs at 25 K (maintained by a Nos\'e-Hoover chain thermostat \cite{Nose1984, Hoover1985}) is performed. Then, the argon atom projectile is introduced in the simulation with a velocity determined to reproduce a given collision energy. The target dimer Py$_2^+$ was positioned at the origin of the simulation referential and randomly rotated to allow all possible impact points on the dimer.
The argon atom is initially positioned at x=10, y=$b$ and z=0~\AA{}, with $b$ being the impact parameter. At each center of mass collision energy $E_{col}$, a series of 300 collision trajectories were conducted (the center of mass of the aggregate was kept at position (0, 0, 0)) for each of the 13 $b$ values which are evenly distributed (interval being 0.5 \AA) between 0 and R+0.5 \AA. R refers to the radius of Py$_2^+$.
600 collision trajectories were performed per isomer of protonated uracil water clusters.
Trajectory calculations have been performed with a time step of 0.5~fs and a total duration of 15 ~ps and 3~ps for the collision of argon with protonated uracil water clusters and Py$_2^+$, respectively.
For the collision of Py$_2^+$ with argon, we have checked that for high collision energies such as 20 and 25 eV, a time step of 0.1 fs does not change significantly our numerical results, which will be shown in section \ref{sec:MDanalysis}.
It should be noted that the quaternion was used for rotation process in the generation of initial inputs.
%In some cases it may be advisable to use the rigid-body approximation.
This approximation allows us to go from $3n-6$ degrees of freedom to $6N-6$, where $n$ and $N$ are the number of atoms and the number of molecules (3 degrees of translation and 3 degrees of rotation) in a system, respectively.
The complex quaternion formalism ($\textbf{\textit{q}}$ = $q_0, q_1, q_2, q_3$) was used o describe the orientation of a solid body with respect to Euler angles (($\theta, \phi, \psi$)) formalism.
%because the divergence problems appear if we are satisfied with the traditional Euler angles ($\theta, \phi, \psi$) formalism.
The quaternions involve an additional degree of freedom (similar to a homothety), which can be offset by using a normalization constraint on the vector \textbf{\textit{q}}:
\begin{align}
q_0^2+ q_1^2+ q_2^2+ q_3^2=1
\label{vectorq}
\end{align}
\figuremacrob{howinputs}{Schematic of the generation of the initial inputs.} \\
\subsection{Trajectory Analysis} \label{trajecanylysis}
During the results collection, the final snapshot was extracted for each trajectory.
For collision of between Py$_2^+$ and argon, when the center of mass of the two pyrene monomer is more than 10 \AA, a dissociation is defined.
For the dissociaton definition of protonated uracil water clusters, it is a little more complicated than Py$_2^+$. A fragment is defined as a group of atoms in which the distance of any pair of adjacent atoms is less than 5.0 \AA . The number of hydrogen, nitrogen and oxygen atoms in one fragment is denoted by $k$, $l$ and $m$, respectively. For instance, a fragment characterised by $l=0$ and $k=2m+1$ is a pure water cluster containing the excess proton. Identifying such a fragment at the end of the trajectory means that a neutral uracil fragment exists, otherwise the excess proton is located on a uracil containing fragment. In practice, at each time step, the fragments are identified on the basis of their $k$, $l$, $m$ values, allowing to record their time-dependent evolution. The mass spectrum is built retaining only the fragments containing the excess proton, as only charged fragments are detected in the experiment.
The opacity $P(b,E_{col})$, {\textit i.e.} the dissociation probability as a function of impact parameter at a given collision energy is computed by averaging the results over the simulations corresponding to these conditions.
The cross sections are then derived from the following formula:
\begin{eqnarray}
\label{integ}
\sigma_{frag}(E_{col}) &=& \int_0^{b_{max}} 2\pi P(b,E_{col})bdb \\ & \simeq&
\sum_{i=0}^{b_{max}} \frac{P(b_i,E_{col})+P(b_{i+1},E_{col})}{2}\pi(b_{i+1}^2-b_{i}^2) \nonumber
\end{eqnarray}
Mean values are computed using the same approach, followed by a division by $\pi b_{max}^2$. When mean values are restricted to trajectories leading to dissociation (noted $-d$) or not (noted $-ud$), additional normalisation by the total number of dissociated or undissociated trajectories is also necessary.
\section{\label{sec:collisionwUH}Dynamical Simulation of Collision-Induced Dissociation of Protonated Uracil Water Clusters}
\subsection{Introduction}
Motivated by the recent CID experiments conducted by Braud \textit{et al.} consisting in (H$_2$O)$_{1-15}$UH$^+$ clusters colliding with an impacting atom or molecule M (M = H$_2$O, D$_2$O, neon, and argon) at a constant center of mass collision energy of 7.2~eV,\cite{Braud2019} the dynamical simulations of the collision between the protonated uracil water clusters (H$_2$O)$_{n=1-7, 11, 12}$UH$^+$ and an argon atom were performed.
%First, it appears important to understand the interaction of DNA or RNA basis with water seeing
%their relevance in living organisms. They can also be subject to radiation damages which is still a medical challenge and thus
%needs to be further investigated. In that context, a number of studies have been conducted on molecules deriving from uracil
%or on uracil with only a few water molecules. \cite{Rasmussen2010,Imhoff2007,Abdoul2000,Champeaux2010,Delaunay2014,
%Bacchus2009,Kossoski2015} \cite{Maclot2011, Domaracka2012, Markush2016, Castrovilli2017}. Second, a very recent
The low collision energy (7.2~eV) only leads to intermolecular bond breaking, without any electronic excitation, rather than intramolecular bond breaking. The branching ratios for different charged fragments were determined in experiment, which allows to deduce the fragmentation cross section for all
(H$_2$O)$_{n=1-15}$UH$^+$ species and the location of the excess proton after collision: on a uracil containing cluster or on a pure water cluster. This allows to determine the proportion of neutral uracil loss (corresponding to cases where the excess proton is located on pure water clusters) as a function of the number $n$ of water molecules. A sharp increase of neutral uracil loss was observed for $n$ = 5-6 (2.8\% and 25.0\% for n = 4 and 7, respectively).
%
Those experiment were complemented by theoretical calculations that aim at characterizing the lowest-energy isomers of (H$_2$O)$_{n}$UH$^+$ ($n$ = 1-7, 11, 12) clusters (see section \ref{structureUH}), which
%They show that (i) For $n$ = 1-2, the uracil is protonated; (ii) For $n$ = 3-4, the excess proton is still on the uracil but has a tendency to be displaced towards adjacent water molecules; (iii) When $n$ is larger than 4, the excess proton is transferred to the water molecules.
shows that the location of the proton after collision recorded in the CID experiment is determined by its position in the lowest-energy parent isomer. In other words, a shattering mechanism occurs after collision. Despite these findings, static calculations can not provide a full picture for the fragmentation process and some issues are still not properly understood:
(i) What is the main path of the fragmentation mechanisms?
(ii) What are the fragments after collision?
(iii) How does the proportion of fragments change according to time?
(iv) Is the proportion of neutral uracil molecules loss only determined by the nature of the lowest-energy isomers?
%(v) What is the impact of nuclear quantum effects (NQE) for such process that occurs at very low temperature?
To answer these questions, this simulations present a complete MD study of the fragmentation process for (H$_2$O)$_{n=1-7, 11, 12}$UH$^+$ aggregates colliding with an argon atom. Section~\ref{resul_disc} discusses the statistical convergence of collision trajectories, theoretical time-dependent proportion of fragments, proportion of neutral uracil loss, total fragmentation cross sections and mass spectra of fragments bearing the excess proton. These data are compared to
available experimental results in order to discuss in details dissociation mechanism as a function of $n$. The main outcomes are summarized in section~\ref{Concl}.
\subsection{Results and Discussion} \label{resul_disc}
%\subsubsection{The proper number of impacting orientation}
\subsubsection{Statistical Convergence} \label{convergence}
In order to ensure that the statistical convergence is reached in the collision trajectories, initial conditions have to reproduce all possible
collision orientation with good statistics. The procedure to generate a set of collision trajectories is described in section \ref{makingtrajectories}.
As a visual proof, pictures a, b and c in Figure ~\ref{3b-sphere} represent 200, 400 and 600 random argon orientations with impact parameter being 0 for cluster (H$_2$O)$_3$UH$^+$, respectively. In these pictures, (H$_2$O)$_3$UH$^+$ is fixed and all initial positions for argon are orientated which leads to distribution maps of the initial positions of argon with respect to fixed (H$_2$O)$_{3}$UH$^+$. It is worth pointing out that in the collision trajectories, argon is fixed and uracil is rotated. Picture d in Figure~\ref{3b-sphere} presents 200 random argon orientations with impact parameter being 0.0 and 6.0, respectively. The similar pictures for cluster (H$_2$O)$_{12}$UH$^+$ are displayed in Figure \ref{12f-sphere}. These Figures demonstrate that the more collision trajectories are performed, the more colliding opportunities of argon at all possible orientations are obtained.
\figuremacro{3b-sphere}{Schematic representation of random argon orientations for the collision with the second lowest-energy isomer of cluster (H$_2$O)$_3$UH$^+$. 200 (a), 400 (b) and 600 (c) random argon orientations are generated with impact parameter being 0. ~200 orientations are generated with impact parameter being 0 and 6 (d), respectively.} \\
\figuremacro{12f-sphere}{Schematic representation of random argon orientations for the collision with the second lowest-energy isomer of cluster (H$_2$O)$_{12}$UH$^+$. 200 (a), 400 (b) and 600 (c) random argon orientations are generated with impact parameter being 0. ~200 orientations are generated with impact parameter value being 0 and 7 (d), respectively.} \\
In addition, to confirm that statistical convergence is reached for the properties discussed in sections \ref{time}, \ref{small}, \ref{large}, and \ref{mass-spectra}, Tables~\ref{tab:converge-1w-5w} and \ref{tab:converge-6w-12w} present the $P_{NUL}$ involved from the following formula \ref{PNUL}
\begin{eqnarray}
\label{PNUL}
%&&P_{NUL}(E_{col})= \int_0^{b_{max}} 2\pi \frac{N_{NUL}(b,E_{col})}{N_{frag}(b,E_{col})}bdb \nonumber \\ &
P_{NUL}(E_{col})&=& \int_0^{b_{max}} N_{NUL}(b,E_{col}) 2\pi bdb / \int_0^{b_{max}} N_{frag}(b,E_{col})2\pi bdb \nonumber \\ & \simeq&
\frac{\sum\limits_{i=0}^{b_{max}}\frac{1}{2}(N_{NUL}(b_i,E_{col})+N_{NUL}(b_{i+1},E_{col}))\pi(b_{i+1}^2-b_{i}^2)}
{\sum\limits_{i=0}^{b_{max}}\frac{1}{2}(N_{frag}(b_i,E_{col})+N_{frag}(b_{i+1},E_{col}))\pi(b_{i+1}^2-b_{i}^2)} \nonumber \\
\end{eqnarray}
and $\sigma_{frag}$ of two isomers (the first lowest energy isomer and the one whose $P_{NUL}$ fits best to the experiment results (in bold)) of each cluster (H$_2$O)$_{n=1-7, 11, 12}$UH$^+$ obtained from 200, 400, and 600 random argon orientations per impact parameter value.
Whatever the considered isomer, the three $P_{NUL}$ and $\sigma_{frag}$ values from 200, 400, and 600 random argon orientations are very close. Indeed, the largest difference is observed for isomer 7a which has $P_{NUL}$ values of 29.5 and 31.3~\% for 200 and 600 random orientations, respectively. This demonstrate that even for 200 initial random orientations, simulation are close to statistical convergence. In the present study,
all results discussed in the main text were obtained with 600 initial random argon orientations per impact parameter value which ensures statistical convergence of the results independently of cluster size.
%\begin{eqnarray}
%\label{PNUL}
% P_{NUL}(E_{col}) &=& \int_0^{b_{max}} 2\pi \frac{N_{NUL}}{N_{frag}}(b,E_{col})bdb \\ &%
% \simeq&
% \frac{\sum\limits_{i=0}^{b_{max}}(N_{NUL}(b_i,E_{col})+N_{NUL}(b_{i+1},E_{col}))\frac{(b_{i+1}^2-b_{i}^2)}{b_{max}^2}}
% {\sum\limits_{i=0}^{b_{max}}(N_{frag}(b_i,E_{col})+N_{frag}(b_{i+1},E_{col}))\frac{(b_{i+1}^2-b_{i}^2)}{b_{max}^2}} \nonumber
%\end{eqnarray}
\begin{table}
\begin{center}
\caption{The proportions of $P_{NUL}$ and $\sigma_{frag}$ of first lowest-energy isomer and the isomer whose $P_{NUL}$ fits the experiment (in bold) of (H$_2$O)$_{1-5}$UH$^+$ with simulations of 200, 400, and 600 as initial conditions.}
\label{tab:converge-1w-5w}
\begin{tabular}{|c|c|c|c|}
\hline
\textbf{Cluster} & \textbf{Simu} & \textbf{\boldm{$P_{NUL}$} (\%)} & \textbf{\boldm{$\sigma_{frag}$ (Å$^2$)}}\\
\hline
\rowcolor{lightgray} \bf{1a} & 200 & 0.1 & 28.4 \\
\rowcolor{lightgray} \bf{1a} & 400 & 0.1 & 28.3 \\
\rowcolor{lightgray} \bf{1a} & 600 & 0.2 & 28.9 \\
1b & 200 & 0.2 & 26.3 \\
1b & 400 & 0.1 & 25.7 \\
1b & 600 & 0.1 & 25.9 \\
\rowcolor{lightgray} 2a & 200 & 0.0 & 35.9 \\
\rowcolor{lightgray} 2a & 400 & 0.0 & 36.5 \\
\rowcolor{lightgray} 2a & 600 & 0.0 & 36.3 \\
\bf{2b} & 200 & 0.0 & 34.7 \\
\bf{2b} & 400 & 0.1 & 34.8 \\
\bf{2b} & 600 & 0.1 & 34.9 \\
\rowcolor{lightgray} 3a & 200 & 5.4 & 37.4 \\
\rowcolor{lightgray} 3a & 400 & 5.2 & 36.2 \\
\rowcolor{lightgray} 3a & 600 & 5.7 & 36.3 \\
\bf{3b} & 200 & 0.0 & 41.2 \\
\bf{3b} & 400 & 0.0 & 41.5 \\
\bf{3b} & 600 & 0.0 & 41.9 \\
\rowcolor{lightgray} 4a & 200 & 26.9 & 40.1 \\
\rowcolor{lightgray} 4a & 400 & 28.2 & 40.3 \\
\rowcolor{lightgray} 4a & 600 & 29.4 & 40.1 \\
\bf{4b} & 200 & 2.7 & 45.3 \\
\bf{4b} & 400 & 2.6 & 45.6 \\
\bf{4b} & 600 & 2.6 & 45.2 \\
\rowcolor{lightgray} 5a & 200 & 37.2 & 45.7 \\
\rowcolor{lightgray} 5a & 400 & 37.8 & 46.1 \\
\rowcolor{lightgray} 5a & 600 & 38.2 & 46.6 \\
\bf{5d} & 200 & 0.1 & 47.3 \\
\bf{5d} & 400 & 0.1 & 47.3 \\
\bf{5d} & 600 & 0.1 & 47.5 \\
\hline
\end{tabular}
\end{center}
\end{table}
\begin{table}
\begin{center}
\caption{The proportions of $P_{NUL}$ and $\sigma_{frag}$ of first lowest-energy isomer and the isomer whose $P_{NUL}$ fits the experiment (in bold) of (H$_2$O)$_{6, 7, 11, 12}$UH$^+$ with simulations of 200, 400, and 600 as initial conditions.}
\label{tab:converge-6w-12w}
\begin{tabular}{|c|c|c|c|}
\hline
\textbf{Cluster} & \textbf{Simu} & \textbf{\boldm{$P_{NUL}$} (\%)} & \textbf{\boldm{$\sigma_{frag}$ (Å$^2$)}}\\
\hline
\rowcolor{lightgray} 6a & 200 & 38.0 & 46.6 \\
\rowcolor{lightgray} 6a & 400 & 38.0 & 45.6 \\
\rowcolor{lightgray} 6a & 600 & 39.3 & 45.8 \\
\bf{6f} & 200 & 18.9 & 54.2 \\
\bf{6f} & 400 & 19.0 & 55.2 \\
\bf{6f} & 600 & 18.5 & 55.0 \\
\rowcolor{lightgray} 7a & 200 & 29.5 & 54.8 \\
\rowcolor{lightgray} 7a & 400 & 31.3 & 53.4 \\
\rowcolor{lightgray} 7a & 600 & 31.3 & 53.4 \\
\bf{7d} & 200 & 22.6 & 55.3 \\
\bf{7d} & 400 & 22.9 & 54.3 \\
\bf{7d} & 600 & 23.0 & 54.0 \\
\rowcolor{lightgray} 11a & 200 & 26.7 & 53.8 \\
\rowcolor{lightgray} 11a & 400 & 28.2 & 53.5 \\
\rowcolor{lightgray} 11a & 600 & 28.3 & 52.9 \\
\bf{11d} & 200 & 14.5 & 55.2 \\
\bf{11d} & 400 & 15.4 & 56.1 \\
\bf{11d} & 600 & 15.6 & 56.5 \\
\rowcolor{lightgray} 12a & 200 & 8.0 & 59.2 \\
\rowcolor{lightgray} 12a & 400 & 7.5 & 60.5 \\
\rowcolor{lightgray} 12a & 600 & 7.6 & 60.2 \\
\bf{12c} & 200 & 10.4 & 55.3 \\
\bf{12c} & 400 & 10.8 & 55.8 \\
\bf{12c} & 600 & 10.8 & 55.4 \\
\hline
\end{tabular}
\end{center}
\end{table}
\subsection{Time-Dependent Proportion of Fragments} \label{time}
The time-dependent proportion of each fragment was extracted from collision trajectories. To illustrate the change in behavior resulting from the difference in cluster size, Figures~\ref{proporEachFrag-1a2a}-\ref{proporEachFrag-7d12c-zoom} display the time-dependent proportion of fragments obtained from the dissociation of the low-lying energy isomers of (H$_2$O)$_{1-7, 11, 12}$UH$^+$.
I will discuss the time-dependent proportion of one small cluster (7a) and one big cluster (12a) in detail as an example.
For the sake of clarity, only the fragments displaying significant proportion, higher than 0.035 and 0.015 for 7a and 12a, respectively are considered in Figure \ref{proporEachFrag-7a12a-zoom}. This corresponds to the eight and ten most prominent fragments for 7a and 12a, respectively.
From Figure~\ref{proporEachFrag-7a12a-zoom}, it is clear that for both aggregates, the proportion of H$_2$O has the sharpest increase after collision and then stay almost constant as a function of time. For 7a, $\sim$3~ps after collision, the proportion of almost all fragments does not change any more. Before that, the proportion of the (H$_2$O)$_6$UH$^+$ fragment increases first and then decreases, which indicates a sequential dissociation of water molecules. For 12a, proportion of (H$_2$O)$_{11}$UH$^+$ and (H$_2$O)$_{10}$UH$^+$ fragments displays a sharp increase quickly after collision which is then followed by a fast decrease, and finally it keeps a minute decrease up to the end of the simulations. The decrease of proportion of
(H$_2$O)$_{10}$UH$^+$ and (H$_2$O)$_{11}$UH$^+$, and the increase of proportion of (H$_2$O)$_{6}$UH$^+$,
(H$_2$O)$_{7}$UH$^+$ and (H$_2$O)$_{8}$UH$^+$ indicate sequential dissociation after collision is occurring. It is worth noting that, in contrast to 7a, the proportions of the main fragments of 12a do not tend to be a constant at the end of the simulations.
This implies that, for this large aggregate, structural rearrangements are more likely to occur prior to complete dissociation. Proportions of the main fragments of clusters 7d and 12c shown in Figure \ref{proporEachFrag-7d12c-zoom} display similar behavior as for 7a and 12a.
As a first conclusion, Figure~\ref{proporEachFrag-7a12a-zoom} suggests that clusters with 7 water molecules experience a direct dissociation mechanism as was hypothesised by Braud \textit{et al.}.\cite{Braud2019} A similar conclusion can be drawn for smaller cluster sizes as supported by Figures \ref{proporEachFrag-1a2a}-\ref{proporEachFrag-5a6a-zoom}. In contrast, cluster with 11 (see Figure \ref{proporEachFrag-11a-zoom}) and 12 water molecules shows a behavior compatible with a certain amount of statistical dissociation, namely a long-time evolution that allows structural rearrangements. These important observations can now be refined by looking at more detailed properties.
\figuremacrob{proporEachFrag-1a2a}{Time-dependent proportions of the main fragments obtained from the dissociation of the lowest-energy isomers of (H$_2$O)$_1$UH$^+$ (left) and (H$_2$O)$_{2}$UH$^+$ (right).} \\
\figuremacro{proporEachFrag-3a4a-zoom}{Time-dependent proportions of the main fragments obtained from the dissociation of the lowest-energy isomers of (H$_2$O)$_3$UH$^+$ (left) and (H$_2$O)$_{4}$UH$^+$ (right). Bottom panels correspond to a zoom over the lower proportions.} \\
\figuremacro{proporEachFrag-5a6a-zoom}{Time-dependent proportions of the main fragments obtained from the dissociation of the lowest-energy isomers of (H$_2$O)$_5$UH$^+$ (left) and (H$_2$O)$_{6}$UH$^+$ (right). Bottom panels correspond to a zoom over the lower proportions.} \\
\figuremacro{proporEachFrag-11a-zoom}{Time-dependent proportions of the main fragments obtained from the dissociation of the lowest-energy isomer of (H$_2$O)$_{11}$UH$^+$. Right panel corresponds to a zoom over the lower proportions.} \\
\figuremacro{proporEachFrag-7a12a-zoom}{Time-dependent proportions of the main fragments obtained from the dissociation of the lowest-energy isomers of (H$_2$O)$_7$UH$^+$ (left) and (H$_2$O)$_{12}$UH$^+$ (right). Bottom panels correspond to a zoom over the lower proportions.} \\
\figuremacro{proporEachFrag-7d12c-zoom}{Time-dependent proportions of the main fragments obtained from the dissociation of the the third lowest-energy isomer of (H$_2$O)$_7$UH$^+$ (left) and the third lowest-energy isomer (H$_2$O)$_{12}$UH$^+$ (right). Bottom panels correspond to a zoom over the lower proportions.} \\
\subsection{Proportion of Neutral Uracil Loss and Total Fragmentation Cross Sections for Small Clusters} \label{small}
In order to get more insights in the fragmentation, molecular dynamics trajectories were analysed in terms of proportion of neutral uracil loss ($P_{NUL}$) defined in section \ref{convergence} and total fragmentation
cross sections ($\sigma_{frag}$) defined in section~\ref{trajecanylysis}. These two properties are also accessible from experiments. Another property extracted from the MD simulations, but not accessible from experiment,
is the proportion of protonated uracil ($P_{PU}$) which is equal to the ratio of the number of simulations leading to a protonated uracil molecule over the number of simulations leading to a fragment containing the uracil and the excess proton. In order to correlate the outcome of the collision and the structure of the aggregate undergoing the collision, all considered low-energy isomers are characterized by there relative energies ($E_{rel.}$) and the location of the excess proton (LEP). For the latter, three distinct configurations were considered: The excess proton is bounded to the uracil molecule (noted U-H); The excess proton is bounded to a water molecule that is adjacent to an oxygen atom of the uracil molecule (noted W-H-U); The excess proton is bounded to a water molecule that is separated by at least one other water molecule from the uracil molecule (noted W-H). All these data are gathered in Table~\ref{tab:full} and we first discuss the behavior of the small species (H$_2$O)$_{1-7}$UH$^+$.
\begin{table*}
\begin{center}
\caption{Relative energy $E_{rel.}$ (in kcal.mol$^{-1}$) at the MP2/Def2TZVP level, LEP, $P_{PU}$ (in \%),
$P_{NUL}$ (in \%), $\sigma_{frag}$ (in \AA$^2$) of the considered low-energy isomers of (H$_2$O)$_{1-7, 11, 12}$UH$^+$
clusters. Isomers which $P_{NUL}$ fit best to the experimental value are indicated in bold. $P_{{NUL}_{exp}}$ and
$\sigma_{{frag}_{exp}}$ are the experimental values for $P_{NUL}$ and $\sigma_{frag}$, respectively. For (H$_2$O)$_{12}$UH$^+$, experimental values were obtained for collision with Ne, whereas all other theoretical and experimental data are for collision with Ar.}\label{tab:full}
\begin{tabular}{|c|c|c|c|c|c|l|c|}
\hline
\textbf{Isomers} & $E_{rel.}$ & LEP & $P_{PU}$ & $P_{NUL}$ & $P_{{NUL}_{exp}}$ & $\sigma_{frag}$ & $\sigma_{{frag}_{exp}}$ \\
\hline
\rowcolor{lightgray} \bf{1a} & 0.0 & U-H & 100 & 0.2 & & 28.9 & \\
\rowcolor{lightgray} 1b & 0.7 & U-H & 100 & 0.1 &\multirow{-2}*{0.9} & 25.9 & \multirow{-2}*{12.3} \\
2a & 0.0 & U-H & 100 & 0.0 & & 36.3 & \\
\bf{2b} & 0.2 &U-H & 100 & 0.1 &\multirow{-2}*{0.4} &34.9 & \multirow{-2}*{22.8}\\
\rowcolor{lightgray} 3a & 0.0 & U-H & 100 & 5.7 & & 36.3 & \\
\rowcolor{lightgray} \bf{3b} & 0.3 & U-H & 100 & 0.0 &\multirow{-2}*{1.7} & 41.9 & \multirow{-2}*{31.2} \\
4a & 0.0 & W-H-U & 98.0 & 29.4 & & 40.1 & \\
\bf{4b} & 0.9 &U-H & 99.7 & 2.6 &\multirow{-2}*{2.8} &45.2 & \multirow{-2}*{43.4}\\
\rowcolor{lightgray} 5a & 0.0 &W-H & 78.5 & 46.6 && 38.2 & \\
\rowcolor{lightgray} 5b & 0.3 &W-H-U & 89.0 & 28.5 && 38.7 & \\
\rowcolor{lightgray} 5c & 2.0 &W-H-U & 87.8 & 27.1 && 44.6 & \\
\rowcolor{lightgray} \bf{5d} & 2.4 &U-H & 100 & 0.1 &\multirow{-4}*{7.5}& 47.5 & \multirow{-4}*{48.0}\\
6a & 0.0 &W-H & 44.1 & 39.3 & & 45.8 & \\
6b & 0.2 &W-H & 43.5 & 33.8 & & 58.6 & \\
6c & 0.3 &W-H & 46.4 & 36.6 & & 46.1 & \\
6d & 0.9 &W-H & 64.6 & 34.7 & & 42.6 & \\
6e & 2.5 &W-H & 45.9 & 34.9 & & 50.5 & \\
\bf{6f} & 2.7 &W-H-U & 76.2 & 18.5 &\multirow{-6}*{18.0}& 55.0 & \multirow{-6}*{54.3} \\
\rowcolor{lightgray} 7a & 0.0 &W-H & 28.2 & 31.3 && 53.4 & \\
\rowcolor{lightgray} 7b & 0.3 & W-H-U & 52.4 & 21.4 && 51.7 &\\
\rowcolor{lightgray} 7c & 0.3 & W-H & 41.3 & 31.1 && 49.5 &\\
\rowcolor{lightgray} \bf{7d} & 0.8 & W-H-U & 40.9 & 23.0 &\multirow{-4}*{25.0}& 54.0 & \multirow{-4}*{59.7} \\
11a & 0.0 &W-H & 4.6 & 28.3 & & 52.9 & \\
11b & 1.4 &W-H & 3.2 & 28.5 & & 54.7 & \\
11c & 1.5 &W-H & 4.2 & 22.8 & & 55.2 & \\
\bf{11d}& 1.9 &W-H & 6.8 & 15.6 &\multirow{-4}*{11.8} & 56.5 & \multirow{-4}*{63.8} \\
11e & 1.9 &W-H & 5.4 & 22.7 & & 52.6 & \\
11f & 2.3 &W-H & 7.9 & 24.3 & & 52.0 & \\
% 11g & 2.5 &W-H & 3.7 & 29.8 &\multirow{-6}*{11.8}& 55.0 & \multirow{-6}*{63.8} \\
\rowcolor{lightgray} 12a & 0.0 & W-H & 6.7 & 7.6 && 60.2 & \\
\rowcolor{lightgray} 12b & 0.6 &W-H & 34.0 & 22.4 && 52.2 & \\
\rowcolor{lightgray} \bf{12c} & 0.7 &W-H & 48.7 & 10.8 && 55.4 & \\
\rowcolor{lightgray} 12d & 1.3 &W-H-U & 5.4 & 9.7 && 54.3 & \\
\rowcolor{lightgray} 12e & 1.8 &W-H-U & 67.5 & 6.0 && 54.2 & \\
\rowcolor{lightgray} 12f & 2.4 &W-H-U & 55.0 & 17.1 &\multirow{-6}*{12.2}& 54.1 & \multirow{-6}*{77.0} \\
\hline
\end{tabular}
\end{center}
\end{table*}
Various information can be inferred from these properties. Firstly, one observes a general increase of $\sigma_{frag}$ as a function of cluster size with values ranging from 25.9~\AA$^2$~for isomer 1b to 60.2~\AA$^2$~for isomer 12a. Interestingly, only slight variations of $\sigma_{frag}$ are observed for different isomers of the same aggregate. In contrast, $P_{NUL}$ is much more sensitive to the nature of the considered isomers, in particular when these isomers display different LEP values. For instance, $P_{NUL}$ is 46.6 ~\% for 5a (W-H) while it is only 0.1~\% for 5d (U-H). More interestingly, there seems to exist a strong correlation between $P_{NUL}$ and LEP.
Indeed, $P_{NUL}$ values below 1.0~\% are characterized by an excess proton initially bounded to uracil (U-H type). This suggests that when uracil is protonated, probability for deprotonation after collision is very low and thus $P_{NUL}$ is close to 0\%. $P_{NUL}$ values between 9.7 and 29.4~\% are obtained from W-H-U configurations while larger $P_{NUL}$ values, above 31.1~\%, arise from W-H configurations in clusters (H$_2$O)$_{5-7}$UH$^+$. This demonstrates that, from the excess proton point of view, the outcome of the collision is highly sensitive to the nature of the isomer undergoing the collision as hypothesised by Braud \textit{ al.} \cite{Braud2019} This important finding can be of help to determine which isomer, or set of isomers, is likely to undergo collision by comparing experimental and theoretical $P_{NUL}$ as this is not necessarily the lowest-energy isomer as discussed below.
For (H$_2$O)$_{1-2}$UH$^+$, the theoretical and experimental $P_{NUL}$ values, close to zero, are in good agreement regardless of the considered isomer. For (H$_2$O)$_3$UH$^+$, the experimental $P_{NUL}$ is 1.7~\% which is well reproduced by both isomers 3a
and 3b although 3b is the one closer to the experimental value, 0.0~\% against 5.7~\% for 3a. This was expected as they are very close in energy, only 0.3 kcal.mol$^{-1}$ difference, and in structure, as displayed in Figure~\ref{fig-1a-3b}, both being of U-H type structure. Consequently, in the experiment, each one of them could be at the origin of the experimental signal. (H$_2$O)$_4$UH$^+$ behaves differently. The two low-energy isomers, 4a and 4b, display very different $P_{NUL}$ values, 29.4 and 2.6~\%, respectively. The experimental value is 2.8~\% which suggests that 4b, although slightly higher in energy by 0.9 kcal.mol$^{-1}$, is the isomer prevailing during the collision process. The difference in behavior can be explained by the U-H configuration of 4b, in which the excess proton is bounded to the uracil, whereas in 4a, it is bounded to a water molecule adjacent to uracil (see Figure~\ref{fig-4a-5d}). The case of (H$_2$O)$_5$UH$^+$ is more complex as this is the first species displaying the three types of LEP configuration among its four lowest-energy isomers as can be seen on Figure~\ref{fig-4a-5d}. This implies very different $P_{NUL}$ values: 46.6~\% for 5a, 28.5 and 27.1~\% for 5b and 5c, respectively, while it is only 0.1~\% for 5d. The experimental $P_{NUL}$ value for (H$_2$O)$_5$UH$^+$ is still relatively low, 7.5~\%, which suggests that a U-H type structure prevails during the collision process. Although 5d is 2.4~kcal.mol$^{-1}$
higher in energy than 5a, this isomer is thus expected to undergo the collision.
\figuremacro{fig-1a-3b}{Selected low-energy configurations of (H$_2$O)$_{1-3}$UH$^+$. Relative energies at the MP2/Def2TZVP level are in kcal.mol$^{-1}$.}
\figuremacro{fig-4a-5d}{Selected low-energy configurations of (H$_2$O)$_{4-5}$UH$^+$. Relative energies at the MP2/Def2TZVP level are in kcal.mol$^{-1}$.}
(H$_2$O)$_6$UH$^+$ and (H$_2$O)$_7$UH$^+$ are the first two aggregates for which no low-energy isomer belongs to
the U-H type structure. As a consequence, in contrast to smaller species, the theoretical $P_{NUL}$ values are all higher
than 15~\%. This is in line with the experimental values which display a net increase at $n$ = 6. Isomers 6a, 6b, 6c, 6d,
and 6e (see Figure~\ref{fig-6a-6f}) are all W-H type structures which leads to $P_{NUL}$ values almost twice higher than
the experimental one. Consequently, as for (H$_2$O)$_5$UH$^+$, one can assume that the isomer of (H$_2$O)$_6$UH$^+$ undergoing the collision is more likely to be a W-H-U type structure although it is higher in relative energy. Isomer 6f can be such a candidate as it displays of $P_{NUL}$ value of 18.5\% which is in agreement with the experimental value, 18.0\%.
Due to its increasing size, (H$_2$O)$_6$UH$^+$ displays W-H configurations with the excess proton at various distances
from the recombining oxygen. Indeed, in 6a, 6c and 6d this distance is 1.774, 1.745 and 1.804~\AA, while in 6b, 6e and 6f,
it is shorter: 1.660, 1.614, and 1.494~\AA, respectively. However, no net correlation is observed between this distance and
the value of $P_{NUL}$: 39.3, 33.8, 36.6, 34.7, 34.9 and 18.5\% for 6a, 6b, 6c, 6d, 6e and 6f, respectively. In particular, the
behavior of 6e is striking. It has almost the same relative energy as 6f and they are structurally similar (see Figure~\ref{fig-6a-6f}) but display different $P_{NUL}$ values. This suggests that, for $n$ larger than 5, the ability of the water molecule network to stabilise the excess proton, \textit{i.e} to promote or prevent its diffusion toward the uracil molecule, starts to be competitive with the configuration type of the isomer. In 6e, the excess proton is in a configuration close to the Zundel ion which may explain its high $P_{NUL}$ value as compared to 6f.
For (H$_2$O)$_7$UH$^+$, a W-U-H type configuration is also expected to fit best the experimental result. And indeed 7d, a W-H-U type structure, which is only 0.8~kcal.mol$^{-1}$ above the lowest-energy isomer (see Figure~\ref{fig-7a-7d}), has a $P_{NUL}$ value of 22.9~\% as compared to 25.0~\% experimentally. Isomers 7a and 7c have a W-H configuration and their $P_{NUL}$ values (31.3 and 31.1~\%, respectively) are higher than the ones of 7b and 7d which have a W-H-U configuration.
Finally, it is worth noting that even when the excess proton is initially bounded to a water molecule, \textit{i.e.} when a W-H
type structure is considered, the maximum $P_{NUL}$ that has been obtained is only 46.6~\%. This demonstrates that for
small aggregates such as (H$_2$O)$_{5-7}$UH$^+$ ((H$_2$O)$_{1-4}$UH$^+$ do not display low-energy W-H type structures), dissociation mainly lead to protonated uracil containing fragments. This is in line with the experimental results. Analysis of $P_{PU}$ values also show that uracil is protonated in a significant amount of these protonated uracil containing fragments. $P_{PU}$ has a clear tendency to decrease with cluster size, but can be quite high even for W-H type structures, for instance 5a, 6d and 7c in Table~\ref{tab:full}. This demonstrates that upon collision, the excess proton is likely to transfer to uracil on a rather short time scale.
\figuremacro{fig-6a-6f}{Selected low-energy configurations of (H$_2$O)$_{6}$UH$^+$. Relative energies at the MP2/Def2TZVP level are in kcal.mol$^{-1}$.}
\figuremacro{fig-7a-7d}{Selected low-energy configurations of (H$_2$O)$_{7}$UH$^+$. Relative energies at the MP2/Def2TZVP level are in kcal.mol$^{-1}$.}
The clusters discussed above are characterized by complex potential energy surfaces characterized by several low-energy isomers, with relative energies that can be lower than 1~kcal.mol$^{-1}$, and which get more complex as the number of water molecules
increases. Consequently, the exact energetic ordering between the low-energy isomers can not be precisely known as this is below chemical accuracy and we thus can not claim here to have found the lowest-energy structure of each aggregate, or the isomer undergoing the collision. Nevertheless, what we show is that $P_{NUL}$ is mainly determined by the initial position
of the proton in the isomer undergoing the collision. Consequently, for the collision energy and the range of cluster size we have considered, the structure of the aggregate undergoing the collision plays a key role in determining the dissociation process and collision
outcomes much more than energetics. This is consistent with the analysis of the time-dependent proportion of fragments which suggests a direct dissociation mechanism.
This is further highlighted on Figure~\ref{neutralUloss-Ne-Ar}, which presents the experimental $P_{NUL}$ for collision with Ar and Ne, respectively as a function of $n$ and the corresponding theoretical values obtained from the lowest-energy isomers as well as from the isomers for which $P_{NUL}$ matches best to the experimental data. As can be seen, a very good agreement can be obtained with the experimental data by considering a specific set of isomers. Interestingly, if a similar plot is drawn for $\sigma_{frag}$ considering the same isomers
(see Figure~\ref{cross-section-Ne-Ar}), a good agreement with the experimental data and much better than $\sigma_{geo}$ (calculated from formula \ref{cross-section-geo})is also obtained with the two sets of isomers which confirms the weaker dependence upon isomer of $\sigma_{frag}$.
\figuremacro{neutralUloss-Ne-Ar}{Theoretical (green and blue lines) and experimental (red line) $P_{NUL}$ values for the (H$_2$O)$_{1-7, 11, 12}$UH$^+$ clusters.
Theory 1 (green line) is obtained from the isomers which $P_{NUL}$ matches best to the experimental data while Theory 2 (blue line) is obtained from lowest-energy isomers.} \\
\figuremacro{cross-section-Ne-Ar}{Theoretical (green and blue lines) and experimental (red line) $\sigma_{frag}$ values for the (H$_2$O)$_{1-7, 11, 12}$UH$^+$ clusters.
Theory 1 (green line) is obtained from the isomers which $P_{NUL}$ matches best to the experimental data while Theory 2 (blue line) is obtained from lowest-energy isomers.} \\
\subsection{Behaviour at Larger Sizes, the Cases of (H$_2$O)$_{11, 12}$UH$^+$} \label{large}
In the experiments conducted by Braud \textit{et al.},\cite{Braud2019} $P_{NUL}$ starts to decrease at $n$=8. This decrease is not consistent with the above argument of a direct dissociation mechanism and larger species more likely characterized by W-H and W-H-U type structures. This apparent discrepancy motivated us to extend the present study to a larger cluster, namely (H$_2$O)$_{11, 12}$UH$^+$. For (H$_2$O)$_{12}$UH$^+$, the only available experimental data is for collisions with Ne instead of Ar, although for the same center of
mass collision energy.
As shown in Figure~\ref{neutralUloss-Ne-Ar}, experimental $P_{NUL}$ values for Ne or Ar, although not equal, display similar trend. In the following,
I thus discuss the experimental data of (H$_2$O)$_{12}$UH$^+$ colliding with Ne. For cluster (H$_2$O)$_{1-7, 11}$UH$^+$, keep discussing the experimental data from colliding with Ar.
The behaviour for (H$_2$O)$_{11}$UH$^+$ and (H$_2$O)$_{12}$UH$^+$ is rather different when looking at detailed properties. Indeed, for (H$_2$O)$_{11}$UH$^+$, $P_{NUL}$ values for isomers 11a, 11b, 11c, 11e, and 11f are very similar as they range from 22.7 to 29.8~\%. For 11d, $P_{NUL}$ equal 15.6~\% which fits best to the experiment. These $P_{NUL}$ values are lower than those of (H$_2$O)$_{6}$UH$^+$, as observed
experimentally, and in the same range as (H$_2$O)$_{7}$UH$^+$. All isomers display a W-H type
configuration as seen in Figure~\ref{fig-11a-f}. $P_{PU}$ is very small for all (H$_2$O)$_{11}$UH$^+$ isomers which shows that on the time scale of the simulations, protonation of uracil hardly occurs.
For (H$_2$O)$_{12}$UH$^+$, 12c isomer, which has a W-H type configuration (see Figure~\ref{fig-12a-f}), has a $P_{NUL}$ value which fits best to the experiment, 10.8~\% against 12.2~\%, while isomer 12a, also a W-H type configuration (see Figure~\ref{fig-12a-f}), has a $P_{NUL}$ value equal to 7.6~\%. Overall, $P_{NUL}$ values calculated for (H$_2$O)$_{12}$UH$^+$ isomers are lower than those of (H$_2$O)$_{6}$UH$^+$
and (H$_2$O)$_{7}$UH$^+$, which is in line with the experiment. The main difference with the (H$_2$O)$_{1-7}$UH$^+$ aggregates is that no clear relation exist between the $P_{NUL}$ value and the initial localisation of the excess proton. Indeed, 12a, 12b and 12c are all W-H type configurations but with $P_{NUL}$ values ranging from 7.6 to 22.4~\%. The same is observed for 12d, 12e and 12f although they are all W-H-U type configurations. Similarly, no difference in
behaviour is obtained between W-H and W-H-U type configurations. This can be explained by
assuming that the dissociation mechanism in (H$_2$O)$_{12}$UH$^+$ involves some amount
of structural rearrangement that softens the impact of the isomer undergoing the collision. Indeed,
as (H$_2$O)$_{12}$UH$^+$ has more degrees of freedom, it can more easily accommodate the kinetic energy transferred by the colliding atom prior to dissociation which thus takes place on a longer time scale. This excess of internal energy thus fosters structural rearrangements, in particular proton transfers toward the uracil, explaining the smaller $P_{NUL}$ value for
(H$_2$O)$_{12}$UH$^+$. This is in full agreement with the conclusions obtained in section~\ref{time}
from Figures~\ref{proporEachFrag-11a-zoom},\ref{proporEachFrag-7a12a-zoom} and \ref{proporEachFrag-7d12c-zoom}. To further support this conclusion, we conducted 200 MD simulations in the micro-canonical ensemble in which the whole kinetic energy of Ar was randomly distributed in all the vibrational modes of isomer 12c by drawing initial velocities in a 1185~K Boltzmann
distribution. Among them, 166 simulations display dissociation with one or two water molecules dissociating from the main cluster. No neutral uracil loss is observed. To conclude, although the present simulations are too short to assert that (H$_2$O)$_{12}$UH$^+$ undergoes a statistical dissociation mechanism, they clearly show that a direct mechanism is not sufficient to account for the theoretical and experimental results.
Consequently, structural rearrangements are very likely to occur prior to dissociation and the experimental
results for $P_{NUL}$ and $\sigma_{frag}$ values can not result from a single (H$_2$O)$_{12}$UH$^+$ isomer.
In contrast, similarities in both $P_{NUL}$ and $P_{PU}$ values for all considered (H$_2$O)$_{11}$UH$^+$
isomers, as well as $P_{NUL}$ values close to (H$_2$O)$_{7}$UH$^+$ ones, do not evidence structural
rearrangements in this species although they could be present.
\figuremacro{fig-11a-f}{Selected low-energy configurations of (H$_2$O)$_{11}$UH$^+$.
Relative energies at the MP2/Def2TZVP level are in kcal.mol$^{-1}$.} \\
\figuremacro{fig-12a-f}{Selected low-energy configurations of (H$_2$O)$_{12}$UH$^+$.
Relative energies at the MP2/Def2TZVP level are in kcal.mol$^{-1}$.} \\
\subsection{Mass Spectra of Fragments with Excess Proton} \label{mass-spectra}
In this section, in order to analyse collision products in more details, the branching ratios of the different fragments containing the excess proton were extracted from the collision simulations of clusters (H$_2$O)$_{1-7, 11, 12}$UH$^+$ and compared with the experimental ones shaped as mass spectra.\cite{Braud2019} For each cluster size, only simulations corresponding to the isomer which $P_{NUL}$ value fits best to the experiment were considered (1a, 2b, 3b, 4b, 5d, 6f, 7d, 11d, 12c). The results are presented in Figures~\ref{MS-BR-1w-4w-Ne-Ar-branch}, \ref{MS-BR-5w-11w-Ne-Ar-branch} and \ref{MS-BR-12w-Ne-branch}. For cluster (H$_2$O)$_{12}$UH$^+$, there is no experimental data for collision with argon.
For (H$_2$O)$_{12}$UH$^+$, experimental results were obtained for collision with neon. From the experimental results for argon and neon for 1a, 2b, 3b, 4b, 5d, 6f, 7d, and 11d, it shows the branch ratios for collision with argon and neon are close and have the same trend. So it should be reasonable to compare the simulated branch ratios of 12c with the ones of experimental data from the collision of (H$_2$O)$_{12}$UH$^+$ with argon.
\figuremacro{MS-BR-1w-4w-Ne-Ar-branch}{Simulated mass spectra (positive area) of the charged fragments after 15~ps simulation time (fragments (H$_2$O)$_n$H$^+$ in red and (H$_2$O)$_n$UH$^+$ in blue for argon; (H$_2$O)$_n$H$^+$ in pink and (H$_2$O)$_n$UH$^+$ in green for neon) from isomers (a) 1a, (b) 2b, (c) 3b, (d) 4b. The counterparts in experiment are plotted (negative area).} \\
\figuremacro{MS-BR-5w-11w-Ne-Ar-branch}{Simulated mass spectra (positive area) of the charged fragments after 15~ps simulation time (fragments (H$_2$O)$_n$H$^+$ in red and (H$_2$O)$_n$UH$^+$ in blue) from isomers (e) 5d, (f) 6f, (g) 7d, and (h) 11d. The counterparts in experiment are plotted (negative area).} \\
\figuremacro{MS-BR-12w-Ne-branch}{Simulated mass spectra (positive area) of the charged fragments after 15~ps simulation time (fragments (H$_2$O)$_n$H$^+$ in red and (H$_2$O)$_n$UH$^+$ in blue) from isomers 12c. The counterparts in experiment obtained for collision with neon are plotted in negative area (H$_2$O)$_n$H$^+$ in pink and (H$_2$O)$_n$UH$^+$ in green).} \\
Overall, the experimental and theoretical spectra present the same general trends: (i) The mass spectra present a broad distribution of sizes, without prominence of a particular peak; (ii) All the spectra are dominated by the heaviest protonated uracil containing fragment (loss of a single water molecule) with the exception of the simulated mass spectrum for 2b; (iii) Fragments containing protonated uracil prevail over pure protonated water fragments, as already observed from the $P_{NUL}$ values provided
in Table~\ref{tab:full}; (iv) Pure protonated water fragments only appear for the largest cluster sizes. Indeed, although very minor contributions
are observed in both the simulated and experimental spectra for parent clusters with $n$=3-5, significant contributions of these species only appear when the parent cluster contains at least 6 water molecules.
A more detailed discussion of the simulated and experimental mass spectra will be made as follows. For (H$_2$O)$_{2}$UH$^+$, fragments (H$_2$O)UH$^+$ and UH$^+$ are observed in both experiment and theory although their relative ratio is different. For (H$_2$O)$_{3}$UH$^+$, the simulated and experimental spectra agree quite well with a dominant peak for (H$_2$O)$_{2}$UH$^+$. For (H$_2$O)$_{4}$UH$^+$, in both experimental and theoretical spectra, the peak intensity of the fragments containing protonated uracil increases with the number of water molecules. For (H$_2$O)$_{5}$UH$^+$ and (H$_2$O)$_{6}$UH$^+$, this is also the case
except for the UH$+$ fragment which is overestimated when compared to the experimental result in Figure \ref{MS-BR-5w-11w-Ne-Ar-branch} (e).
For (H$_2$O)$_{7, 11, 12}$UH$^+$, the intensities for the heaviest fragments are overestimated.
From Figures \ref{MS-BR-1w-4w-Ne-Ar-branch}, \ref{MS-BR-5w-11w-Ne-Ar-branch} and \ref{MS-BR-12w-Ne-branch}, it is clear that the smaller the cluster (except Figure \ref{MS-BR-1w-4w-Ne-Ar-branch} (b)) is, the better the agreement between the simulated and experimental branching ratios is. This trend indicates that for small clusters, \textit{i.e.} for $n=1-6$,
short simulation time is enough to capture the full dissociation pattern, in other words, the dissociation mechanism is direct with no noticeable contribution of long term evolution. However, for larger clusters, starting at $n$=7, owing to the larger number of degrees of freedom, short simulation time does not capture the full dissociation pattern, \textit{i.e.} long term statistical dissociation is more
likely to play a noticeable role. This is fully in line with the conclusions obtained in section~\ref{large} for (H$_2$O)$_{12}$UH$^+$
and refine the interpretation given in section~\ref{small} for (H$_2$O)$_{7}$UH$^+$. This also shows that although the data presented
in section~\ref{large} for (H$_2$O)$_{11}$UH$^+$ do no evidence the contribution of structural re-arrangements on the short
time scale, they are very likely to occur as in (H$_2$O)$_{12}$UH$^+$.
One has to keep in mind that modeling the complete duration of the experiment (up to $\mu$s) is out of reach with MD/SCC-DFTB simulations. In this work, the simulation time was 15~ps, for all cluster sizes. Large fragments such as (H$_2$O)$_{6-12}$UH$^+$
may lose more water molecules if long enough simulation time were available, as suggested from the time dependent evolution of selected trajectories in section~\ref{time}. To certify this, the total energy of (H$_2$O)$_6$UH$^+$ fragments at SCC-DFTB level is calculated originating from the dissociation of (H$_2$O)$_7$UH$^+$ (7d) from all the 1421 trajectories producing fragment (H$_2$O)$_6$UH$^+$ over the total 600 $\times$ 15 trajectories. Then the energies of the lowest-energy isomer of (H$_2$O)$_5$H$^+$ and H$_2$O at SCC-DFTB level are subtracted. The deduced relative
energies $\Delta E$ are reported in Table~\ref{tab:fragenergy} for five cases. When $\Delta E$ is greater than zero, it is possible for
the (H$_2$O)$_6$UH$^+$ fragment to lose a water molecule. The percentage of $\Delta E$ being positive in all the trajectories leading to fragment (H$_2$O)$_6$UH$^+$ is 53.0~\%, which indicates that many (H$_2$O)$_6$UH$^+$ fragments have still the potential to
lose one more water molecule after the end of the simulation.
\begin{table}
\begin{center}
\caption{Energies of different (H$_2$O)$_6$UH$^+$ fragments selected from the dissociation of 7d at SCC-DFTB level, and the lowest energies (H$_2$O)$_5$UH$^+$ and (H$_2$O) at SCC-DFTB level. The relative energy $\Delta E$ = $E_{(H_2O)_6UH^+}$ -($E_{(H_2O)_5UH^+}$ +$ E_{H_2O}$). All energies here are given in eV.}
\label{tab:fragenergy}
\begin{tabular}{|c|c|c|c|}
\hline
\textbf{\boldm{$E_{(H_2O)_6UH^+}$}} & \textbf{\boldm{$E_{(H_2O)_5UH^+}$}} & \textbf{\boldm{$E_{H_2O}$}} & \textbf{\boldm{$\Delta E$}}\\
\hline
-44.310 & -40.312 & -4.057 & 1.605 \\
\hline
-44.322 & -40.312 & -4.057 & 1.279\\
\hline
-44.307 & -40.312 & -4.057 & 1.687 \\
\hline
-44.344 & -40.312 & -4.057 & 0.680 \\
\hline
-44.373 & -40.312 & -4.057 & -0.109\\
\hline
\end{tabular}
\end{center}
\end{table}
\subsection{Conclusions about CID of (H$_2$O)$_{n}$UH$^+$} \label{Concl}
Collision-induced dissociation of protonated uracil water clusters (H$_2$O)$_{1-7, 11, 12}$UH$^+$
at constant center of mass collision energy has been investigated by molecular dynamics simulations
using the SCC-DFTB method. The very good agreement between the simulated and measured $P_{NUL}$
and $\sigma_{frag}$ as well as branching ratios indicate that the essence of the dissociation induced by collisions is well captured by the simulations.
The $P_{NUL}$ values from the different isomers of the (H$_2$O)$_{1-7}$UH$^+$ cluster show that
the localization of the excess proton after dissociation is strongly determined by the initial configuration of the isomer undergoing the collision. This suggests that (H$_2$O)$_{1-7}$UH$^+$ aggregates primarily engage a direct dissociation path after collision that takes place on a very short time scale, \textit{i.e.} lower than 15~ps. More strikingly, in most cases, the proposed lowest-energy isomer does not lead to the best fit to the experiment. However, the relative energy between the lowest-energy isomers and the isomers best fitting to the experiment is less than 1.0 kcal.mol$^{-1}$ for (H$_2$O)$_{1-4, 7}$UH$^+$ clusters and less than 2.7 kcal.mol$^{-1}$ for (H$_2$O)$_{5,6}$UH$^+$ clusters. This is in line with the strong sensitivity of the collision outcome with the nature of the isomer undergoing the collision. This even suggests that the LEP can help in determining the main characteristic of the isomer involved in the collision. For (H$_2$O)$_{11, 12}$UH$^+$, these conclusions do not apply any more which shows that significant structural rearrangements occur after collision. This is confirmed by the time-dependent proportion of fragments which continue to vary even at 15~ps for (H$_2$O)$_{11, 12}$UH$^+$ whereas it is almost flat for (H$_2$O)$_{1-7}$UH$^+$.
Analysis of the fragment branching ratios helps in clarifying these points. Indeed, for the smallest clusters, (H$_2$O)$_{1-5}$UH$^+$, the short simulation time well reproduces the corresponding experimental
results which is in line with a direct mechanism. In contrast, for (H$_2$O)$_{6-7}$UH$^+$, although $P_{NUL}$ is well reproduced by the simulations, the experimental and theoretical branching ratios differ which show that more time is needed to properly describe the dissociation. For (H$_2$O)$_{11, 12}$UH$^+$, neither theoretical nor experimental branching ratios and $P_{NUL}$ are in agreement which is a strong indication that a significant contribution of structural rearrangements occur; This suggests that a contribution of a statistical mechanism is more likely to occur for larger species such as (H$_2$O)$_{11, 12}$UH$^+$.
This work demonstrates that explicit molecular dynamics simulations performed at a quantum chemical
level can provide a wealth of information about collision-induced mechanism in molecular clusters, in particular, hydrated molecular species. Such simulations thus represent a key tool to complement CID experiments and hope the present study will motivate similar computational studies on future CID experiments of hydrated molecular aggregates.
%In a near future, we think it would be of great interest to pursue this study by looking at the influence of collision energy, both lower or higher, on the dissociation mechanism as a function of the cluster size. Furthermore, inclusion of nuclear quantum effects in the simulations could also help to increase the accuracy of the model and improve the comparison with the experiments.
\section{Dynamical Simulation of Collision-Induced Dissociation for Pyrene Dimer Cation}
\subsection{Introduction}
PAH clusters have been investigated in several scientific fields.
In combustion science, the role of PAH clusters in combustion processes is still under debate, in particular they might or not be the intermediate systems in the growth of soot particles. \cite{Chung2011, Saggese2015, Eaves2015, Mao2017, Wang2018}
In atmospheric and environmental science, PAHs are known as the pollutants, which is harmful to human health. For instance, the carcinogenic PAHs associated with particulate matter in air pollution has showed clear evidence of genotoxic effects, such as DNA adducts, chromosome aberrations. \cite{Kyrtopoulos2001, Farmer2003}
In new energy resources field, for the understanding of the properties of organic crystal or the design of new organic solar cell devices, PAH stacks are investigated as the prototypes.\cite{Aumaitre2019}
In astrophysics, PAHs species are believed to be ubiquitous and abundant in the interstellar medium because of their compact and stable structure. \cite{Tielens2008} The PAH clusters are important contributors to the diffuse interstellar bands and UV-visible absorption bands. PAH clusters have been proposed to be the origin of a series of infrared emission bands, which are ubiquitous in the Universe. \cite{Leger1984,Allamandola1985} The broadening of these bands in regions protected from the star's UV flux suggests the following scenario: PAHs are trapped in clusters in UV-protected regions and photo-evaporated by star's UV photons in the so-called photodissociated region. \cite{Rapacioli2005, Berne2008} For all these topics, it is necessary to make a better understanding of the fundamental properties of PAH clusters. The crucial quantities are the stability, molecular growth processes, dissociation energies and their evolution with PAH charge, species, cluster size.
The investigation of PAH clusters has been performed in experiment. Many studies focused on the investigation of structural properties of these clusters at the most stable geometrical configurations
\cite{Eschenbach1998, Schmidt2006, Goulart2017, Wang2018, Lei2019}. Their energetic properties such as ionisation potentials have been recorded \cite{Joblin2017} as well as their spectral properties \cite{Roser2015,Lemmens2019}.
clusters may evaporate, breaking the PAH units themselves or leading to chemical reactivity between the different units, which shows the role of PAH clusters in the growth of PAHs themselves.
If free flying PAHs are possibly from the evaporation of larger clusters, then this calls for more experimental data on their dissociation properties.
The evolution of PAH clusters has been explored from experiments following the evaporation after absorption of UV photons, collision with low or high energetic particles or in a high-pressure environment. \cite{Schmidt2006, Holm2010, Gatchell2015, Joblin2017, Gatchell2017, Zamith2019thermal}
The range of collision energies considered experimentally is quite large, ranging from eV to high energy collision at a few keV. Low energy collision experiments allow for the derivation of dissociation energies \cite{Zamith2019thermal} whereas the oligomerization of PAHs within the cluster induced by high energy collisions \cite{Delaunay2015} or photoabsorption \cite{Zhen2018} suggests the possible role of clusters in the interstellar PAHs growth process \cite{Chen2018}.
The quantitative data from experiments of PAH clusters are still rather limited, which motivates the modeling studies of them. In the calculation of PAH clusters, the size of the systems limits the use of {\it ab initio} wave function methods to the investigation of properties of the smallest clusters, namely dimers \cite{Piacenza2005, Birer2015}, whereas larger clusters can be addressed either at the DFT level or with more semi-empirical schemes \cite{Zhao2008truhlar, Rapacioli2009corr, Mao2017, Bowal2019}. Many of these studies, focused on structural properties, evidence a stacking growth process in agreement with experimental results. In addition, IR properties were also reported at the DFT level \cite{Ricca2013}. Most of the theoretical studies involve neutral clusters, mostly due to the fact that treating charge resonance process in ions is a challenging task for DFT based methods \cite{Grafenstein2009}. The singly charged PAH clusters are more stable than their neutral counterparts due to charge resonance stabilization.\cite{Rapacioli2009} Cationic PAH clusters are expected to be abundant in the photo-dissociation regions because the ionization energy of the PAH cluster is lower than that of the isolated PAH, which leads to the efficient formation of cationic PAH clusters. In addition, the ionized PAH clusters are easier to control, so it is more important to study them. It should be mentioned the recent studies computing ionisation potentials \cite{Joblin2017} as well as structural \cite{Dontot2019} and spectral (electronic \cite{Dontot2016} and vibrational \cite{Dontot2020}) properties of cations, performed with an original model combining DFTB \cite{Porezag1995,
Seifert1996, Elstner1998, Spiegelman2020} with a configuration interaction scheme\cite{Rapacioli2011}.
With respect to these studies, very few is known about the dynamical aspects of PAH clusters carrying internal energy. High energy collisions of PAH clusters with energetic ions have been simulated by Gatchel {\textit et al.} \cite{Gatchell2016, Gatchell2016knockout} at the semi-empirical and DFTB levels.
Recently experiments at lower collision energies were performed by Zamith \textit{et al.} from LCAR \cite{Zamith2020threshold} (the principle of this experiment and the experimental setup were shown in sections \ref{principleTCID} and \ref{EXPsetup}), which were analysed by treating statistically the dissociation after collision energy deposition. Namely, the dissociation rate of pyrene clusters has been computed using phase space theory (PST)\cite{Zamith2019thermal}. A fair agreement with experimental results was obtained concerning the collision energy dependence of the dissociation cross section. However, the employed model failed at reproducing in details the shape of the peaks in the time-of-flight (TOF) spectra. In this section, it is aimed at extending the description of such low energy collision processes (less than several tens of eV) combining a dynamical simulations to describe the fast processes in addition to the statistical theory to address dissociation at longer timescales. With this approach, (i) good agreement between simulated and experimental mass spectra will be shown, thus validating the model, (ii) dissociation cross sections as a function of the collision energy is derived, (iii) the kinetic energy partition between dissociative and non-dissociative modes will be discussed and (iv) the energy transfer efficiency between intra and intermolecular modes will also be discussed.
% \ref{sec:compapp},
\subsection{Calculation of Energies}
In the analysis, we will discuss the kinetic energy contributors, applying the following decomposition of the total kinetic energy $E^k_{tot}$ of the dimer:
\begin{align}
\label{Eparti}
E^k_{tot}&=E^k_{Ar} + E^k_{td} + E^k_{Py^1} + E^k_{Py^2} + E^k_{Re} \nonumber \\
E^k_{tot} &=\frac{1}{2}\sum_{i=1}^{52}m_i(\Vec{v}_i)^2 \nonumber \\
E^k_{Ar} &= \frac{1}{2}m_{Ar}\Vec{v}_{Ar}^2 \nonumber \\
E^k_{td} & =\frac{1}{2}m_{Py_2}\Vec{v}_t^2(Py_2) \\
E^k_{Re} &= \frac{1}{2} \frac{m_{Py^1}m_{Py^2}}{m_{Py^1}+m_{Py^2}}(\Vec{v}_t(Py^2)-\Vec{v}_t(Py^1))^2 \nonumber \\
E^k_{Py^n} &= \frac{1}{2}\sum_{i=1}^{{26}}m_i^n (\Vec{v}_i^n-\Vec{v}_t(Py^n))^2 \nonumber
%\label{Eparti}
\end{align}
In these equations and in the following, $Py_2$ refers to the pyrene dimer (possibly dissociated) whereas $Py^1$ and $Py^2$ refer to the first and second monomers, respectively. $E^k_{tot}$ can be also calculated from the masses $m_i^n$ and velocities $\Vec{v}_i$ of its atoms. $E^k_{Ar}$ refers to the kinetic energy of the argon (with mass $m_{Ar}$ and velocity $\Vec{v}_{Ar}$).
$E^k_{td}$ is the translation kinetic energy of the dimer (with mass $m_{Py_2}$ and velocity $\Vec{v}_t(Py_2)$).
$E^k_{Re}$ is the relative kinetic energy of the two pyrene monomers, computed from their masses of $m_{Py^1}=m_{Py^2}$ and monomer global translation velocities $\Vec{v}_t(Py^{n=1,2})$.
$E^k_{Py^{n}}$ is the rovibrational kinetic energy of the monomer $n$ computed from the masses and velocities of its atoms ($m_i^n$ and $\Vec{v}_i^n$, respectively).
The intramolecular vibrational kinetic energy ($E^k_{intra^{n}}$) of monomer $n$ obtained after removing the contributions associated to the monomer translation and rotation modes is calculated as follows:
\begin{align}
E^k_{intra^n}&=
\frac{1}{2}\sum_{i=1}^{{26}}m_i^n (\Vec{v}_i^n-\Vec{v}_t(Py^n)-\Vec{v}_{ir}^n)^2
\label{Eintra}
\end{align}
where $\Vec{v}_{ir}^n$ is the velocity of atom $i$ associated to the monomer global rotation.
In addition, the dimer intermolecular kinetic energy ($E^k_{inter}$) is calculates as follows:
\begin{align}
E^k_{inter}&=E^k_{tot}-E^k_{Ar}-E^k_{td}-E^k_r-E^k_{intra^1}-E^k_{intra^2}
\label{Einter}
\end{align}
where $E^k_r$ refers to the rotation kinetic energy of the dimer.
$\Vec{v}_{ir}^n$ and $E^k_r$ are calculated using the following formulas.
\begin{align}
\Vec{L}(Py^n) &= \sum_{i=1}^{26}m_i^n (\Vec{r}_i^n-\Vec{r}_{_{CM}}(Py^n)) \times (\Vec{v}_i^n-\Vec{v}_t(Py^{n})) \nonumber \\
\Vec{L}(Py_2) &= \sum_{i=1}^{52} m_i (\Vec{r}_i-\Vec{r}_{_{CM}}(Py_2)) \times (\Vec{v}_i-\Vec{v}_t(Py_{2})) \nonumber \\
I &= mr^2 \nonumber \\
\Vec{\omega} &= [I]^{-1} \times \Vec{L} \nonumber \\
\Vec{v}_{ir}^n &= \Vec{\omega}(Py^n) \times (\Vec{r}_i^n - \Vec{r}_{_{CM}}(Py^n)) \\
E^k_{tot^n} &=E^k_{r^n} + E^k_{td^n} + E^k_{intra^n} \nonumber \\
E^k_{tot^n} &=\frac{1}{2}\sum_{i=1}^{26}m_i^n(\Vec{v}_i^n)^2 \nonumber \\
E^k_{td^n} &=\frac{1}{2}m_{Py^n}\Vec{v}_t^2(Py^n) \nonumber \\
E^k_{r} &= \frac{1}{2} \Vec{\omega}(Py_2) \times [I](Py_2) \times\Vec{\omega}(Py_2) = \frac{1}{2} \Vec{L}(Py_2) \times [I]^{-1}(Py_2) \times \Vec{L}(Py_2) \nonumber \\
\label{Erotation}
\end{align}
$E^k_{tot^n}$ is the total kinetic energy of monomer $n$.
$E^k_{td^n}$ is the translation kinetic energy of pyrene monomer $n$.
$\Vec{L}(Py^n)$ is the angular momentum of pyrene monomer $n$.
$\Vec{L}(Py_2)$ is the angular momentum of the dimer.
$[I]$ refers to the moment of inertia tensor.
$[I]^{-1}$ is the inverse of $[I]$.
$\Vec{\omega}$ is the angular velocity.
$\Vec{r}_{i}^n$ and $\Vec{r}_{_{CM}}(Py^n)$ denote the coordinates of atom $i$ and center of mass of dimer of monomer $n$, respectively.
$\Vec{r}_{i}$ and $\Vec{r}_{_{CM}}(Py_2)$ and denote the coordinates of atom $i$ and center of mass of dimer, respectively.
From the endpoint of the simulation, we can also compute the total energy transferred towards internal rovibrational modes of the pyrene dimer as:
\begin{equation}
\Delta E_{int}^{Py_2} = E^{k,0}_{Ar} - E^k_{Ar} - E^k_{td}
\end{equation}
where $E^{k,0}_{Ar}$ is the initial argon kinetic energy whereas $E^k_{Ar}$ and $E^k_{td}$ correspond to kinetic energies at the end of the MD simulation.
In the case of dissociated dimers at the end of the simulations, we can also deduce the energy deposited in the rovibrational modes of the monomers as:
\begin{equation}
\Delta E_{int}^{Py^1+Py^2} = E^{k,0}_{Ar} - E^k_{Ar} - E^k_{td} - E^k_{Re}
\end{equation}
\subsection{Simulation of the Experimental TOFMS}
The experimental TOFMS are reproduced by simulating the ion trajectories through the experimental setup in the presence of the electric fields. These are calculated by solving numerically the Laplace equation. Equations of motion are integrated using the fourth order Runge-Kutta method with adaptive step size. The occurrence of collision or dissociation is decided at each time step of the ion trajectory based on the collision and dissociation probabilities.
In the work of Zamith {\textit et al.}, \cite{Zamith2020threshold} the energy transfer was treated upon collision by using the Line of Center model (LOC) \cite{Levine1987}. In the LOC model, the transferred energy is the kinetic energy along the line of centers. Evaporation rates were then estimated using PST, in which only statistical dissociation to be possible after energy deposition in the cluster by collision was conside. Although this approach, which will be referred to as PST in the following, has been proved to be able to satisfactorily reproduce CID cross section experiments,\cite{Zamith2020threshold} it fails to reproduce in details the shape and position of the fragment peaks in the TOFMS, as will be shown in section \ref{sec:MS}.
In order to better reproduce the position and peak shapes, the MD and PST methods were combined. The outputs of the MD simulations were used to treat the collisions in the ion trajectories. At each time step the probability for a collision is evaluated. The principle of MD+PST is displayed in Figure \ref{MDPST}.
\figuremacrob{MDPST}{Principle of MD+PST.}
One MD trajectory (with proper weighting of the $b$ values) was randomly picked from all outputs of MD simulations at a given collision energy. Then two cases have to be considered. First, if the dissociation occurred during the picked MD calculation (short time dissociation), then we use the MD final velocities of the fragments to further calculate the ion trajectories. On the other hand, if the pyrene dimer is still intact at the end of the picked MD calculation, then we update the dimer velocity and use the collision energy transfer $\Delta E_{int}^{Py_2}$ deduced from the MD calculation to increase the internal energy of the cluster. The dissociation rate resulting from this new internal energy is then evaluated using PST.
In the latter case, if dissociation occurs (long time dissociation), the relative velocities of the fragment are evaluated using the PST outcome. The whole process of MD+PST is performed many times for different trajectories to ensure the reliability of the final obtained data. For each time, the TOFMS of Py$^+$ or Py$_2^+$ is updated.
%Then we can obtain the update TOFMS histogram of the monomer cation Py$^+$ from the short and long time dissociation.
Here we emphasize that, due to the short time scale of the MD calculations (3 ps), only direct dissociation can be captured by the MD simulations. Therefore, one has to evaluate the probability of dissociation at longer time scales after the energy deposition by collision. This is done here by considering that at longer time scales, dissociation occurs statistically and is treated by using PST.
\subsection{\label{sec:results}Results and Discussion}
In the following, we will discuss the dissociation at short, experimental and infinite timescales. The first two ones correspond to dissociation occurring during the MD simulation only or with the MD+PST model. The dissociation at infinite time accounts for all MD trajectories where the amount of energy transferred to the internal dimer rovibrational modes $\Delta E_{int}^{Py_2}$ is larger than the dissociation energy of 1.08~eV (value from references \cite{Dontot2019, Zamith2020threshold}). It can be regarded as the dissociation occurring after an infinite time neglecting any cooling processes, such as thermal collisions or photon emissions.
\subsubsection{\label{sec:MS}TOFMS Comparison}
An example of TOFMS is given in Figure~\ref{expTOF}. Figure~\ref{expTOF}(a) is centered around the intact parent mass (Py$_2^+$) whereas in (b) is displayed the region around the fragment peak (Py$^+$).
In Figure~\ref{expTOF}(a) are displayed three curves corresponding to the experimental one and the results of the two simulations (PST and MD+PST) for the parent ion. One can see that the peak shape and position are properly reproduced using the simulations; therefore, the essential of the ion propagation is captured by the simulations. Although some of the detected parent ions have undergone a collision without dissociation, no difference is seen in the parent peak since the collision rate is kept very small.
\figuremacrob{expTOF}{Normalized time of flight mass spectra of the parent pyrene dimer cation (a), and the pyrene fragment Py$^+$ (b) resulting from the collision of Py$_2^+$ with argon at a center of mass collision energy of 17.5~eV. The black line is for the experimental result whereas red and green curves are the MD+PST and PST model results. The blue curve is the PST subcontribution of the MD+PST model.}
%\figuremacro{2}{}
In Figure~\ref{expTOF}(b), the experimental result is compared to the PST and MD+PST simulations. Clearly, the PST based simulation fails to reproduce both the position and the shape of the peak. On the other hand, a much better agreement is found when using the output of the MD+PST simulations. This agreement is a good indication that this scheme captures the essence of the pyrene dimer cation dissociation induced by argon collisions at this collision energy. Actually, in this scheme, the largest contribution to the TOFMS results from dimers dissociating on short timescales, $i.e.$ during the MD simulation. The remaining contribution, $i.e.$ resulting from dimers dissociating at longer timescales and computed from the second step PST calculation, is minor and represented in blue in Figure \ref{expTOF}(b).
\subsubsection{\label{sec:MDanalysis}Molecular Dynamics Analysis}
\textbf{Description of selected trajectories}
A first qualitative description of the collision processes can be obtained from the analysis of some arbitrarily selected MD trajectories. Figure \ref{collisions} (top and bottom) reports some snapshots extracted from two trajectories with the same collision energy (17.5~eV) and impact parameter (3.5~\AA). Only the top one leads to the Py$_2^+$ dissociation. During the results collection, we extract the final snapshot for each trajectory and consider that the dimer is dissociated if the distance between the two monomers molecular mass centers is larger than 10~\AA.
Figures \ref{collisions}-1/1* represent the system after its preliminary thermalization, when the argon atom introduced in the simulation with its initial velocity.
Figures \ref{collisions}-2/2* and 3/3* represent the beginning and end of the collision. From these points, the two trajectories show different behaviors.
For the top trajectory in Figure \ref{collisions}, snapshot 5 corresponds to the step where the two pyrene monomers start to go away from each other. After this, the intermolecular distance continues to increase further in snapshot 6. For the bottom trajectory in Figure \ref{collisions}, Figures \ref{collisions}-5* and 6* correspond to the middle and ending snapshots of the simulation, respectively. The snapshots 4*,~5* and 6* show the process of energy redistribution within the clusters. In particular, the soft modes associated to global deformation of the molecular planes appear to be excited.
\figuremacrob{collisions}{Snapshots for two different molecular dynamics trajectories. Top and bottom: trajectories with impact parameter of 3.5~\AA{} and a collision energy of 17.5~eV, leading to dissociation and non-dissociation (top and bottom, respectively).}
From these two particular cases, it can be seen that the evolution of the trajectory either toward a dissociation or a redistribution of the transferred energy strongly depends on the process of energy transfer during the collision. In the top trajectory in Figure \ref{collisions}, the argon atom is pushing the two monomers far away from each other, $i.e.$ the transferred energy is mostly localised in an intermolecular dissociative mode. On the opposite, in the bottom trajectory in Figure \ref{collisions}, the collision mostly involves an intramolecular soft vibrational mode.
The transferred energy is then redistributed over all the other modes. The statistical distribution
of this energy is then hardly favorable to the dissociation due to the large number of
intramolecular modes (72 per pyrene) with respect to the 6 intermolecular modes, only 3 of them (1 breathing and 2 parallel displaced modes) being dissociative modes.
The amount of transferred energy is also a major ingredient for the fate of the cluster. Depending on the details of the collision such as impact parameter or cluster orientation, very different amounts of energy can be transferred.
This is illustrated in Figure~\ref{distriPerc-Etf-175eV-d-bin03} where the distribution of transferred energy $\Delta E_{int}^{Py_2}$ restricted to trajectories
that would dissociate after infinite time, is plotted for simulations at the experimental collision energy of 17.5~eV. This distribution could hardly be guessed without a dynamical description of the collision at the atomic level. Indeed, a simpler model such as the LOC model (used in the pure PST approach) would lead to a constant distribution between the binding energy and the maximum collision energy as shown in Figure \ref{distriPerc-Etf-175eV-d-bin03}. In the distribution resulting from MD simulations, lower transferred energies are favored with respect to the distribution extracted from the LOC model.
All these effects are intrinsically taken into account in the MD simulations on the opposite to the pure PST model, explaining the better agreement of the MD+PST scheme with the experimental results.
% 1/17.5=x*(17.5-1.08)
\figuremacro{distriPerc-Etf-175eV-d-bin03}{Distribution of transferred energy in rovibrational modes $\Delta E_{int}^{Py_2}$ for trajectories leading to dissociation at the end of MD (center of mass collision energy of 17.5~eV). The dashed line shows the distribution of transferred energy used in the LOC model.}
Finally, we note that the pyrene monomers remained intact (no fragmentation) up to collision energies of 25~eV.
The snapshots of a fragmentation trajectory at collision energy of 27.5~eV are shown in Figure \ref{fragmentation}.
It can be seen that the pyrene molecule impacted by the argon undergoes an opening of an aromatic cycle and the loss of two hydrogen atoms, leaving as a H$_2$ molecule.
As the study of monomer's fragmentation is beyond the scope of the present paper, we will focus on trajectories with collision energies below this fragmentation threshold energy in the following.
\figuremacrob{fragmentation}{Snapshots for molecular dynamics trajectory with impact parameter of 0.5~\AA{} and a collision energy of 27.5 eV leading to intramolecular fragmentation.}
\textbf{Dissociation cross section}
The opacity curves are presented in Figure \ref{opacitycurves} for various collision energies.
At low impact parameters, the dissociation is very efficient even at low collision energy. At the lowest collision energy of 2.5~eV, the opacity curve presents a smooth decrease from 2 to 5~\AA, whereas for collision energies larger than 10~eV, all curves are very similar. These high energy curves show high dissociation probability below 3.5~\AA, reach 50\% at about 4.5~\AA{} and drop to zero for values larger than 5.5~\AA. These values can be compared to the van der Waals radius of argon (1.88~\AA) plus half of (i) the distance between the two molecules centers of masses (3.04~\AA), (ii) the smallest (6.82~\AA) or (iii) largest pyrene axes (9.25~\AA) leading to distances of 3.40, 5.29 and 6.50~\AA, respectively. Below 3.40~\AA, all trajectories involve a frontal impact of the argon on the dimer carbonaceous system and almost all of them lead to dissociation. Unexpectedly, the opacity curve drops to zero at 5.5~\AA{} which is lower than the largest computed value of 6.5~\AA. Interestingly, taking the largest distance between carbon atoms in pyrene (7.0~\AA) instead of that between hydrogen atoms (9.25~\AA) leads to a value of 5.4~\AA{} which is in line with the opacity curves. This suggests that the dissociation is efficient only if the carbonaceous skeleton area is impacted, the impact in the region of external hydrogen atoms resulting mostly in an intramolecular C-H mode excitation at the expense of dissociative modes. As a conclusion, it seems that for energies larger than 10~eV, the opacity curves are similar as they are driven by simple geometric rules, in other words, if the dimer receives a direct impact of the argon on the carbonaceous skeleton area, it will dissociate. Interestingly, this seems to be in agreement with previous works \cite{Chen2014, Gatchell2016knockout} which also pointed out the efficient nuclear stopping power of carbon atoms in a very different context (higher energy collisions leading to knock-out process).
\figuremacro{opacitycurves}{Opacity curves as a function of the impact parameter $b$ for several selected center of mass collision energies.}
The blue curve in Figure \ref{cross-section} shows the MD dissociation cross sections of pyrene dimers obtained from the opacity curves following eq. \ref{integ}. It presents a steep increase for energies bellow 7.5~eV before remaining almost constant around 65~\AA$^2$ for collision energies greater than 10-15~eV. This is a direct consequence from the already discussed similarity of opacity curves for the high collision energies.
The purple curve corresponds to dissociation at infinite timescales. Figure \ref{cross-section} also reports the cross sections computed from the MD+PST model.
It can be seen that, for low collision energies, the MD and MD+PST cross sections are very close, indicating that most of the dissociations occur on the short timescales. On the opposite, at high collision energies, a non-negligible fraction of the dimers, which are not dissociated at the end of the MD simulation, carry enough energy to evaporate on the experimental timescales.
At the experimental center of mass collision energy of 17.5~eV, the MD+PST cross section (about 70~\AA$^2$) is slightly above the pure MD dissociation ratio, which indicates that the dissociation at long timescales represents a small fraction of the dissociated pyrene dimers as already seen from the TOF spectra analysis (see Figure \ref{expTOF}).
We have also plotted in Figure~\ref{cross-section} the model cross section $\sigma_\infty$ that successfully reproduced the threshold collision-induced dissociation experimental results \cite{Zamith2020threshold}. This model cross section is obtained by considering that the collision energy transfer is given by the LOC model and the expression for the cross section is given by:
\begin{equation}
\sigma_{LOC}(E_{col}) = \sigma_0 (E_{col} - D)/(E_{col}).
\end{equation}
where $D=1.08$~eV is the dissociation energy \cite{Dontot2019, Zamith2020threshold} and $\sigma_0=63$~\AA$^2$ is a scaling factor usually thought as the geometrical cross section. This model cross section is usually further convolved with dissociation rates, collision energy distributions and internal energy distributions in order to be compared with experimental results. However, since here for the theoretical calculations there is no collision energy distribution, this curve could in principle be directly compared with the purple one in Figure~\ref{cross-section}, namely the cross section for infinite time.
One can see that the MD, MD+PST results and the model cross section have similar collision energy dependence. The magnitude of the two cross sections is rather different at high collision energy, with about 60~\AA$^2$ and 74~\AA$^2$ for the model and infinite timescale cross sections respectively. Nevertheless, this difference is probably within the error bars of the experimental cross section measurement.
The dissociation cross sections for MD timescales with time step being 0.1 fs at collision energy of 20 and 25 ~eV ($\sigma_\mathrm{MD}$(0.1)) in Figure~\ref{cross-section} are close to the ones of time step being 0.5 fs ($\sigma_\mathrm{MD}$), which indicates a time step of 0.1 fs used in the MD simulation does not change significantly the corresponding dissociation cross section.
\figuremacro{cross-section}{Dissociation cross sections of Py$_2^+$ after collision with argon as a function of center of mass collision energy for the short (MD), experimental (MD+PST) and infinite timescales. Cross sections resulting from the LOC model are also plotted. $\sigma_\mathrm{MD}$ (0.1) denotes the dissociation cross section for short (MD) timescale with a time step of 0.1 fs.}
\textbf{Energy partition}
The mean value obtained for the transferred energy after removing the translation kinetic energy of the dimer, namely $\Delta E_{int}^{Py_2}$, is plotted in Figure \ref{transferredE-Ar-300} as a function of the collision energy. Although this quantity evolves almost linearly with the collision energy, the curves are different when one considers only the trajectories leading to dissociation or non-dissociation.
For trajectories where the dimer does not dissociate, $\Delta E_{int-ud}^{Py_2}$ remains small for all collision energies below 20~eV and shows a very slight increase for collision energies larger than 20~eV.
For trajectories leading to dissociation, $E_{int-d}^{Py_2}$ grows almost linearly, but above 10-15~eV most of the absorbed energy is actually used to heat the individual monomers (the green curve) whereas the energy given in the dissociative mode (difference between the blue and green curves) remains almost constant.
We note that, despite the trends of the mean energy values derived from all simulations or restricted to the undissociated cases are interesting, their absolute values have small meaning as they depend on the arbitrarily chosen $b_{max}$ value, {\it i.e.} increasing $b_{max}$ would result in more undissociated trajectories with less and less energy transfer. On the opposite, absolute values of mean energies for the dissociation trajectories are relevant, as increasing the $b_{max}$ value would not result in new dissociation trajectories.
For MD simulations with time step being 0.1 fs at collision energy of 20 and 25 ~eV, the corresponding energies in Figure~\ref{transferredE-Ar-300} are close to the ones of time step being 0.5 fs, which indicates a time step of 0.1 fs used in the MD simulation does not change significantly the corresponding deposition of the total transferred energy.
\figuremacro{transferredE-Ar-300}{At the end of the MD collision simulations with a time step of 0.1 and 0.5 fs, the total transferred energy $\Delta E_{int}^{Py_2}$ to the rovibrational modes or restricted to the sole dissociated ($\Delta E_{int-d}^{Py_2}$) or undissociated ($\Delta E_{int-ud}^{Py_2}$) pyrene dimers as a function of collision energy. The transeferred energy to the monomers rovibrational modes for the dissociated dimers $\Delta E_{int-d}^{Py^1+Py^2}$ is also plotted.}
It is also interesting to focus on the kinetic energy partition, in particular because its decomposition in sub-contributions (dissociative vs non-dissociative modes) is easier (see eqs. \ref{Eparti}) than that of the potential (and consequently total) energy.
For each simulated collision energy, the values for the kinetic energy sub-contributions (eqs. \ref{Eparti}) are averaged over all the trajectories and reported in Table \ref{tab:table1} and Figure \ref{Epartition-Ar-300-SP}.
In addition, the averaged kinetic energy sub-contributions are also calculated over the dissociated and undissociated trajectories separately for each simulated collision energy. Then sum the contributions of dissociated and undissociated trajectories (black curves in Figure \ref{Epartition-Ar-300-SP}) calculated by the following eqs \ref{separately},
\begin{align}
\label{separately}
E_{1}^k &=E_{td-d}^k*P+E_{td-ud}^k*(1-P) \nonumber \\
E_{2}^k &=E_{Re-d}^k*P+E_{Re-ud}^k*(1-P) \\
E_{3}^k &=(E_{Py^1}^k + E_{Py^2}^k)_{-d}*P+(E_{Py^1}^k + E_{Py^2}^k)_{-ud}*(1-P) \nonumber
\end{align}
where $P$ refers to the dissociation probability at a given center of mass collision energy.
The results of sum the contributions of dissociated and undissociated trajectories are the same with the ones over all the trajectories (see Figure \ref{Epartition-Ar-300-SP}).
This ensures our calculations for the mean kinetic energy sub-contributions are right.
\begingroup
\setlength{\tabcolsep}{6pt}
\renewcommand{\arraystretch}{1.1}
\begin{table}
\begin{center}
\caption{The kinetic energy partition after the collision of pyrene dimer with argon at different collision energies $E_{col}$. All energies are in eV.}
\label{tab:table1}
\begin{tabular}{|c|c|c|c|c|c|}
\hline
\boldm{$E_{col}$} & \boldm{$E^k_{td}$} & \boldm{$E^k_{Ar}$} & \boldm{$E^k_{Py^1}$} & \boldm{$E^k_{Py^2}$} & \boldm{$E^k_{Re}$} \\ [0.08cm]
\hline
2.5 & 0.17 & 1.67 & 0.25 & 0.25 & 0.19\\
\hline
5.0 & 0.30 & 3.52 & 0.40 & 0.41 & 0.41\\
\hline
7.5 & 0.42 & 5.38 & 0.55 & 0.56 & 0.64\\
\hline
10.0 & 0.53 & 7.32 & 0.71 & 0.70 & 0.80\\
\hline
12.5 & 0.65 & 9.20 & 0.89 & 0.88 & 0.95\\
\hline
15.0 & 0.74 & 11.20 & 1.03 & 1.03 & 1.06\\
\hline
% He & 17.5 & 0.15 & 15.40 & 0.56 & 0.55 & 0.26\\
% Ne & 17.5 & 0.52 & 11.95 & 1.07 & 1.08 & 0.84\\
17.5 & 0.82 & 13.16 & 1.16 & 1.22 & 1.18\\
\hline
20.0 & 0.89 & 15.12 & 1.37 & 1.32 & 1.30\\
\hline
22.5 & 0.96 & 17.09 & 1.52 & 1.51 & 1.36\\
\hline
25.0 & 1.01 & 19.18 & 1.61 & 1.69 & 1.45\\
\hline
% 27.5 & 1.09 & 21.16 & 1.78 & 1.83 & 1.49\\
% 30.0 & 1.16 & 23.01 & 2.09 & 1.98 & 1.54\\
\end{tabular}
\end{center}
\end{table}
\endgroup
\figuremacro{Epartition-Ar-300-SP}{Mean kinetic energy partition at the end of the MD simulations.}
The comparison of these kinetic energy sub-contributions between the time step being 0.1 and 0.5 fs used in the MD simulations is shown in Table \ref{tab:table2} and Figure \ref{Epartition-Ar-300-Tstep-01}, which indicate a time step of 0.1 fs almost didn't affect the results of kinetic energy sub-contributions.
\begingroup
\setlength{\tabcolsep}{6pt} % Default value: 6pt
\renewcommand{\arraystretch}{1.1} % Default value: 1
\begin{table}
\begin{center}
\caption{The kinetic energy partition and cross section at the end of MD simulations with time step being 0.1 and 0.5 at different collision energies of 20 and 25. All energies are in eV. Time step ($Tstep$) is in fs. Cross section $\sigma_{_{MD}}$ is in ~\AA.}
\label{tab:table2}
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
\boldm{$E_{col}$} & \boldm{$Tstep$} & \boldm{$E^k_{td}$} & \boldm{$E^k_{Ar}$} & \boldm{$E^k_{Py^1}$} & \boldm{$E^k_{Py^2}$} & \boldm{$E^k_{Re}$} & \boldm{$\sigma_{_{MD}}$} \\ [0.08cm]
\hline
20.0 & 0.1 & 0.89 & 15.18 & 1.34 & 1.35 & 1.28 & 64.11\\
\hline
20.0 & 0.5 & 0.89 & 15.12 & 1.37 & 1.32 & 1.30 & 64.45\\
\hline
25.0 & 0.1 & 1.03 & 19.04 & 1.71 & 1.67 & 1.44 & 62.86\\
\hline
25.0 & 0.5 & 1.01 & 19.18 & 1.61 & 1.69 & 1.45 & 64.77\\
\hline
% 30.0 & 1.16 & 23.01 & 2.09 & 1.98 & 1.54\\
\end{tabular}
\end{center}
\end{table}
\endgroup
\figuremacro{Epartition-Ar-300-Tstep-01}{Mean kinetic energy partition at the end of the MD simulations with time step being 0.5 fs at the center of mass collision energy from 2.5 to 25 eV. The mean kinetic energy partition with time step being 0.1 fs at center of mass collision energies of 20 and 25 eV are plotted with filled round circles.}
In Figure~\ref{prot-Ar-300} are reported the ratios of the pyrene dimer translational kinetic energy $E^k_{td}$, relative kinetic energy $E^k_{Re}$ and monomers rovibrational kinetic energies $E^k_{Py^1}+E^k_{Py^2}$ over the total pyrene dimer kinetic energy $E^k_{tot}-E^k_{Ar}$.
It clearly appears that, whereas the contribution of the dimer translation kinetic energy ($E^k_{td}$) remains almost constant (very slight decrease from about 20\% to 18\% of the dimer kinetic energy), this is not the case for the other two contributions. For collision energies below 7.5~eV, the proportion of the kinetic energy associated to the center of mass relative velocities increases whereas the opposite is observed for the monomers rovibrational kinetic energy. These two trends are reversed above 7.5~eV.
\figuremacro{prot-Ar-300}{Kinetic energy proportion after collision of Py$_2^+$ with argon as a function of collision energy.}
Again, it is convenient to analyse separately the kinetic energy partition for trajectories leading to dissociation or not as done in Figure \ref{Epartition-Ar-300-d-ud} for $E^k_{td}$, $E^k_{Re}$ and $E^k_{Py^1}+E^k_{Py^2}$.
For both dissociated and undissociated trajectories, the total energy in the system computed from the initial energy at 25 K (0.32 eV) plus the transferred energy is twice the final kinetic energy computed from velocities shown in Figure \ref{Epartition-Ar-300-d-ud} (black curves). This is exactly what one should expect from the Virial theorem.
%which proves that the calculations of kinetic energy are as good as the dynamics.
In the absence of dissociation, the transferred energy is either small or redistributed over all the vibrational modes of the dimer, leading to small values for $E^k_{Re-ud}$ (mean value always below 0.04~eV). The monomers rovibrational kinetic energies remain constant with an increase for collision energies above 20~eV, indicating that the slight increase of transferred energy results in a heating of the monomers, as already inferred from Figure \ref{transferredE-Ar-300}.
Once a dimer dissociates, the two pyrene molecules relative kinetic energy $E^k_{Re-d}$ can not be transferred back to the intramolecular modes and its mean value is never negligible with respect to the monomers rovibrational kinetic energies $(E^k_{Py^1}+E^k_{Py^2})_{-d}$. However, although the slope of $(E^k_{Py^1}+E^k_{Py^2})_{-d}$ remains constant with collision energies, that of $E^k_{Re-d}$ decreases clearly. This is in line with the analysis of Figure \ref{transferredE-Ar-300}, which shows the amount of energy transferred to the dissociative modes remains constant for high collision energies whereas the monomers are getting more internal energy.
\figuremacro{Epartition-Ar-300-d-ud}{Kinetic energy partition for dissociated (-d) and undissociated (-ud) trajectories at the end of the MD simulation as a function of collision energy.}
Finally, some characteristic timescales are computed, which are presented in Figure \ref{figuretimescale}. They correspond to the timescales for the argon with its initial velocity to travel across some characteristic distances, namely, a C-H (1.10~\AA) or a C-C bond (1.40~\AA) and the largest molecular axis (9.25~\AA). These timescales can be compared with those of the pyrene dimer vibrational modes as an efficient energy transfer would be favored by similar orders of magnitudes. The intermolecular dimer modes possibly mixed with very soft folding modes are lying within the 70-120 $cm^{-1}$
spectral range \cite{Dontot2020} with corresponding half-periods of 130-240 fs. These timescales are of the same order of magnitude as the time for the argon to travel across the largest pyrene axis for collision energies below 10~eV.
Typical frequencies for intramolecular non-soft modes are lying from 500 $cm^{-1}$ to 3000 $cm^{-1}$ (C-H stretching modes), leading to half-periods of 5-33 fs. For all the simulated collision energies, the characteristic times required for the argon to travel across typical C-H or C-C bond distances belong to the same order of magnitude as some of the intramolecular hard modes.
Therefore, it appears from this qualitative description that the collision energy transfer toward the intermolecular modes is easier at collision energies lower than 10 eV whereas the transfer toward intramolecular modes is efficient for all the simulated collision energies.
This is actually in line with the fact that the part of the absorbed collision energy taken by the non-soft intramocular modes is increasing with the collision energy at the expense of that taken by the intermolecular and soft intramolecular modes, which is in agreement with the previous energy analysis (Figures~\ref{transferredE-Ar-300}, \ref{prot-Ar-300} and \ref{Epartition-Ar-300-d-ud}).
\figuremacro{figuretimescale}{Timescales, as a function of center of mass collision energy, for argon to travel across some typical distances: a carbon-carbon bond (green), a carbon-hydrogen bond (purple) or the largest axis of the pyrene molecule (blue).}
\textbf{Efficiency of energy transfer within the dimer}
\figuremacro{T-time-zoom_abcdef}{Instantaneous kinetic temperatures as a function of time for intra and intermolecular modes of the pyrene dimer at a collision energy of 22.5~eV. Impact parameters $b$ are (a) 2, (b) 3, (c) 0, (d) 2.5, (e) 2, and (f) 2~\AA{}. In cases (a) and (b) dissociation takes place whereas in the other cases the dimer remains undissociated at the end of the MD simulation. In (c) to (f) the lower panel is a vertical zoom of the corresponding intramolecular parts in upper panel.}
\figuremacrob{E-time-abcdef}{Instantaneous kinetic energies as a function of time for intra and intermolecular modes of the pyrene dimer at a collision energy of 22.5 eV. Impact parameters $b$ are (a) 2, (b) 3, (c) 0, (d) 2.5, (e) 2, and (f) 2 \AA{}. In cases (a) and (b), dissociation takes place whereas in the other cases the dimer remains undissociated at the end of the MD simulation.}
In this section, we address how the energy is shared inside the dimer after the collision. In particular, we look at the efficiency of energy transfer between the intramolecular modes of each unit and the intermolecular modes. The amount of deposited energy as well as its partition between the intramolecular modes of each molecule and the intermolecular modes is strongly dependent on the collision condition: the impact parameter, the orientation of the dimer, whether a head on collision occurs with one of the dimer atoms (and its nature, carbon or hydrogen). This results in very different evolutions of the subsequent energy flows for which precise values concerning timescales can hardly be derived. Nevertheless, the analysis of the trajectories allows to identify some characteristic behaviors. In order to estimate the thermalization process efficiency, the instantaneous intra and intermolecular kinetic temperatures are evaluated using the following formula:
\begin{align}
\label{kineticT}
T^k=2 \frac{<E^k>}{nk_b}
\end{align}
%$$ T^k=2 \frac{<E^k>}{nk_b} $$
where $k_b$ refers to the Boltzmann constant. $n$ is the number of involved modes and $E^k$ is the kinetic energy for the intra or intermolecular modes (see eqs.~\ref{Eparti}). $T^k$ is plotted in Figure \ref{T-time-zoom_abcdef} for some selected trajectories obtained for collision energies of 22.5 eV and various impact parameters.
The evolution of the corresponding energies ($E^k_{intra^1}$, $E^k_{intra^2}$ and $E^k_{inter}$) are presented in Figure \ref{E-time-abcdef}. In Figures \ref{T-time-zoom_abcdef} and \ref{E-time-abcdef}, simulations (a) and (b) correspond to trajectories for which dissociation occurred, whereas the dimer remained intact in the other simulations. In the simulation (a), a larger amount of energy is deposited in the first monomer with respect to the second one. The dissociation occurs before an efficient energy transfer takes place between the two monomers, leading to one hot monomer and one cold monomer at the end of the simulation. The situation is slightly different in the dissociation trajectory (b): there is a much smaller difference between the energies received during the collission by each of the monomers. One can observe that the equilibration of the two monomers intramolecular energies can take place before dissociation, leaving the two monomers with similar energies/kinetic temperatures. In the other four pictures (c, d, e, and f), corresponding to undissociated trajectories, one can see that the thermalization between the two monomers intramolecular modes occurs with timescales from 0.2 to 1.5 ps shown in Figure \ref{T-time-zoom_abcdef}. On the other side, the energy equilibration between intra and intermolecular modes takes more time. Indeed, the thermalization is almost achieved in simulations (c) and (d) at 1.5 and 2.5 ps, respectively, but would take more than the simulated duration 3 ps for trajectories (e) and (f) displayed in Figure \ref{T-time-zoom_abcdef}.
As a conclusion of these trajectories analyses, it seems that the thermalization between intramolecular modes of the two monomers is relatively efficient (on the order of ps). On the other hand, the thermalization with the intermolecular modes is less efficient and sometimes is not observed during the simulated time of 3 ps. The direct dissociation of the dimer is a fast process (on the order of a few tenths of ps) which may prevent the thermalization taking place, leading to monomer temperatures reflecting the initial energy deposition.
\subsection{Conclusions about CID of Py$_2^+$}
A QM/MM dynamics study of the collision of Py$_2^+$ with argon at various collision energies were carried out. Argon was treated as a polarisable MM particle and Py$_2^+$ was treated using the SCC-DFTB method.
In the dynamical simulations, a time step of 0.5 fs is proper even for high collision energies 25 eV.
The TOF mass spectra of parent Py$_2^+$ and dissociation product Py$^+$ were simulated by the PST using the MD outputs at a centre of mass collision energy of 17.5~eV. With respect to TOF mass spectra extracted from pure PST simulations, considering non-statistical dissociation processes that take place before the energy redistribution from MD simulations improves the match between experimental and theoretical TOF spectra.
The agreement between the measured and simulated mass spectra peak shapes and positions shows that the essence of the collision-induced dissociation is captured by the simulation. It appears that the TOF spectra mostly result from dimers dissociating on short timescales (during the MD simulation) and the remaining minor contribution is from dimers dissociating at longer timescales (the second step, during PST calculation). This indicates that Py$_2^+$ primarily engages a direct dissociation path after collision.
The extraction of snapshots from the MD simulations allows to visualize the collision processes. It shows that the evolution of the trajectories either toward a dissociation or a redistribution of the transferred energy strongly depends on the initial collision conditions. Intramolecular fragmentation of the monomers occurred only for collision energies above 25 eV. The dissociation cross sections show a steep increase for collision energies below 7.5~eV and remain almost constant for collision energies greater than 10~eV. The dissociation cross section of Py$_2^+$ increases when dissociation occurring on longer timescale is included. As such, the dissociation cross section computed from the MD+PST model at the centre of mass collision energy of 17.5~eV is slightly higher than the value derived from pure MD simulations.
The analysis of the partition of the final kinetic energy as a function of the collision energy shows how the absorbed energy is shared between the dissociative modes and the heating of individual monomers. It shows that above 7.5~eV, increasing the collision energy mostly results in an increase of the intramolecular energy. The qualitative analysis of the different timescales involved in the collision further supports the kinetic energy partition analysis.
Finally, the analysis of energy transfer efficiency within the dimer suggests that direct dissociation is too fast to allow significant thermalization of the system. On the other hand, when there is no dissociation, thermalization can occur with a faster equilibration between the intramolecular modes of the two units than with the intermolecular modes.
The present results can be compared with experimental and theoretical works discussing the direct and indirect fragmentation of PAH and PAH clusters submitted to higher energy collisions \cite{Chen2014, Gatchell2016knockout}. These authors showed that the nuclear stopping power dominates over the electronic one below 1 keV, giving a justification to our approach based on classical MD and PST. They also showed that the direct non-statistical PAH fragmentation (knock-out) is an efficient process above 20 eV. This is in line with the fact that monomer fragmentation was only observed in our MD simulations above 25 eV. Our work shows that, for PAH clusters, a regime exists below this collision energy where the dimer dissociation is governed by non-statistical processes.
In this study, the collision process, dissociation path, energy partition and distribution, and the efficiency of energy transfer were deeply explored for the Py$_2^+$ system, which can provide valuable reference for the CID study of larger PAH cation clusters.
%Beyond the specific study of Py$_2^+$ dissociation, the methodology paves the way for future analysis of CID experiments like dissociation of molecular clusters such as water-Uracil clusters.
%: ----------------------- paths to graphics ------------------------
% change according to folder and file names
\ifpdf
\graphicspath{{X/figures/PNG/}{X/figures/PDF/}{X/figures/}}
\else
\graphicspath{{X/figures/EPS/}{X/figures/}}
\fi

BIN
thesis/4/figures/.DS_Store vendored Normal file
View File

Binary file not shown.

BIN
thesis/4/figures/12f-sphere.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 1.7 MiB

BIN
thesis/4/figures/3b-sphere.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 1.6 MiB

BIN
thesis/4/figures/E-time-abcdef.pdf Normal file
View File

Binary file not shown.

BIN
thesis/4/figures/Epartition-Ar-300-SP-eps-converted-to.pdf Normal file
View File

Binary file not shown.

BIN
thesis/4/figures/Epartition-Ar-300-SP.pdf Normal file
View File

Binary file not shown.

BIN
thesis/4/figures/Epartition-Ar-300-Tstep-01-eps-converted-to.pdf Normal file
View File

Binary file not shown.

BIN
thesis/4/figures/Epartition-Ar-300-Tstep-01.pdf Normal file
View File

Binary file not shown.

BIN
thesis/4/figures/Epartition-Ar-300-d-ud-eps-converted-to.pdf Normal file
View File

Binary file not shown.

BIN
thesis/4/figures/Epartition-Ar-300-d-ud.pdf Normal file
View File

Binary file not shown.

BIN
thesis/4/figures/MDPST.pdf Normal file
View File

Binary file not shown.

BIN
thesis/4/figures/MS-BR-12w-Ne-branch.pdf Normal file
View File

Binary file not shown.

BIN
thesis/4/figures/MS-BR-1w-4w-Ar-branch.pdf Normal file
View File

Binary file not shown.

BIN
thesis/4/figures/MS-BR-1w-4w-Ne-Ar-branch.pdf Normal file
View File

Binary file not shown.

BIN
thesis/4/figures/MS-BR-5w-11w-Ar-branch.pdf Normal file
View File

Binary file not shown.

BIN
thesis/4/figures/MS-BR-5w-11w-Ne-Ar-branch.pdf Normal file
View File

Binary file not shown.

BIN
thesis/4/figures/T-time-zoom_abcdef.pdf Normal file
View File

Binary file not shown.

Some files were not shown because too many files have changed in this diff Show More