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\chapter{General Introduction} \label{chap:general_intro}

%\section{Molecular Clusters}

The term \textit{cluster} was coined by F. A. 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, U. Landman \textit{et al.} reported that anionic gold clusters favor planar structures
up to $\sim$13 atoms.\cite{Hakkinen2002} J.-M. L'Hermite \textit{et al.} also reported that the transition temperature extracted from he
heat capacity curve of protonated water clusters (H$_{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, J. 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, I focused on water clusters containing an impurity, \textit{i.e.} an additional ion or molecule. I have first focused my
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. Then I  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, I 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
% ---------------------------------------------------------------------------
