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@ -26,12 +26,12 @@ Cette thèse vise à étudier en détails le comportement d’agrégats molécul
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.
L’intérêt porté aux agrégats uracile/eau protonés vise à fournir une description détaillée d’expériences récentes de dissociation induite par collision (CID). \newline 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
SCC-DFTB, CID, dynamique moléculaire, agrégats aqueux d'ammonium/ammoniac, agrégats protonés uracile-eau
\end{abstracts}

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%%\chapter{Aims of the project} % top level followed by section, subsection
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@ -20,9 +20,9 @@ and [Re$_2$Br$_8$]$^{2-}$.\cite{Cotton1964} He defined metal atom cluster compou
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.
an ensemble of bound atoms or molecules which can be isolated or incorporated within 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
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.
@ -54,7 +54,7 @@ Finally, \textbf{clusters composed of non-metal atoms or molecules} are usually
\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
These listed various kinds of clusters, which 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}
@ -69,7 +69,7 @@ and other atomic aggregates made of non-metallic atoms.
\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}
\item[$\bullet$] \textbf{Ionic bond} which exists in ionic clusters such as NaCl\cite{Ayuela1993} or NaF clusters.\cite{ Calvo2018}
\end{itemize}
@ -79,48 +79,47 @@ and other atomic aggregates made of non-metallic atoms.
%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
Properties of clusters stem from both their size and composition. Clusters can therefore exhibit very specific physical and chemical properties
that are strongly influenced 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
This becomes all the more true as the chemical complexity of the cluster increases, \textit{i.e.} when it consists 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
This is true for atomic or molecular clusters when 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.
heat capacity curve of protonated water clusters (H$_{2}$O)$_{n}$H$^{+}$ has a strong size dependence as seen in Figure~\ref{Ttrans}.\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 in revealing microscopic aspects which are hardly observable in the bulk only.
\begin{figure}[h]
\begin{center}
\includegraphics[width=12cm]{T_trans.png}
\includegraphics[width=12cm]{Ttrans.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}
(black stars).\cite{Hock2009} Figure extracted from reference~\cite{Boulon2014}.}
%>>>>>>> 92023a10c3aa8b7dc4ace43987c1d571fb99a738
\label{Ttrans}
\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
which paved the way for modern work on both metal clusters and the interaction of photons with clusters.\cite{Faraday1857} Cluster research has 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
to develop new kinds of materials,\cite{Castleman2009} to carry out chemical reactions in new ways,\cite{Henglein1989} and to gain 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
@ -129,22 +128,22 @@ The study of clusters also helps to understand nucleation phenomena, for instanc
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
solution. Consequently, their study allows to explore the effects of solvents 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
isomer of the probed species. The first major task is then 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 require 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.}
In more difficult cases, the proper properties result from the contribution of several isomers which has to be taken into account. When
considering finite-temperature properties, an ergodic exploration of the PES also needs 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
calculations allow to understand dissociation mechanisms and energy partition that 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:
@ -166,7 +165,7 @@ and solvent-solvent interactions at the molecular level.\cite{Wang2010} From a
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 climate models.\cite{Vaida2003} This is not actually the case due to the lack of data regarding 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}:
@ -175,7 +174,7 @@ From a theoretical point of view, the study of water clusters is not straightfor
\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
makes it 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
@ -184,8 +183,8 @@ The theoretical description of water clusters thus requires simulation tools spe
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.
\textit{ab initio} or empirical, that makes it possible to reproduce all the properties of the
different phases of water, that are applicable to large systems and are 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
@ -238,14 +237,14 @@ 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}.
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}
\includegraphics[width=12cm]{PAHs-sample.png}
\caption{Examples of several PAH molecules.}
\label{PAHs_sample}
\label{PAHs-sample}
\end{center}
\end{figure}
@ -309,13 +308,13 @@ of system with hundred of atoms for several hundred nanoseconds, but they can po
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
simulation time of several hundred picoseconds. This approach has therefore 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
with 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
low-energy isomers for various cluster sizes. Then I tackled 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.
@ -348,7 +347,7 @@ The molecular dynamics simulations allow to probe the nature of the formed fragm
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}.
\item[$\bullet$] Finally, the conclusions of this thesis, as well as a number of perspectives, are presented in the \textbf{fifth chapter}.
\end{itemize}

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20
thesis/2_Introduction/introduction.tex
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@ -394,7 +394,7 @@ key variable in the determination of the electronic energy of a system.
%From the electronic wavefunction of the system, $\rho$($\mathbf{r}$) is written as:
%>>>>>>> 92023a10c3aa8b7dc4ace43987c1d571fb99a738
This idea originates from the the model of the uniform electron gas in the phase space around an atom developed in 1927 by L. H. Thomas \cite{Thomas1927} and E. Fermi \cite{Fermi1928}, which is the predecessor to density functional theory. Nevertheless, the Thomas-Fermi model is unable to correctly describe molecular bonds because it does not take into account the exchange and correlation energies.
This idea originates from the model of the uniform electron gas in the phase space around an atom developed in 1927 by L. H. Thomas \cite{Thomas1927} and E. Fermi \cite{Fermi1928}, which is the predecessor to density functional theory. Nevertheless, the Thomas-Fermi model is unable to correctly describe molecular bonds because it does not take into account the exchange and correlation energies.
The first HK theorem shows that, for a many-electron system in its ground state, the energy is uniquely determined by the electron density $\rho$(\textbf{r}).
In other words, the first HK theorem shows that it is not necessary to know the wavefunction of the system to obtain its energy and that the knowledge of the electron
@ -438,7 +438,7 @@ energy of the system can be calculated. The total energy of the real system is c
\label{E_KS}
E_\mathrm{DFT}[\rho(\mathbf{r})]=T_\mathrm{no}[\rho(\mathbf{r})]+\underbrace{E_\mathrm H[\rho(\textbf{r})] + \int V_\mathrm{ext}(\textbf{r})\rho(\mathbf{r})d(\mathbf{r}) +E_\mathrm{xc}[\rho(\mathbf{r})]}_{E_\mathrm{eff}[\rho(\mathbf{r})]}
\end{eqnarray}
where the sum of last three terms on the right-hand side is the effective energy $E_\mathrm{eff}$[$\rho(\textbf{r}$)]. \\
where the sum of the last three terms on the right-hand side is the effective energy $E_\mathrm{eff}$[$\rho(\textbf{r}$)]. \\
$T_\mathrm{no}$[$\rho$(\textbf{r})] is the kinetic energy of a system of non-interacting electrons:
\begin{eqnarray}
@ -691,7 +691,7 @@ H^0_{\mu\nu}=
\label{Hmatrix}
\end{align}
It should be noted that the $H^0_{\mu\nu}$ elements only depend on atoms $\alpha$ and $\beta$. Therefore only the two-center matrix elements and
It should be noted here that the $H^0_{\mu\nu}$ elements only depend on atoms $\alpha$ and $\beta$. Therefore only the two-center matrix elements and
the two-center elements of the overlap matrix can be explicitly calculated, in other words, interactions at three or more centers are neglected as stated above.
%In order to obtain a good evaluation of $\rho_{_0}(\textbf{r})$, it is approximated as a overlap of atom-like densities centered on the nuclei $\alpha$:
@ -754,7 +754,7 @@ E_\mathrm{2nd}=\frac{1}{2}\sum_{\alpha}^{N}\sum_{\beta}^{N} \frac{\Delta q_{\alp
where U$_\alpha$, U$_\beta$ are the Hubbard parameters: $\gamma_{\alpha\alpha} \approx I_\alpha-A_\alpha \approx 2\eta\alpha \approx U_\alpha$.
$I$ is the ionisation potential and $A$ is the electonic affinity of atom $\alpha$. $\eta_\alpha$ refers to the chemical hardness of atom $\alpha$.\cite{Elstner1998}
It is worth noting that the electronic density $\rho(\mathbf{r})$ influences explicitly the calculation of the electrostatic energy in DFT.
It is worth noting that the electronic density $\rho(\mathbf{r})$ explicitly influences the calculation of the electrostatic energy in DFT.
In the context of DFTB, point charges are used and the electronic density around the atom is condensed at a point. In practice, Mulliken's
definition of charge is often used,\cite{Mulliken1955} which is defined as:
\begin{align}
@ -834,7 +834,7 @@ This procedure is repeated until the atomic charges are converged.
%The self-consistent charge correction allows to treat the charge transfer effects explicitly in which the transfer-ability of $E_{rep}$ is fairly better compared to the non-self-consistent scheme.
DFTB is derived from DFT, it therefore inherits the specific problems of DFT. For instance, the traditional DFT functionals can not describe properly
dispersion interaction and charge resonance phenomena in charged aggregates. DFTB also display some specific problems because of its own
dispersion interaction and charge resonance phenomena in charged aggregates. DFTB also displays some specific problems because of its own
approximations such as the use of Mulliken atomic charges, the absence of atomic polarization, the absence of coupling between atomic orbitals
located on the same atom. This differs from DFT that explicitly considers atomic polarization.
@ -893,11 +893,11 @@ where $f(\textbf R_{\alpha\beta})$ is a cutoff function, which allows to avoid t
\subsection{Force Field Methods}
Force field is a computational method utilized to estimate the forces between particles, in other words it is the functional form and parameter sets applied to calculate the potential energy of a system.
FF is interatomic potential and use the same concept with force field in classical physics, a vector field which describes a non-contact force acting on a particle at different positions in space.
FF is interatomic potential and uses the same concept with force field in classical physics, a vector field which describes a non-contact force acting on a particle at different positions in space.
The acting force on each particle is derived as a gradient of the potential energy with respect to the particle positions.\cite{Frenkel2001}
In such case, the interactions in a system are determined from parameterized potentials in which the electronic structure can not be described explicitly because each particle is treated as a material point. The particles interact with each other through the FF and the integration algorithm is applied to the particles. In most cases, this leads to a big decrease of the precision level in the description of the system but it can reduce the calculation cost drastically, which allows to model systems containing several thousands of particles.
Different potentials have been proposed,\cite{Jones1924, Lennard1924, Morse1929, Born1932, Stillinger1985, Kaplan2006} which can be classified two main groups: pair potentials and multi-body potentials. For pair potentials, harmonic interaction is the most basic form:\cite{Bahar1997}
Different potentials have been proposed,\cite{Jones1924, Lennard1924, Morse1929, Born1932, Stillinger1985, Kaplan2006} which can be classified into two main groups: pair potentials and multi-body potentials. For pair potentials, harmonic interaction is the most basic form:\cite{Bahar1997}
\begin{align}
V(R_{\alpha\beta}) = k(R_{\alpha\beta}-R_{eq})^2
\label{harmonic}
@ -1150,7 +1150,7 @@ MD is a powerful tool for analyzing the physical movements of atoms and molecule
MD was originally developed following the earlier successes of Monte Carlo simulations. The first work about
MD was published in 1957 by B. Alder \textit{et al.} which focused on the integration of classical equations of
motion for a system of hard spheres.\cite{Alder1957} Before long, radiation damage at low and moderate
energies were studied using MD in 1960 and MD was also applied to simulate liquid argon in 1964.\cite{Gibson1960, Rahman1964}
energies was studied using MD in 1960 and MD was also applied to simulate liquid argon in 1964.\cite{Gibson1960, Rahman1964}
MD experienced an extremely rapid development in the years that followed. MD simulations have been applied
in chemistry, biochemistry, physics, biophysics, materials science, and branches of engineering, which is
often coupled with experimental measurements to facilitate interpretation. MD has a strong predictive
@ -1331,7 +1331,7 @@ be explored exhaustively. For high temperatures, one has a high probability to c
bottoms of the wells can not be explored comprehensively. Therefore, it is very difficult to both cross the energy barriers
and thoroughly explore the bottom of the wells using a unique MD simulation at a given temperature.
Many methods have been proposed to solve this question and are referred to as \textbf{enhanced sampling methods}
They are classified into two groups: \textbf{biased methods} and \textbf{non-biased methods}.
They are classified into two groups: \textbf{biased methods} and \textbf{unbiased methods}.
In \textbf{biased methods}, the dynamics of the system is influenced by a external factor, usually a non-physical force, which makes it possible to push the system outside of the wells even at low $T$.\cite{Torrie1977, Hansmann1993, Marchi1999, Bartels2000, Darve2001}
For instance, Metadynamics is a biased method.\cite{Laio2002, Iannuzzi2003, Barducci2011}
In \textbf{non-biased methods}, the dynamics of the system is not modified directly. Examples are simulated annealing,\cite{Kirkpatrick1983, Van1987}
@ -1399,7 +1399,7 @@ all particles can be renormalized as follows:
\textbf{Global optimization} refers to the determination of the lowest energy point on a PES, \textit{i.e.} the global minimum. As this latter usually
includes a large number of stationary points, it is not straightforward to find the global minimum. Local optimization methods do not
make it possible to cross the energy barriers between local minima. Therefore, a global optimization scheme such as MD or Monte Carlo
simulations is needed to perform a more exhaustive exploration of the PES to get to the lowest energy minimum.
simulations is needed to perform a more exhaustive exploration of the PES to get the lowest energy minimum.
There exits a vast amount of methods to perform global optimization and each one has its strength and weaknesses. The ergodicity problem appears in all of these global optimization methods. In principle, one can only be sure of having found the real global minimum after an infinite number of iterations.
The Basin-Hopping method is a particular useful global optimization technique in high-dimensional landscapes

243
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52
thesis/3/structure_stability.tex
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@ -16,7 +16,7 @@ This \textbf{third chapter} of my thesis merges two independent studies dealing
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 PES and the \textbf{PTMD} approach for their exploration. All low-energy isomers
combination of the \textbf{SCC-DFTB} method for the efficient calculation of the PES and the \textbf{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, an improve set of parameters is proposed to describe sp$^3$ nitrogen
@ -122,7 +122,7 @@ level. In that case, the resulting structures are referred to as \textquotedblle
%\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}
\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,
@ -331,7 +331,7 @@ isomers of clusters (H$_2$O)$_{4-10}${NH$_4$}$^+$ and (H$_2$O)$_{4-10}$NH$_3$ ar
\subsubsection{Properties of (H$_2$O)$_{4-10}${NH$_4$}$^+$ Clusters}
The five lowest-energy isomers of (H$_2$O)$_{4}${NH$_4$}$^+$ are depicted in Figure~\ref{fig:nh4-4-6w}. 4-a is the lowest-energy isomer obtained
\textbf{Cluster (H$_2$O)$_{4}${NH$_4$}$^+$.} The five lowest-energy isomers of (H$_2$O)$_{4}${NH$_4$}$^+$ are depicted in Figure~\ref{fig:nh4-4-6w}. 4-a is the lowest-energy isomer obtained
from the global SCC-DFTB optimization and also the lowest-energy configuration after optimization at MP2/Def2TZVP level with ZPVE
corrections. This result is consistent with previous computational studies\cite{Wang1998, Jiang1999, Douady2008, Lee2004, Pickard2005} and
the experimental studies by H. Chang and co-workers.\cite{Chang1998, Wang1998} Isomer 4-a displays four hydrogen bonds around the ionic
@ -400,15 +400,15 @@ energy ordering of the five lowest-energy isomers was the same as ours which cer
The relative binding energy of SCC-DFTB method to MP2/Def2TZVP method with BSSE correction for isomers 4-a to 4-e are listed in Table \ref{reBindE}. When the four water molecules are considered as a whole part to calculate the binding energy, the relative binding energy of isomers 4-a to 4-e are -1.67, 0.00, 0.77, 0.77 and -4.04 kcal·mol\textsuperscript{-1}. As shown in Table \ref{reBindE}, for isomers 4-a to 4-e, when the four water molecules are separately considered using the geometry in the cluster to calculate the binding energy, the biggest absolute value of the relative binding energy is 0.87 kcal·mol\textsuperscript{-1}. This shows the results of SCC-DFTB are in good agreement with those of MP2/Def2TZVP with BSSE correction for (H$_2$O)$_{4}${NH$_4$}$^+$. From the relative binding energy of (H$_2$O)$_{4}${NH$_4$}$^+$, it indicates that all the water molecules considered as a whole part or separately has an effect on the relative binding energy for the cluster (H$_2$O)$_{4}${NH$_4$}$^+$ and the overall $\Delta E_{bind.}^{whole}$ are bigger than $\Delta E_{bind.}^{sep.}$.
For cluster (H$_2$O)$_{5}${NH$_4$}$^+$, the five low-energy isomers are illustrated in Figure \ref{fig:nh4-4-6w}. The isomer 5-a is the most stable one, which is consistent with F. Spiegelman’s result using the global Monte Carlo optimization and G. Shields’s results obtained with a mixed molecular dynamics/quantum mechanics moldel.\cite{Douady2008, Morrell2010} The energy order of 5-a to 5-e at SCC-DFTB level is consistent with that at MP2/Def2TZVP level with ZPVE correction. 5-a, 5-d and 5-e have a complete solvation shell while one dangling N-H bond is exposed in 5-b and 5-c. For the five low-energy isomers, the energy order of our results are not exactly the same with H. Chang’s calculation results at MP2/6-31+G(d)level with ZPVE correction.\cite{Jiang1999} In H. Chang’s results, 5-d is the low-energy isomer and 5-a is the second low-energy isomer. They didn’t find isomers 5-b and 5-c. From the comparison, it implies the combination of SCC-DFTB and PTMD is good enough to find the low-energy isomer and the basis set can affect the energy order when using the MP2 approach.
\textbf{Cluster (H$_2$O)$_{5}${NH$_4$}$^+$.} For cluster (H$_2$O)$_{5}${NH$_4$}$^+$, the five low-energy isomers are illustrated in Figure \ref{fig:nh4-4-6w}. The isomer 5-a is the most stable one, which is consistent with F. Spiegelman’s result using the global Monte Carlo optimization and G. Shields’s results obtained with a mixed molecular dynamics/quantum mechanics moldel.\cite{Douady2008, Morrell2010} The energy order of 5-a to 5-e at SCC-DFTB level is consistent with that at MP2/Def2TZVP level with ZPVE correction. 5-a, 5-d and 5-e have a complete solvation shell while one dangling N-H bond is exposed in 5-b and 5-c. For the five low-energy isomers, the energy order of our results are not exactly the same with H. Chang’s calculation results at MP2/6-31+G(d)level with ZPVE correction.\cite{Jiang1999} In H. Chang’s results, 5-d is the low-energy isomer and 5-a is the second low-energy isomer. They didn’t find isomers 5-b and 5-c. From the comparison, it implies the combination of SCC-DFTB and PTMD is good enough to find the low-energy isomer and the basis set can affect the energy order when using the MP2 approach.
When all the water molecules are considered as a whole part, the obtained binding energy has a deviation due to the interaction of water molecules. As listed in Table \ref{reBindE}, for isomers 5-a to 5-e, the relative binding energy $\Delta E_{bind.}^{whole}$ are -1.62, 0.72, 0.69, -1.08 and -2.08 kcal·mol\textsuperscript{-1} and $\Delta E_{bind.}^{sep.}$ are -0.56, 0.48, 0.55, -0.78 and 0.88 kcal·mol\textsuperscript{-1}, respectively. The $\Delta E_{bind.}^{whole}$ is bigger than corresponding $\Delta E_{bind.}^{sep.}$, which indicates it is better to calculate the binding energy with considering the water molecules separately. The $\Delta E_{bind.}^{sep.}$ is less than 1.00 kcal·mol\textsuperscript{-1} for the five low-energy isomers of cluster (H$_2$O)$_{5}${NH$_4$}$^+$, so the SCC-DFTB method is good enough compared to MP2/Def2TZVP with BSSE correction for cluster (H$_2$O)$_{5}${NH$_4$}$^+$.
For cluster (H$_2$O)$_{6}${NH$_4$}$^+$, no N-H bond is exposed in the five low-energy isomers displayed in Figure \ref{fig:nh4-4-6w}. 6-a is the first low-energy isomer at SCC-DFTB level, which is a symmetric double-ring species connected together by eight hydrogen bonds making it a robust structure. 6-a is also the first low-energy isomer obtained using the Monte Carlo optimizations with the intermolecular polarizable potential.\cite{Douady2008} 6-d is the first low-energy isomer at MP2/Def2TZVP level with ZPVE correction but it is only 0.22 kcal·mol\textsuperscript{-1} lower than 6-a. In Shields’s results, 6-d is also the first low-energy isomer at MP2/aug-cc-pVDZ level.\cite{Morrell2010} In H. Chang’s study, 6-b with a three-coordinated H$_2$O molecule is the first low-energy isomer for cluster (H$_2$O)$_{6}${NH$_4$}$^+$ at B3LYP/6-31+G(d) level.\cite{Wang1998} 6-b is also the first low-energy isomer at B3LYP/6-31++G(d,p) level including the harmonic ZPE contribution.\cite{Douady2008} The energy of 6-b is only 0.14 kcal·mol\textsuperscript{-1} higher than that of 6-a at MP2/Def2TZVP level with ZPVE correction. The energies of 6-a, 6-b and 6-d are very close at both SCC-DFTB and MP2/Def2TZVP with ZPVE correction levels, which implies it is easy to have a transformation among 6-a, 6-b and 6-d. It shows SCC-DFTB is good to find the low-energy isomers of cluster (H$_2$O)$_{6}${NH$_4$}$^+$ compared to MP2 and B3LYP methods.
\textbf{Cluster (H$_2$O)$_{6}${NH$_4$}$^+$.} For cluster (H$_2$O)$_{6}${NH$_4$}$^+$, no N-H bond is exposed in the five low-energy isomers displayed in Figure \ref{fig:nh4-4-6w}. 6-a is the first low-energy isomer at SCC-DFTB level, which is a symmetric double-ring species connected together by eight hydrogen bonds making it a robust structure. 6-a is also the first low-energy isomer obtained using the Monte Carlo optimizations with the intermolecular polarizable potential.\cite{Douady2008} 6-d is the first low-energy isomer at MP2/Def2TZVP level with ZPVE correction but it is only 0.22 kcal·mol\textsuperscript{-1} lower than 6-a. In Shields’s results, 6-d is also the first low-energy isomer at MP2/aug-cc-pVDZ level.\cite{Morrell2010} In H. Chang’s study, 6-b with a three-coordinated H$_2$O molecule is the first low-energy isomer for cluster (H$_2$O)$_{6}${NH$_4$}$^+$ at B3LYP/6-31+G(d) level.\cite{Wang1998} 6-b is also the first low-energy isomer at B3LYP/6-31++G(d,p) level including the harmonic ZPVE contribution.\cite{Douady2008} The energy of 6-b is only 0.14 kcal·mol\textsuperscript{-1} higher than that of 6-a at MP2/Def2TZVP level with ZPVE correction. The energies of 6-a, 6-b and 6-d are very close at both MP2/Def2TZVP with ZPVE correction and SCC-DFTB levels, which implies it is easy to have a transformation among 6-a, 6-b and 6-d. It shows SCC-DFTB is good to find the low-energy isomers of cluster (H$_2$O)$_{6}${NH$_4$}$^+$ compared to MP2 and B3LYP methods.
As shown in Table \ref{reBindE}, for isomers 6-a to 6-e, the relative binding energy $\Delta E_{bind.}^{whole}$ are -1.71, -1.14, -2.06, -2.90 and -1.18 kcal·mol\textsuperscript{-1} and the $\Delta E_{bind.}^{sep.}$ are -0.38, -0.76, 0.27, -1.06 and -0.60 kcal·mol\textsuperscript{-1}, respectively. It indicates the binding energies are very close at SCC-DFTB and MP2/Def2TZVP with BSSE correction levels when water molecules are calculated separately. The $\Delta E_{bind.}^{whole}$ is bigger than corresponding $\Delta E_{bind.}^{sep.}$ because of the interaction of water molecules when all the water molecules are considered as a whole part.
As shown in Table \ref{reBindE}, for isomers 6-a to 6-e, the relative binding energy $\Delta E_{bind.}^{whole}$ are -1.71, -1.14, -2.06, -2.90 and -1.18 kcal·mol\textsuperscript{-1} and the $\Delta E_{bind.}^{sep.}$ are -0.38, -0.76, 0.27, -1.06 and -0.60 kcal·mol\textsuperscript{-1}, respectively. It indicates the binding energies are very close at SCC-DFTB and MP2/Def2TZVP with BSSE correction levels when water molecules are calculated separately. The $\Delta E_{bind.}^{whole}$ is bigger than corresponding $\Delta E_{bind.}^{sep.}$ because of the interaction of water molecules when all the water molecules are considered as a whole part.
For cluster (H$_2$O)$_{7}${NH$_4$}$^+$, the five low-energy isomers are shown in Figure \ref{fig:nh4-7-10w}. The ion core {NH$_4$}$^+$ has a complete solvation shell in isomers 7-a to 7-e. 7-a and 7-b with three three-coordinated H$_2$O molecules are the first low-energy isomers at SCC-DFTB level. In F. Spiegelman’s study, 7-a is also the first low-energy isomer using the Monte Carlo optimizations with the intermolecular polarizable potential.\cite{Douady2008} 7-c is the first low-energy isomer at MP2/Def2TZVP with ZPVE correction level including three three-coordinated water molecules. 7-c is also the first low-energy isomer at B3LYP/6-31++G(d,p) level including the harmonic ZPE contribution.\cite{Douady2008} 7-e is the first low-energy isomer with three three-coordinated H$_2$O molecules at MP2/aug-cc-pVDZ level in G. Shields’s study.\cite{Morrell2010} As illustrated in Figure \ref{fig:nh4-7-10w}, the energy difference between 7-a, 7-c and 7-e at SCC-DFTB and MP2/Def2TZVP with ZPVE correction levels are less than 0.61 kcal·mol\textsuperscript{-1} so it is possible that the first low-energy isomer is different when different method are applied. The energy of 7-a and 7-b are the same at both SCC-DFTB and MP2/Def2TZVP with ZPVE correction levels and their structures are similar, which indicates it is easy for them to transform to each other. The results for cluster (H$_2$O)$_{7}${NH$_4$}$^+$ verify the accuracy of SCC-DFTB approach.
\textbf{Cluster (H$_2$O)$_{7}${NH$_4$}$^+$.} For cluster (H$_2$O)$_{7}${NH$_4$}$^+$, the five low-energy isomers are shown in Figure \ref{fig:nh4-7-10w}. The ion core {NH$_4$}$^+$ has a complete solvation shell in isomers 7-a to 7-e. 7-a and 7-b with three three-coordinated H$_2$O molecules are the first low-energy isomers at SCC-DFTB level. In F. Spiegelman’s study, 7-a is also the first low-energy isomer using the Monte Carlo optimizations with the intermolecular polarizable potential.\cite{Douady2008} 7-c is the first low-energy isomer at MP2/Def2TZVP with ZPVE correction level including three three-coordinated water molecules. 7-c is also the first low-energy isomer at B3LYP/6-31++G(d,p) level including the harmonic ZPVE contribution.\cite{Douady2008} 7-e is the first low-energy isomer with three three-coordinated H$_2$O molecules at MP2/aug-cc-pVDZ level in G. Shields’s study.\cite{Morrell2010} As illustrated in Figure \ref{fig:nh4-7-10w}, the energy difference between 7-a, 7-c and 7-e at MP2/Def2TZVP with ZPVE correction and SCC-DFTB levels are less than 0.61 kcal·mol\textsuperscript{-1} so it is possible that the first low-energy isomer is different when different method are applied. The energy of 7-a and 7-b are the same at both MP2/Def2TZVP with ZPVE correction and SCC-DFTB levels and their structures are similar, which indicates it is easy for them to transform to each other. The results for cluster (H$_2$O)$_{7}${NH$_4$}$^+$ verify the accuracy of SCC-DFTB approach.
\begin{figure}[h!]
\includegraphics[width=1.0\linewidth]{nh4-7-10w.png}
@ -419,22 +419,22 @@ For cluster (H$_2$O)$_{7}${NH$_4$}$^+$, the five low-energy isomers are shown in
As shown in Table \ref{reBindE}, for isomers 7-a to 7-e, the relative binding energy $\Delta E_{bind.}^{whole}$ are -2.95, -2.92, -2.17, -1.28 and -3.22 kcal·mol\textsuperscript{-1} and the $\Delta E_{bind.}^{sep.}$are only -0.39, -0.38, 0.09, -1.35 and -2.27 kcal·mol\textsuperscript{-1}, respectively. It indicates the binding energies of 7-a to 7-e at SCC-DFTB agree well especially for 7-a to 7-d with those at MP2/Def2TZVP with BSSE correction level when water molecules are calculated separately. When all the water molecules are regarded as a whole part, the results of SCC-DFTB are not as good as those of the MP2 with BSSE method.
For cluster (H$_2$O)$_{8}${NH$_4$}$^+$, 8-a to 8-e are the five low-energy isomers displayed in Figure \ref{fig:nh4-7-10w}. In 8-a to 8-d, the ion core {NH$_4$}$^+$ has a complete solvation shell. 8-a is the first low-energy isomer in our calculation at SCC-DFTB level. In F. Spiegelman’s study, 8-b is the first low-energy isomer at B3LYP/6-31++G(d,p) level including the harmonic ZPE contribution.\cite{Douady2008} The structures of 8-a and 8-b are very similar and the energy differences are only 0.09 and 0.18 kcal·mol\textsuperscript{-1} at SCC-DFTB and MP2/Def2TZVP with ZPVE correction levels, respectively. 8-d with seven three-coordinated H$_2$O molecules in the cube frame is the first low-energy isomer in our calculation at MP2/Def2TZVP with ZPVE correction level, which is consistent with F. Spiegelman’s results obtained using Monte Carlo optimizations.\cite{Douady2008} In 8-e, {NH$_4$}$^+$ has an exposed N-H bond and it also has seven three-coordinated H$_2$O molecules in its cage frame. The energies of isomers 8-a to 8-e are very close calculated using SCC-DFTB and MP2 methods, so it’s possible that the energy order will change when different methods or basis sets are applied. The results certificate the SCC-DFTB is good enough to find the low-energy isomers for cluster (H$_2$O)$_{8}${NH$_4$}$^+$.
\textbf{Cluster (H$_2$O)$_{8}${NH$_4$}$^+$.} For cluster (H$_2$O)$_{8}${NH$_4$}$^+$, 8-a to 8-e are the five low-energy isomers displayed in Figure \ref{fig:nh4-7-10w}. In 8-a to 8-d, the ion core {NH$_4$}$^+$ has a complete solvation shell. 8-a is the first low-energy isomer in our calculation at SCC-DFTB level. In F. Spiegelman’s study, 8-b is the first low-energy isomer at B3LYP/6-31++G(d,p) level including the harmonic ZPVE contribution.\cite{Douady2008} The structures of 8-a and 8-b are very similar and the energy differences are only 0.18 and 0.09 kcal·mol\textsuperscript{-1} at MP2/Def2TZVP with ZPVE correction and SCC-DFTB levels, respectively. 8-d with seven three-coordinated H$_2$O molecules in the cube frame is the first low-energy isomer in our calculation at MP2/Def2TZVP with ZPVE correction level, which is consistent with F. Spiegelman’s results obtained using Monte Carlo optimizations.\cite{Douady2008} In 8-e, {NH$_4$}$^+$ has an exposed N-H bond and it also has seven three-coordinated H$_2$O molecules in its cage frame. The energies of isomers 8-a to 8-e are very close calculated using SCC-DFTB and MP2 methods, so it’s possible that the energy order will change when different methods or basis sets are applied. The results certificate the SCC-DFTB is good enough to find the low-energy isomers for cluster (H$_2$O)$_{8}${NH$_4$}$^+$.
As shown in Table \ref{reBindE}, for isomers 8-a to 8-e, the relative binding energy $\Delta E_{bind.}^{whole}$are -2.20, -1.61, -3.71, -2.43 and -0.55 kcal·mol\textsuperscript{-1}, respectively and the biggest $\Delta E_{bind.}^{sep.}$ is -2.01 kcal·mol\textsuperscript{-1}. It shows the binding energies at SCC-DFTB level agree well with those at MP2/Def2TZVP with BSSE correction level when water molecules are calculated separately. From these results, when all the water molecules are considered as a whole part, the results of SCC-DFTB didn’t agree well with those of the MP2 with BSSE correction method.
For cluster (H$_2$O)$_{9}${NH$_4$}$^+$, the five low-energy structures of (H$_2$O)$_{9}${NH$_4$}$^+$ are illustrated in Figure \ref{fig:nh4-7-10w}. 9-a with seven three-coordinated H$_2$O molecules in the cage frame is the first low-energy isomer at SCC-DFTB level. 9-a is also the first low-energy structure at B3LYP/6-31++G(d,p) level including the harmonic ZPE contribution in F. Spiegelman’s study.\cite{Douady2008} 9-b with one N-H bond exposed in {NH$_4$}$^+$ is the second low-energy isomer whose energy is only 0.22 kcal·mol\textsuperscript{-1} higher than that of 9-a in the results of SCC-DFTB calculation. 9-b is the first low-energy isomer at MP2/Def2TZVP with ZPVE correction level in our calculation and it is also the first low-energy isomer at B3LYP/6-31++G(d,p) level in F. Spiegelman’s study.\cite{Douady2008} 9-c, 9-d and 9-e have a complete solvation shell. All the water molecules are connected together in the structure of 9-c. The structures of 9-a and 9-e are very similar and their energy difference is only 0.11 kcal·mol\textsuperscript{-1} at MP2/Def2TZVP with ZPVE correction level. The energy difference of isomers 9-a to 9-e is less than 0.51 kcal·mol\textsuperscript{-1} at SCC-DFTB and less than 0.86 kcal·mol\textsuperscript{-1} at MP2/Def2TZVP with ZPVE correction, so it’s easy for them to transform to each other making it possible for the variation of the energy order. The results certificate the SCC-DFTB is good enough to find the low-energy isomers for cluster (H$_2$O)$_{9}${NH$_4$}$^+$.
\textbf{Cluster (H$_2$O)$_{9}${NH$_4$}$^+$.} For cluster (H$_2$O)$_{9}${NH$_4$}$^+$, the five low-energy structures of (H$_2$O)$_{9}${NH$_4$}$^+$ are illustrated in Figure \ref{fig:nh4-7-10w}. 9-a with seven three-coordinated H$_2$O molecules in the cage frame is the first low-energy isomer at SCC-DFTB level. 9-a is also the first low-energy structure at B3LYP/6-31++G(d,p) level including the harmonic ZPVE contribution in F. Spiegelman’s study.\cite{Douady2008} 9-b with one N-H bond exposed in {NH$_4$}$^+$ is the second low-energy isomer whose energy is only 0.22 kcal·mol\textsuperscript{-1} higher than that of 9-a in the results of SCC-DFTB calculation. 9-b is the first low-energy isomer at MP2/Def2TZVP with ZPVE correction level in our calculation and it is also the first low-energy isomer at B3LYP/6-31++G(d,p) level in F. Spiegelman’s study.\cite{Douady2008} 9-c, 9-d and 9-e have a complete solvation shell. All the water molecules are connected together in the structure of 9-c. The structures of 9-a and 9-e are very similar and their energy difference is only 0.11 kcal·mol\textsuperscript{-1} at MP2/Def2TZVP with ZPVE correction level. The energy difference of isomers 9-a to 9-e is less than 0.51 kcal·mol\textsuperscript{-1} at SCC-DFTB and less than 0.86 kcal·mol\textsuperscript{-1} at MP2/Def2TZVP with ZPVE correction, so it’s easy for them to transform to each other making it possible for the variation of the energy order. The results certificate the SCC-DFTB is good enough to find the low-energy isomers for cluster (H$_2$O)$_{9}${NH$_4$}$^+$.
As shown in Table \ref{reBindE}, for isomers 9-a to 9-e, the relative binding energy $\Delta E_{bind.}^{whole}$ are -2.20, -1.61, -3.71, -2.43 and -0.55 kcal·mol\textsuperscript{-1} and the relative binding energy $\Delta E_{bind.}^{sep.}$ are -1.39, -0.84, -0.85, -1.78, and -0.91 kcal·mol\textsuperscript{-1}, respectively.
It is obvious that the absolute values of $\Delta E_{bind.}^{whole}$ are bigger than the corresponding $\Delta E_{bind.}^{sep.}$. It shows the binding energies at SCC-DFTB level agree well with those at MP2/Def2TZVP with BSSE correction level when water molecules are calculated separately. According to the results, when all the water molecules are considered as a whole part, the results of SCC-DFTB didn’t agree well with those of the MP2 with BSSE correction method.
For cluster (H$_2$O)$_{10}${NH$_4$}$^+$, 10-a to 10-e are the five low-energy isomers in which the ion core {NH$_4$}$^+$ has a complete solvation shell shown in Figure \ref{fig:nh4-7-10w}. 10-a with eight three-coordinated H$_2$O molecules in its big cage structure is the first low-energy isomer calculated using the SCC-DFTB approach. 10-a is also the first low-energy structure at B3LYP/6-31++G(d,p) level including the harmonic ZPE contribution in F. Spiegelman’s study.\cite{Douady2008} In 10-b and 10-e, there is a four-coordinated H$_2$O molecule in their cage structures. 10-d is the first low-energy structure in our calculation results using MP2/Def2TZVP with ZPVE correction, which is also the first low-energy isomer at B3LYP/6-31++G(d,p) level in F. Spiegelman’s study.\cite{Douady2008} The energy of 10-b is only 0.17 kcal·mol\textsuperscript{-1} higher than that of 10-a at SCC-DFTB level, and it is only 0.31 kcal·mol\textsuperscript{-1} lower than that of 10-a at MP2/Def2TZVP with ZPVE correction level. The energy of isomers 10-a to 10-e are very close at both SCC-DFTB and MP2/Def2TZVP levels, which indicates the results with SCC-DFTB agree well with those using MP2/Def2TZVP method for cluster (H$_2$O)$_{10}${NH$_4$}$^+$.
\textbf{Cluster (H$_2$O)$_{10}${NH$_4$}$^+$.} For cluster (H$_2$O)$_{10}${NH$_4$}$^+$, 10-a to 10-e are the five low-energy isomers in which the ion core {NH$_4$}$^+$ has a complete solvation shell shown in Figure \ref{fig:nh4-7-10w}. 10-a with eight three-coordinated H$_2$O molecules in its big cage structure is the first low-energy isomer calculated using the SCC-DFTB approach. 10-a is also the first low-energy structure at B3LYP/6-31++G(d,p) level including the harmonic ZPVE contribution in F. Spiegelman’s study.\cite{Douady2008} In 10-b and 10-e, there is a four-coordinated H$_2$O molecule in their cage structures. 10-d is the first low-energy structure in our calculation results using MP2/Def2TZVP with ZPVE correction, which is also the first low-energy isomer at B3LYP/6-31++G(d,p) level in F. Spiegelman’s study.\cite{Douady2008} The energy of 10-b is only 0.17 kcal·mol\textsuperscript{-1} higher than that of 10-a at SCC-DFTB level, and it is only 0.31 kcal·mol\textsuperscript{-1} lower than that of 10-a at MP2/Def2TZVP with ZPVE correction level. The energy of isomers 10-a to 10-e are very close at both SCC-DFTB and MP2/Def2TZVP levels, which indicates the results with SCC-DFTB agree well with those using MP2/Def2TZVP method for cluster (H$_2$O)$_{10}${NH$_4$}$^+$.
As shown in Table \ref{reBindE}, for isomers 10-a to 10-e, the relative binding energies $\Delta E_{bind.}^{whole}$ and $\Delta E_{bind.}^{sep.}$ are not as small as the corresponding ones of clusters (H$_2$O)$_{1-9}${NH$_4$}$^+$, which implies the error of the relative binding energy increases with the number of water molecules in the cluster. The whole results of $\Delta E_{bind.}^{whole}$ are still bigger than those of $\Delta E_{bind.}^{sep.}$ for isomers 10-a to 10-e.
\subsubsection{Properties of (H$_2$O)$_{4-10}${NH$_3$} Clusters}
For cluster (H$_2$O)$_{4}${NH$_3$}, the five low-energy structures 4$^\prime$-a to 4$^\prime$-e are displayed in Figure \ref{fig:nh3-4-7w}. 4$^\prime$-a with three N-H bonds exposed is the first low-energy isomer at SCC-DFTB level. 4$^\prime$-b with two N-H bonds exposed is the second low-energy isomer at SCC-DFTB level but it is the first low-energy isomer at MP2/Def2TZVP with ZPVE correction level. The energy differences between 4$^\prime$-a to 4$^\prime$-b are only 0.07 and 0.2 kcal·mol\textsuperscript{-1} at MP2/Def2TZVP with ZPVE correction level and SCC-DFTB level, respectively. The energy difference of isomers 4$^\prime$-a to 4$^\prime$-e is less than 0.75 kcal·mol\textsuperscript{-1} at MP2/Def2TZVP with ZPVE correction, so it’s possible for the variation of the energy order when different methods or basis sets are used. 4$^\prime$-d with a nearly planar pentagonal structure with nitrogen atom and the four oxygen atoms at the apexes is the first low-energy isomer at MP2/6-31+G(d,p) studied by J. Novoa et al\cite{Lee1996} 4$^\prime$-d is also the first low-energy isomer in D. Bacelo’s study using QCISD(T) for a single-point energy calculation based on the MP2/6-311++G(d,p) results.\cite{Bacelo2002} In addition, 4$^\prime$-a to 4$^\prime$-e are also the five low-energy isomers in D. Bacelo’s study even the energy order is different.\cite{Bacelo2002} The results show the SCC- DFTB is good enough to find the low-energy isomers isomers for cluster (H$_2$O)$_{4}${NH$_3$}.
\textbf{Cluster (H$_2$O)$_{4}${NH$_3$}.} For cluster (H$_2$O)$_{4}${NH$_3$}, the five low-energy structures 4$^\prime$-a to 4$^\prime$-e are displayed in Figure \ref{fig:nh3-4-7w}. 4$^\prime$-a with three N-H bonds exposed is the first low-energy isomer at SCC-DFTB level. 4$^\prime$-b with two N-H bonds exposed is the second low-energy isomer at SCC-DFTB level but it is the first low-energy isomer at MP2/Def2TZVP with ZPVE correction level. The energy differences between 4$^\prime$-a to 4$^\prime$-b are only 0.07 and 0.2 kcal·mol\textsuperscript{-1} at MP2/Def2TZVP with ZPVE correction level and SCC-DFTB level, respectively. The energy difference of isomers 4$^\prime$-a to 4$^\prime$-e is less than 0.75 kcal·mol\textsuperscript{-1} at MP2/Def2TZVP with ZPVE correction, so it’s possible for the variation of the energy order when different methods or basis sets are used. 4$^\prime$-d with a nearly planar pentagonal structure with nitrogen atom and the four oxygen atoms at the apexes is the first low-energy isomer at MP2/6-31+G(d,p) studied by J. Novoa et al\cite{Lee1996} 4$^\prime$-d is also the first low-energy isomer in D. Bacelo’s study using QCISD(T) for a single-point energy calculation based on the MP2/6-311++G(d,p) results.\cite{Bacelo2002} In addition, 4$^\prime$-a to 4$^\prime$-e are also the five low-energy isomers in D. Bacelo’s study even the energy order is different.\cite{Bacelo2002} The results show the SCC- DFTB is good enough to find the low-energy isomers isomers for cluster (H$_2$O)$_{4}${NH$_3$}.
\begin{figure}[h!]
\includegraphics[width=1.0\linewidth]{nh3-4-7w.png}
@ -445,19 +445,19 @@ For cluster (H$_2$O)$_{4}${NH$_3$}, the five low-energy structures 4$^\prime$-a
The relative binding energies of isomers 4$^\prime$-a to 4$^\prime$-e are shown in Table \ref{reBindE}. Except 4$^\prime$-d, the values of $\Delta E_{bind.}^{whole}$ for 4$^\prime$-a to 4$^\prime$-e are smaller than the corresponding values of $\Delta E_{bind.}^{sep.}$. The $\Delta E_{bind.}^{sep.}$ of 4$^\prime$-d is smaller than those of other isomers. 4$^\prime$-d has a nearly planar pentagonal structure that only contains three O-H···O hydrogen bonds among the four water molecules while other isomers contain four O-H···O hydrogen bonds among the four water molecules. So the intermolecular interaction of the four water molecules in 4$^\prime$-d is not as strong as it is in other isomers, this may explain the $\Delta E_{bind.}^{sep.}$ of 4$^\prime$-d is smaller than those of other isomers. In general, both relative binding energies $\Delta E_{bind.}^{sep.}$ and $\Delta E_{bind.}^{sep.}$ are not big that indicates SCC-DFTB performs well compared to the MP2 method with BSSE correction for calculating the binding energy of cluster (H$_2$O)$_{4}${NH$_3$}.
For cluster (H$_2$O)$_{5}${NH$_3$}, 5$^\prime$-a to 5$^\prime$-e are the five low-energy isomers shown in Figure \ref{fig:nh3-4-7w}. 5$^\prime$-a with four three-coordinated water molecules is the first low-energy structure at both MP2/Def2TZVP with ZPVE correction and SCC-DFTB levels. 5$^\prime$-b and 5$^\prime$-c are the second and third isomers at SCC-DFTB level and they are the third and second isomers at MP2/Def2TZVP level with ZPVE. The energy difference between 5$^\prime$-b and 5$^\prime$-c is only 0.44 and 0.05 kcal·mol\textsuperscript{-1} at MP2/Def2TZVP with ZPVE correction level and SCC-DFTB level, respectively. In addition, the structures of 5$^\prime$-b and 5$^\prime$-c are very similar so it is possible for them to transform to each other. 5$^\prime$-d with two three-coordinated water molecules is the fourth low-energy structure at both MP2/Def2TZVP with ZPVE correction and SCC-DFTB levels. 5$^\prime$-e with four three-coordinated water molecules is the fifth low-energy structure at both MP2/Def2TZVP with ZPVE correction and SCC-DFTB levels. The frames of 5$^\prime$-a and 5$^\prime$-e are almost the same but the water molecule who offers the hydrogen or oxygen to form the O-H···O hydrogen bonds has a small difference. The energy of 5$^\prime$-e is 1.51 kcal·mol\textsuperscript{-1} higher than that of 5$^\prime$-a at MP2/Def2TZVP with ZPVE correction level, which implies the intermolecular connection mode has an influence on the stability of the isomers. The results show the SCC-DFTB approach performs well to find the low-energy isomers for cluster (H$_2$O)$_{5}${NH$_3$} compared with MP2/Def2TZVP with ZPVE correction method.
\textbf{Cluster (H$_2$O)$_{5}${NH$_3$}.} For cluster (H$_2$O)$_{5}${NH$_3$}, 5$^\prime$-a to 5$^\prime$-e are the five low-energy isomers shown in Figure \ref{fig:nh3-4-7w}. 5$^\prime$-a with four three-coordinated water molecules is the first low-energy structure at both MP2/Def2TZVP with ZPVE correction and SCC-DFTB levels. 5$^\prime$-b and 5$^\prime$-c are the second and third isomers at SCC-DFTB level and they are the third and second isomers at MP2/Def2TZVP level with ZPVE. The energy difference between 5$^\prime$-b and 5$^\prime$-c is only 0.44 and 0.05 kcal·mol\textsuperscript{-1} at MP2/Def2TZVP with ZPVE correction level and SCC-DFTB level, respectively. In addition, the structures of 5$^\prime$-b and 5$^\prime$-c are very similar so it is possible for them to transform to each other. 5$^\prime$-d with two three-coordinated water molecules is the fourth low-energy structure at both MP2/Def2TZVP with ZPVE correction and SCC-DFTB levels. 5$^\prime$-e with four three-coordinated water molecules is the fifth low-energy structure at both MP2/Def2TZVP with ZPVE correction and SCC-DFTB levels. The frames of 5$^\prime$-a and 5$^\prime$-e are almost the same but the water molecule who offers the hydrogen or oxygen to form the O-H···O hydrogen bonds has a small difference. The energy of 5$^\prime$-e is 1.51 kcal·mol\textsuperscript{-1} higher than that of 5$^\prime$-a at MP2/Def2TZVP with ZPVE correction level, which implies the intermolecular connection mode has an influence on the stability of the isomers. The results show the SCC-DFTB approach performs well to find the low-energy isomers for cluster (H$_2$O)$_{5}${NH$_3$} compared with MP2/Def2TZVP with ZPVE correction method.
The relative binding energies of isomers 5$^\prime$-a to 5$^\prime$-e are shown in Table \ref{reBindE}. The values of $\Delta E_{bind.}^{whole}$ are less than 0.82 kcal·mol\textsuperscript{-1} for 5$^\prime$-a to 5$^\prime$-e. The values of $\Delta E_{bind.}^{sep.}$ are bigger than the corresponding values of $\Delta E_{bind.}^{whole}$. It indicates SCC-DFTB agrees better with MP2/Def2TZVP $\Delta E_{bind.}^{whole}$ when all the water molecules are regarded as a whole part than considering separately for calculating the binding energy of cluster (H$_2$O)$_{5}${NH$_3$}.
For cluster (H$_2$O)$_{6}${NH$_3$}, the five low-energy structures 6$^\prime$-a to 6$^\prime$-e are displayed in Figure \ref{fig:nh3-4-7w}. 6$^\prime$-a is the first low-energy structure at SCC-DFTB level. All water molecules in 6$^\prime$-a are three-coordinated. 6$^\prime$-b is the second low-energy isomer at SCC-DFTB level and it’s only 0.42 and 0.05 kcal·mol\textsuperscript{-1} higher than the ones of 6$^\prime$-a at MP2/Def2TZVP with ZPVE correction level and SCC-DFTB level, respectively. 6$^\prime$-c to 6$^\prime$-d are the third and fourth low-energy isomers in which the six water molecules form a triangular prism structure and there are one and two four-coordinated water molecules in 6$^\prime$-c to 6$^\prime$-d, respectively. 6$^\prime$-e is the fifth low-energy structure at SCC-DFTB level but it’s the first low-energy isomer at MP2/Def2TZVP with ZPVE correction level. The energy of 6$^\prime$-a to 6$^\prime$-e are very close at both both MP2/Def2TZVP with ZPVE correction and SCC-DFTB levels that it is difficult to keep the energy order when different methods or basis sets are applied. This also shows the SCC-DFTB method used is efficient to find the low-energy isomers of cluster (H$_2$O)$_{6}${NH$_3$}.
\textbf{Cluster (H$_2$O)$_{6}${NH$_3$}.} For cluster (H$_2$O)$_{6}${NH$_3$}, the five low-energy structures 6$^\prime$-a to 6$^\prime$-e are displayed in Figure \ref{fig:nh3-4-7w}. 6$^\prime$-a is the first low-energy structure at SCC-DFTB level. All water molecules in 6$^\prime$-a are three-coordinated. 6$^\prime$-b is the second low-energy isomer at SCC-DFTB level and it’s only 0.42 and 0.05 kcal·mol\textsuperscript{-1} higher than the ones of 6$^\prime$-a at MP2/Def2TZVP with ZPVE correction level and SCC-DFTB level, respectively. 6$^\prime$-c to 6$^\prime$-d are the third and fourth low-energy isomers in which the six water molecules form a triangular prism structure and there are one and two four-coordinated water molecules in 6$^\prime$-c to 6$^\prime$-d, respectively. 6$^\prime$-e is the fifth low-energy structure at SCC-DFTB level but it’s the first low-energy isomer at MP2/Def2TZVP with ZPVE correction level. The energy of 6$^\prime$-a to 6$^\prime$-e are very close at both both MP2/Def2TZVP with ZPVE correction and SCC-DFTB levels that it is difficult to keep the energy order when different methods or basis sets are applied. This also shows the SCC-DFTB method used is efficient to find the low-energy isomers of cluster (H$_2$O)$_{6}${NH$_3$}.
The relative binding energies of isomers 6$^\prime$-a to 6$^\prime$-e are listed in Table \ref{reBindE}. The smallest and the biggest values of $\Delta E_{bind.}^{whole}$ are -0.05 and -1.11 kcal·mol\textsuperscript{-1}, respectively. The smallest absolute value of $\Delta E_{bind.}^{sep.}$ is 1.96 kcal·mol\textsuperscript{-1}. The binding energies calculated with SCC-DFTB agree well with those calculated at MP2/Def2TZVP level for cluster (H$_2$O)$_{6}${NH$_3$} when all the water molecules are considered as a whole part.
For cluster (H$_2$O)$_{7}${NH$_3$}, the five low-energy isomers 7$^\prime$-a to 7$^\prime$-e are illustrated in Figure \ref{fig:nh3-4-7w}. 7$^\prime$-a with a cubic structure is the first low-lying energy structure at both MP2/Def2TZVP with ZPVE correction and SCC-DFTB levels. 7$^\prime$-b is the second low-energy structure at both MP2/Def2TZVP with ZPVE correction and SCC-DFTB levels. 7$^\prime$-b has a similar structure with 7$^\prime$-a but the NH$_3$ in it has two exposed N-H bonds. 7$^\prime$-c and 7$^\prime$-d have similar structures and they are the third and fourth low-lying energy isomers at SCC-DFTB level and their energy difference is only 0.74 kcal·mol\textsuperscript{-1}. 7$^\prime$-e with three exposed N-H bonds is the fifth low-energy isomer at both MP2/Def2TZVP with ZPVE correction and SCC-DFTB levels. The results of SCC-DFTB method agree well with those of MP2/Def2TZVP with ZPVE correction for the five low-energy isomers of cluster (H$_2$O)$_{7}${NH$_3$}.
\textbf{Cluster (H$_2$O)$_{7}${NH$_3$}.} For cluster (H$_2$O)$_{7}${NH$_3$}, the five low-energy isomers 7$^\prime$-a to 7$^\prime$-e are illustrated in Figure \ref{fig:nh3-4-7w}. 7$^\prime$-a with a cubic structure is the first lowest energy structure at both MP2/Def2TZVP with ZPVE correction and SCC-DFTB levels. 7$^\prime$-b is the second low-energy structure at both MP2/Def2TZVP with ZPVE correction and SCC-DFTB levels. 7$^\prime$-b has a similar structure with 7$^\prime$-a but the NH$_3$ in it has two exposed N-H bonds. 7$^\prime$-c and 7$^\prime$-d have similar structures and they are the third and fourth lowest energy isomers at SCC-DFTB level and their energy difference is only 0.74 kcal·mol\textsuperscript{-1}. 7$^\prime$-e with three exposed N-H bonds is the fifth low-energy isomer at both MP2/Def2TZVP with ZPVE correction and SCC-DFTB levels. The results of SCC-DFTB method agree well with those of MP2/Def2TZVP with ZPVE correction for the five low-energy isomers of cluster (H$_2$O)$_{7}${NH$_3$}.
The smallest and the biggest values of $\Delta E_{bind.}^{whole}$ of isomers 7$^\prime$-a to 7$^\prime$-e are -0.02 and -1.11 kcal·mol\textsuperscript{-1}, respectively and the smallest absolute value of $\Delta E_{bind.}^{sep.}$ is 2.02 kcal·mol\textsuperscript{-1} shown in Table \ref{reBindE}. The binding energies calculated with SCC-DFTB agree well with those obtained using MP2/Def2TZVP for cluster (H$_2$O)$_{7}${NH$_3$} when all the water molecules are considered as a whole part.
For cluster (H$_2$O)$_{8}${NH$_3$}, 8$^\prime$-a to 8$^\prime$-e are the five low-energy structures shown in Figure \ref{fig:nh3-8-10w}. 8$^\prime$-a in which eight water molecules constitute a cube is the first low-lying energy structure in SCC-DFTB calculation results. 8$^\prime$-b also with a water-cube structure is the second low-energy structure at SCC-DFTB level and it is the first low-energy isomer at MP2/Def2TZVP with ZPVE correction level. The energy differences between 8$^\prime$-a and 8$^\prime$-b are only 0.30 and 0.93 kcal·mol\textsuperscript{-1} at MP2/Def2TZVP with ZPVE correction level and SCC-DFTB level. From Figure \ref{fig:nh3-8-10w}, the fifth low-energy isomer 8$^\prime$-e includes less hydrogen bonds than other isomers and its energy has a clearly increase compared to other isomers. The results show the SCC-DFTB method performs well to obtain the low-energy isomers of cluster (H$_2$O)$_{8}${NH$_3$}.
\textbf{Cluster (H$_2$O)$_{8}${NH$_3$}.} For cluster (H$_2$O)$_{8}${NH$_3$}, 8$^\prime$-a to 8$^\prime$-e are the five low-energy structures shown in Figure \ref{fig:nh3-8-10w}. 8$^\prime$-a in which eight water molecules constitute a cube is the first lowest energy structure in SCC-DFTB calculation results. 8$^\prime$-b also with a water-cube structure is the second low-energy structure at SCC-DFTB level and it is the first low-energy isomer at MP2/Def2TZVP with ZPVE correction level. The energy differences between 8$^\prime$-a and 8$^\prime$-b are only 0.30 and 0.93 kcal·mol\textsuperscript{-1} at MP2/Def2TZVP with ZPVE correction level and SCC-DFTB level. From Figure \ref{fig:nh3-8-10w}, the fifth low-energy isomer 8$^\prime$-e includes less hydrogen bonds than other isomers and its energy has a clearly increase compared to other isomers. The results show the SCC-DFTB method performs well to obtain the low-energy isomers of cluster (H$_2$O)$_{8}${NH$_3$}.
\begin{figure}[h!]
\includegraphics[width=1.0\linewidth]{nh3-8-10w.png}
@ -468,11 +468,11 @@ For cluster (H$_2$O)$_{8}${NH$_3$}, 8$^\prime$-a to 8$^\prime$-e are the five lo
The smallest and the biggest values of $\Delta E_{bind.}^{whole}$ of isomers 8$^\prime$-a to 8$^\prime$-e are -0.1 and -1.28 kcal·mol\textsuperscript{-1}, respectively while the smallest absolute value of $\Delta E_{bind.}^{sep.}$ is 3.04 kcal·mol\textsuperscript{-1} shown in Table \ref{reBindE}. The binding energies calculated with SCC-DFTB agree better with those obtained at MP2/Def2TZVP level when all the water molecules are considered as a whole part in cluster (H$_2$O)$_{8}${NH$_3$} than the ones when water molecules calculated separately.
For cluster (H$_2$O)$_{9}${NH$_3$}, 9$^\prime$-a to 9$^\prime$-e are the five low-lying energy structures displayed in Figure \ref{fig:nh3-8-10w}. 9$^\prime$-a with a “chair” structure is the first low-energy structure at SCC-DFTB level. 9$^\prime$-b, 9$^\prime$-c and 9$^\prime$-d in which the nine water molecules have the similar configuration are the second, third and fourth isomers. In 9$^\prime$-b and 9$^\prime$-c, the NH$_3$ has three exposed N-H bonds and the energies of 9$^\prime$-b and 9-c are very close at both SCC-DFTB and MP2/Def2TZVP with ZPVE correction levels. The NH$_3$ has two exposed N-H bonds in 9$^\prime$-d. 9$^\prime$-e is the fifth low-energy isomer in the SCC-DFTB calculation results but it is the first low-energy isomer in the calculation results of MP2/Def2TZVP with ZPVE correction. 9$^\prime$-e has a pentagonal prism structure and all the water molecules in it are three-coordinated. The relative energy for each isomer between SCC-DFTB level and MP2/Def2TZVP with ZPVE correction level is less than 1.23 kcal·mol\textsuperscript{-1}. This shows our SCC-DFTB calculation results are consistent with the calculation results of MP2/Def2TZVP with ZPVE correction for low-energy isomers optimization of cluster (H$_2$O)$_{9}${NH$_3$}.
\textbf{Cluster (H$_2$O)$_{9}${NH$_3$}.} For cluster (H$_2$O)$_{9}${NH$_3$}, 9$^\prime$-a to 9$^\prime$-e are the five lowest energy structures displayed in Figure \ref{fig:nh3-8-10w}. 9$^\prime$-a with a “chair” structure is the first low-energy structure at SCC-DFTB level. 9$^\prime$-b, 9$^\prime$-c and 9$^\prime$-d in which the nine water molecules have the similar configuration are the second, third and fourth isomers. In 9$^\prime$-b and 9$^\prime$-c, the NH$_3$ has three exposed N-H bonds and the energies of 9$^\prime$-b and 9-c are very close at both MP2/Def2TZVP with ZPVE correction and SCC-DFTB levels. The NH$_3$ has two exposed N-H bonds in 9$^\prime$-d. 9$^\prime$-e is the fifth low-energy isomer in the SCC-DFTB calculation results but it is the first low-energy isomer in the calculation results of MP2/Def2TZVP with ZPVE correction. 9$^\prime$-e has a pentagonal prism structure and all the water molecules in it are three-coordinated. The relative energy for each isomer between SCC-DFTB level and MP2/Def2TZVP with ZPVE correction level is less than 1.23 kcal·mol\textsuperscript{-1}. This shows our SCC-DFTB calculation results are consistent with the calculation results of MP2/Def2TZVP with ZPVE correction for low-energy isomers optimization of cluster (H$_2$O)$_{9}${NH$_3$}.
The relative binding energies of isomers 9$^\prime$-a to 9$^\prime$-e are shown in Table \ref{reBindE}. The absolute values of $\Delta E_{bind.}^{whole}$ are less than 1.09 kcal·mol\textsuperscript{-1} while the smallest absolute value of $\Delta E_{bind.}^{sep.}$ is 2.57 kcal·mol\textsuperscript{-1}. The binding energies calculated with SCC-DFTB agree well with those acquired at MP2/Def2TZVP level when all the water molecules are considered as a whole part for cluster (H$_2$O)$_{9}${NH$_3$}.
For cluster (H$_2$O)$_{10}${NH$_3$}, 10$^\prime$-a to 10$^\prime$-e are the five low-energy structures illustrated in Figure \ref{fig:nh3-8-10w}. The energy order for the five low-energy structures is the same at SCC-DFTB and MP2/Def2TZVP with ZPVE correction levels. 10$^\prime$-a and 10$^\prime$-b are the first and second low-energy isomer in which the ten water molecules constitute the pentagonal prism. The energy differences of 10$^\prime$-a and 10$^\prime$-b are only 0.27 and 0.58 kcal·mol\textsuperscript{-1} at SCC-DFTB and MP2/Def2TZVP with ZPVE correction levels. 10$^\prime$-c and 10$^\prime$-d are the third and fourth low-energy isomers in which eight water molecules constitute a cube and the energy differences between 10$^\prime$-c and 10$^\prime$-d are very small calculated with SCC-DFTB or MP2/Def2TZVP with ZPVE correction. 10$^\prime$-e is the fifth low-energy structure in which eight water molecules also constitute a cube but its energy is obviously higher than those of 10$^\prime$-c and 10$^\prime$-d. The calculation results of SCC-DFTB are consistent with those of MP2/Def2TZ for the optimization of the low-energy isomers of cluster (H$_2$O)$_{10}${NH$_3$}. According to the structures of the five low-energy isomers of clusters (H$_2$O)$_{1-10}${NH$_3$}, in most cases, the NH$_3$ usually contains two or three exposed N-H bonds.
\textbf{Cluster (H$_2$O)$_{10}${NH$_3$}.} For cluster (H$_2$O)$_{10}${NH$_3$}, 10$^\prime$-a to 10$^\prime$-e are the five low-energy structures illustrated in Figure \ref{fig:nh3-8-10w}. The energy order for the five low-energy structures is the same at SCC-DFTB level and MP2/Def2TZVP with ZPVE correction level. 10$^\prime$-a and 10$^\prime$-b are the first and second low-energy isomer in which the ten water molecules constitute the pentagonal prism. The energy differences of 10$^\prime$-a and 10$^\prime$-b are only 0.58 and 0.27 kcal·mol\textsuperscript{-1} at MP2/Def2TZVP with ZPVE correction and SCC-DFTB levels. 10$^\prime$-c and 10$^\prime$-d are the third and fourth low-energy isomers in which eight water molecules constitute a cube and the energy differences between 10$^\prime$-c and 10$^\prime$-d are very small calculated with SCC-DFTB or MP2/Def2TZVP with ZPVE correction. 10$^\prime$-e is the fifth low-energy structure in which eight water molecules also constitute a cube but its energy is obviously higher than those of 10$^\prime$-c and 10$^\prime$-d. The calculation results of SCC-DFTB are consistent with those of MP2/Def2TZ for the optimization of the low-energy isomers of cluster (H$_2$O)$_{10}${NH$_3$}. According to the structures of the five low-energy isomers of clusters (H$_2$O)$_{1-10}${NH$_3$}, in most cases, the NH$_3$ usually contains two or three exposed N-H bonds.
The smallest and biggest values of $\Delta E_{bind.}^{whole}$ of isomers 10$^\prime$-a to 10$^\prime$-e are -0.03 and -1.10 kcal·mol\textsuperscript{-1} while the smallest absolute value of $\Delta E_{bind.}^{sep.}$ is 4.80 kcal·mol\textsuperscript{-1} shown in Table \ref{reBindE}. The values of $\Delta E_{bind.}^{whole}$ implies that SCC-DFTB agree very well with MP2/Def2TZVP for cluster (H$_2$O)$_{10}$NH$_3$ when all the water molecules are regarded as a whole part.
@ -565,7 +565,7 @@ for nucleation of atmospheric particles and SCC-DFTB could play a major in the
\section{Structural and Energetic Properties of Protonated Uracil Water Clusters} \label{structureUH}
\subsection{General introduction}
\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.
@ -573,7 +573,7 @@ The gas phase study needs to be extended towards more realistic biomolecular sys
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 , 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}
Uracil, 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 B. 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, A. 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.
@ -664,7 +664,7 @@ This analysis based on PA is however quite crude. Indeed, it assumes that the pr
\subsubsection{Calculated Structures of Protonated Uracil Water Clusters} \label{calcul_ur}
As discussed in section~\ref{sec:ammoniumwater}, I have proposed a modified set of NH parameters to describe sp$^3$ nitrogen atoms. For,
As discussed in section~\ref{sec:ammoniumwater}, I have proposed a modified set of N---H parameters to describe sp$^3$ nitrogen atoms. For,
sp$^2$ nitrogen atoms there is no need to modify 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} presents the binding energies of the two
(H$_2$O)U isomers represented in Figure~\ref{uracil_i} at MP2/Def2TZVP and SCC-DFTB levels of theory. Both $D_\textrm{NH}$ = 0.12 and
@ -709,28 +709,28 @@ have used $D_\textrm{NH}$ = 0.12 in the following.
The lowest-energy isomers determined theoretically for
hydrated uracil protonated clusters (H$_2$O)$_{1-7, 11, 12}$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 six lowest-energy structures of U(H$_2$O)$_{1-7, 11, 12}$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
\textbf{Cluster (H$_2$O)UH$^+$.} 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, S. 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 I obtained. Similarly, J. 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 I did. 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 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$^+$.
\textbf{Cluster (H$_2$O)$_{2-3}$UH$^+$.} Figures \ref{2a-f} and \ref{3a-f} display the 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 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}).
\textbf{Cluster (H$_2$O)$_{4-5}$UH$^+$.} The 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 lowest 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 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, for both species (H$_2$O)$_6$UH$^+$ and (H$_2$O)$_7$UH$^+$ have 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).
\textbf{Cluster (H$_2$O)$_{6-7}$UH$^+$.} Figures \ref{6a-f} and \ref{7a-f} display the 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, for both species (H$_2$O)$_6$UH$^+$ and (H$_2$O)$_7$UH$^+$ have 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 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}.
\textbf{Cluster (H$_2$O)$_{11-12}$UH$^+$.} 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 six lowest 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 do not intended to find them all. Furthermore, due to the limited number of MP2 geometry optimization I performed, there are few chances that I 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 I am 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.
@ -743,7 +743,7 @@ For 12a, 12b, 12c, and 12d, it is obvious that the excess proton is not directly
\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)$_{1-7, 11, 12}$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)$_{1-15}$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 I 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.
All the aforementioned lowest energy structures are relevant to describe the \newline (H$_2$O)$_{1-7, 11, 12}$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)$_{1-15}$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 I 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.

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thesis/4/collision.tex
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@ -546,6 +546,7 @@ The quantitative data from experiments of PAH clusters are still rather limited,
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 M. Gatchel {\textit et al.} \cite{Gatchell2016, Gatchell2016knockout} at the semi-empirical and DFTB levels.
Recently experiments at lower collision energies were performed by S. Zamith \textit{et al.} \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.
This work focused on the experimental investigation has been published in 2020 in the \textit{The Journal of Chemical Physics}.\cite{Zheng2021} and focused on the theoretical simulation has been published in 2021 in the \textit{Theoretical Chemistry Accounts}.\cite{Zheng2021}
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% Thesis statement of originality -------------------------------------
% Depending on the regulations of your faculty you may need a declaration like the one below. This specific one is from the medical faculty of the university of Dresden.
\begin{declaration} %this creates the heading for the declaration page
I herewith declare that I have produced this paper without the prohibited assistance of third parties and without making use of aids other than those specified; notions taken over directly or indirectly from other sources have been identified as such. This paper has not previously been presented in identical or similar form to any other examination board.

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% this file is called up by thesis.tex
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{\Large \textbf{Publications}}
\begin{itemize}
\item[$\bullet$] \textbf{L. Zheng}, M. Rapacioli, S. Zamith, J. -M. L’Hermite and J. Cuny, \textit{Collision-induced dissociation of protonated uracil water clusters probed by molecular dynamics simulations, to be submitted soon.}
\item[$\bullet$] \textbf{L. Zheng} and J. Cuny, \textit{Structure and stability of (H$_2$O)$_n$NH$_4^+$ and (H$_2$O)$_n$NH$_3$ clusters: A SCC-DFTB study, to be submitted soon.} \\
\item[$\bullet$] \textbf{L. Zheng}, S. Zamith and M. Rapacioli, \textit{Dynamical simulation of collision‑induced dissociation of pyrene dimer cation}, Theor. Chem. Acc. \textbf{2021}, 140(19), 1-14. \\
\item[$\bullet$] I. Braud, S. Zamith, J. Cuny, \textbf{L. Zheng}, and J. -M. L’Hermite, \textit{Size-dependent proton localization in hydrated uracil clusters: A joint experimental and theoretical study}, J. Chem. Phys. \textbf{2019}, 150(1), 014303. \\
\item[$\bullet$] A. Simon, M. Rapacioli, E. Michoulier, \textbf{L. Zheng}, K. Korchagina and J. Cuny, \textit{Contribution of the density-functional-based tight-binding scheme to the description of water clusters: methods, applications and extension to bulk systems}, Mol. Simul. \textbf{2019}, 45(4-5), 249-268. \\
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\BOOKMARK [2][]{subsection.3.1.3}{3.1.3 MP2 Geometry Optimizations, Relative and Binding Energies}{section.3.1}% 20
\BOOKMARK [2][]{subsection.3.1.4}{3.1.4 Structure Classification}{section.3.1}% 21
\BOOKMARK [1][]{section.3.2}{3.2 Structural and Energetic Properties of Ammonium/Ammonia including Water Clusters}{chapter.3}% 22
\BOOKMARK [2][]{subsection.3.2.1}{3.2.1 General introduction}{section.3.2}% 23
\BOOKMARK [2][]{subsection.3.2.1}{3.2.1 General Introduction}{section.3.2}% 23
\BOOKMARK [2][]{subsection.3.2.2}{3.2.2 Results and Discussion}{section.3.2}% 24
\BOOKMARK [3][]{subsubsection.3.2.2.1}{3.2.2.1 Dissociation Curves and SCC-DFTB Potential}{subsection.3.2.2}% 25
\BOOKMARK [3][]{subsubsection.3.2.2.2}{3.2.2.2 Small Species: \(H2O\)1-3NH4+ and \(H2O\)1-3NH3}{subsection.3.2.2}% 26
@ -29,7 +29,7 @@
\BOOKMARK [3][]{subsubsection.3.2.2.5}{3.2.2.5 Properties of \(H2O\)20NH4+ Cluster}{subsection.3.2.2}% 29
\BOOKMARK [2][]{subsection.3.2.3}{3.2.3 Conclusions for Ammonium/Ammonia Including Water Clusters}{section.3.2}% 30
\BOOKMARK [1][]{section.3.3}{3.3 Structural and Energetic Properties of Protonated Uracil Water Clusters}{chapter.3}% 31
\BOOKMARK [2][]{subsection.3.3.1}{3.3.1 General introduction}{section.3.3}% 32
\BOOKMARK [2][]{subsection.3.3.1}{3.3.1 General Introduction}{section.3.3}% 32
\BOOKMARK [2][]{subsection.3.3.2}{3.3.2 Results and Discussion}{section.3.3}% 33
\BOOKMARK [3][]{subsubsection.3.3.2.1}{3.3.2.1 Experimental Results}{subsection.3.3.2}% 34
\BOOKMARK [3][]{subsubsection.3.3.2.2}{3.3.2.2 Calculated Structures of Protonated Uracil Water Clusters}{subsection.3.3.2}% 35

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@ -176,8 +176,8 @@ Day of the defense:
\frontmatter
\include{0_frontmatter/abstract}
\include{0_frontmatter/dedication}
\include{0_frontmatter/acknowledgement}
%%%\include{0_frontmatter/dedication}
%%%\include{0_frontmatter/acknowledgement}
%\include{0_frontmatter/glossary}
@ -300,7 +300,7 @@ Day of the defense:
%\include{0_frontmatter/abstract}
%: Declaration of originality
/%\include{6_backmatter/acronyms}
%\include{6_backmatter/publications}
\include{6_backmatter/declaration}

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@ -1,66 +1,66 @@
\babel@toc {english}{}
\contentsline {chapter}{Glossary}{xi}{chapter*.2}
\contentsline {chapter}{\numberline {1}General Introduction}{1}{chapter.1}
\contentsline {chapter}{\numberline {2}Computational Methods}{13}{chapter.2}
\contentsline {section}{\numberline {2.1}Schr{\"o}dinger Equation}{15}{section.2.1}
\contentsline {section}{\numberline {2.2}Born-Oppenheimer Approximation}{16}{section.2.2}
\contentsline {section}{\numberline {2.3}Computation of Electronic Energy}{18}{section.2.3}
\contentsline {subsection}{\numberline {2.3.1}Wavefunction based Methods}{19}{subsection.2.3.1}
\contentsline {subsection}{\numberline {2.3.2}Density Functional Theory}{21}{subsection.2.3.2}
\contentsline {subsection}{\numberline {2.3.3}Density Functional based Tight-Binding Theory}{26}{subsection.2.3.3}
\contentsline {subsection}{\numberline {2.3.4}Force Field Methods}{33}{subsection.2.3.4}
\contentsline {section}{\numberline {2.4}Exploration of PES}{35}{section.2.4}
\contentsline {subsection}{\numberline {2.4.1}Monte Carlo Simulations}{36}{subsection.2.4.1}
\contentsline {subsection}{\numberline {2.4.2}Classical Molecular Dynamics}{39}{subsection.2.4.2}
\contentsline {subsection}{\numberline {2.4.3}Parallel-Tempering Molecular Dynamics}{44}{subsection.2.4.3}
\contentsline {subsection}{\numberline {2.4.4}Global Optimization}{46}{subsection.2.4.4}
\contentsline {chapter}{\numberline {3}Investigation of Structural and Energetic Properties}{49}{chapter.3}
\contentsline {section}{\numberline {3.1}Computational Details}{50}{section.3.1}
\contentsline {subsection}{\numberline {3.1.1}SCC-DFTB Potential}{50}{subsection.3.1.1}
\contentsline {subsection}{\numberline {3.1.2}SCC-DFTB Exploration of PES}{50}{subsection.3.1.2}
\contentsline {subsection}{\numberline {3.1.3}MP2 Geometry Optimizations, Relative and Binding Energies}{51}{subsection.3.1.3}
\contentsline {subsection}{\numberline {3.1.4}Structure Classification}{52}{subsection.3.1.4}
\contentsline {section}{\numberline {3.2}Structural and Energetic Properties of Ammonium/Ammonia including Water Clusters}{53}{section.3.2}
\contentsline {subsection}{\numberline {3.2.1}General introduction}{53}{subsection.3.2.1}
\contentsline {subsection}{\numberline {3.2.2}Results and Discussion}{55}{subsection.3.2.2}
\contentsline {subsubsection}{\numberline {3.2.2.1}Dissociation Curves and SCC-DFTB Potential}{55}{subsubsection.3.2.2.1}
\contentsline {subsubsection}{\numberline {3.2.2.2}Small Species: (H$_2$O)$_{1-3}${NH$_4$}$^+$ and (H$_2$O)$_{1-3}${NH$_3$}}{58}{subsubsection.3.2.2.2}
\contentsline {subsubsection}{\numberline {3.2.2.3}Properties of (H$_2$O)$_{4-10}${NH$_4$}$^+$ Clusters}{61}{subsubsection.3.2.2.3}
\contentsline {subsubsection}{\numberline {3.2.2.4}Properties of (H$_2$O)$_{4-10}${NH$_3$} Clusters}{68}{subsubsection.3.2.2.4}
\contentsline {subsubsection}{\numberline {3.2.2.5}Properties of (H$_2$O)$_{20}${NH$_4$}$^+$ Cluster}{73}{subsubsection.3.2.2.5}
\contentsline {subsection}{\numberline {3.2.3}Conclusions for Ammonium/Ammonia Including Water Clusters}{75}{subsection.3.2.3}
\contentsline {section}{\numberline {3.3}Structural and Energetic Properties of Protonated Uracil Water Clusters}{76}{section.3.3}
\contentsline {subsection}{\numberline {3.3.1}General introduction}{76}{subsection.3.3.1}
\contentsline {subsection}{\numberline {3.3.2}Results and Discussion}{78}{subsection.3.3.2}
\contentsline {subsubsection}{\numberline {3.3.2.1}Experimental Results}{79}{subsubsection.3.3.2.1}
\contentsline {subsubsection}{\numberline {3.3.2.2}Calculated Structures of Protonated Uracil Water Clusters}{84}{subsubsection.3.3.2.2}
\contentsline {subsection}{\numberline {3.3.3}Conclusions on (H$_2$O)$_{n}$UH$^+$ clusters}{94}{subsection.3.3.3}
\contentsline {chapter}{\numberline {4}Dynamical Simulation of Collision-Induced Dissociation}{99}{chapter.4}
\contentsline {section}{\numberline {4.1}Experimental Methods}{99}{section.4.1}
\contentsline {subsection}{\numberline {4.1.1}Principle of TCID}{101}{subsection.4.1.1}
\contentsline {subsection}{\numberline {4.1.2}Experimental Setup}{102}{subsection.4.1.2}
\contentsline {section}{\numberline {4.2}Computational Details}{104}{section.4.2}
\contentsline {subsection}{\numberline {4.2.1}SCC-DFTB Potential}{104}{subsection.4.2.1}
\contentsline {subsection}{\numberline {4.2.2}Collision Trajectories}{105}{subsection.4.2.2}
\contentsline {subsection}{\numberline {4.2.3}Trajectory Analysis}{106}{subsection.4.2.3}
\contentsline {section}{\numberline {4.3}Dynamical Simulation of Collision-Induced Dissociation of Protonated Uracil Water Clusters}{107}{section.4.3}
\contentsline {subsection}{\numberline {4.3.1}Introduction}{107}{subsection.4.3.1}
\contentsline {subsection}{\numberline {4.3.2}Results and Discussion}{108}{subsection.4.3.2}
\contentsline {subsubsection}{\numberline {4.3.2.1}Statistical Convergence}{108}{subsubsection.4.3.2.1}
\contentsline {subsection}{\numberline {4.3.3}Time-Dependent Proportion of Fragments}{111}{subsection.4.3.3}
\contentsline {subsection}{\numberline {4.3.4}Proportion of Neutral Uracil Loss and Total Fragmentation Cross Sections for Small Clusters}{114}{subsection.4.3.4}
\contentsline {subsection}{\numberline {4.3.5}Behaviour at Larger Sizes, the Cases of (H$_2$O)$_{11, 12}$UH$^+$}{124}{subsection.4.3.5}
\contentsline {subsection}{\numberline {4.3.6}Mass Spectra of Fragments with Excess Proton}{128}{subsection.4.3.6}
\contentsline {subsection}{\numberline {4.3.7}Conclusions about CID of (H$_2$O)$_{n}$UH$^+$}{131}{subsection.4.3.7}
\contentsline {section}{\numberline {4.4}Dynamical Simulation of Collision-Induced Dissociation for Pyrene Dimer Cation}{133}{section.4.4}
\contentsline {subsection}{\numberline {4.4.1}Introduction}{133}{subsection.4.4.1}
\contentsline {subsection}{\numberline {4.4.2}Calculation of Energies}{135}{subsection.4.4.2}
\contentsline {subsection}{\numberline {4.4.3}Simulation of the Experimental TOFMS}{137}{subsection.4.4.3}
\contentsline {subsection}{\numberline {4.4.4}Results and Discussion}{139}{subsection.4.4.4}
\contentsline {subsubsection}{\numberline {4.4.4.1}TOFMS Comparison}{139}{subsubsection.4.4.4.1}
\contentsline {subsubsection}{\numberline {4.4.4.2}Molecular Dynamics Analysis}{140}{subsubsection.4.4.4.2}
\contentsline {subsection}{\numberline {4.4.5}Conclusions about CID of Py$_2^+$}{156}{subsection.4.4.5}
\contentsline {chapter}{\numberline {5}General Conclusions and Perspectives}{159}{chapter.5}
\contentsline {section}{\numberline {5.1}General Conclusions}{159}{section.5.1}
\contentsline {section}{\numberline {5.2}Perspectives}{162}{section.5.2}
\contentsline {chapter}{References}{165}{chapter*.83}
\contentsline {chapter}{\nonumberline Glossary}{ix}{chapter*.2}%
\contentsline {chapter}{\numberline {1}General Introduction}{1}{chapter.1}%
\contentsline {chapter}{\numberline {2}Computational Methods}{13}{chapter.2}%
\contentsline {section}{\numberline {2.1}Schr{\"o}dinger Equation}{15}{section.2.1}%
\contentsline {section}{\numberline {2.2}Born-Oppenheimer Approximation}{16}{section.2.2}%
\contentsline {section}{\numberline {2.3}Computation of Electronic Energy}{18}{section.2.3}%
\contentsline {subsection}{\numberline {2.3.1}Wavefunction based Methods}{19}{subsection.2.3.1}%
\contentsline {subsection}{\numberline {2.3.2}Density Functional Theory}{21}{subsection.2.3.2}%
\contentsline {subsection}{\numberline {2.3.3}Density Functional based Tight-Binding Theory}{26}{subsection.2.3.3}%
\contentsline {subsection}{\numberline {2.3.4}Force Field Methods}{33}{subsection.2.3.4}%
\contentsline {section}{\numberline {2.4}Exploration of PES}{35}{section.2.4}%
\contentsline {subsection}{\numberline {2.4.1}Monte Carlo Simulations}{36}{subsection.2.4.1}%
\contentsline {subsection}{\numberline {2.4.2}Classical Molecular Dynamics}{39}{subsection.2.4.2}%
\contentsline {subsection}{\numberline {2.4.3}Parallel-Tempering Molecular Dynamics}{44}{subsection.2.4.3}%
\contentsline {subsection}{\numberline {2.4.4}Global Optimization}{46}{subsection.2.4.4}%
\contentsline {chapter}{\numberline {3}Investigation of Structural and Energetic Properties}{49}{chapter.3}%
\contentsline {section}{\numberline {3.1}Computational Details}{49}{section.3.1}%
\contentsline {subsection}{\numberline {3.1.1}SCC-DFTB Potential}{49}{subsection.3.1.1}%
\contentsline {subsection}{\numberline {3.1.2}SCC-DFTB Exploration of PES}{50}{subsection.3.1.2}%
\contentsline {subsection}{\numberline {3.1.3}MP2 Geometry Optimizations, Relative and Binding Energies}{52}{subsection.3.1.3}%
\contentsline {subsection}{\numberline {3.1.4}Structure Classification}{52}{subsection.3.1.4}%
\contentsline {section}{\numberline {3.2}Structural and Energetic Properties of Ammonium/Ammonia including Water Clusters}{53}{section.3.2}%
\contentsline {subsection}{\numberline {3.2.1}General Introduction}{53}{subsection.3.2.1}%
\contentsline {subsection}{\numberline {3.2.2}Results and Discussion}{55}{subsection.3.2.2}%
\contentsline {subsubsection}{\numberline {3.2.2.1}Dissociation Curves and SCC-DFTB Potential}{55}{subsubsection.3.2.2.1}%
\contentsline {subsubsection}{\numberline {3.2.2.2}Small Species: (H$_2$O)$_{1-3}${NH$_4$}$^+$ and (H$_2$O)$_{1-3}${NH$_3$}}{58}{subsubsection.3.2.2.2}%
\contentsline {subsubsection}{\numberline {3.2.2.3}Properties of (H$_2$O)$_{4-10}${NH$_4$}$^+$ Clusters}{61}{subsubsection.3.2.2.3}%
\contentsline {subsubsection}{\numberline {3.2.2.4}Properties of (H$_2$O)$_{4-10}${NH$_3$} Clusters}{68}{subsubsection.3.2.2.4}%
\contentsline {subsubsection}{\numberline {3.2.2.5}Properties of (H$_2$O)$_{20}${NH$_4$}$^+$ Cluster}{73}{subsubsection.3.2.2.5}%
\contentsline {subsection}{\numberline {3.2.3}Conclusions for Ammonium/Ammonia Including Water Clusters}{75}{subsection.3.2.3}%
\contentsline {section}{\numberline {3.3}Structural and Energetic Properties of Protonated Uracil Water Clusters}{76}{section.3.3}%
\contentsline {subsection}{\numberline {3.3.1}General Introduction}{76}{subsection.3.3.1}%
\contentsline {subsection}{\numberline {3.3.2}Results and Discussion}{78}{subsection.3.3.2}%
\contentsline {subsubsection}{\numberline {3.3.2.1}Experimental Results}{79}{subsubsection.3.3.2.1}%
\contentsline {subsubsection}{\numberline {3.3.2.2}Calculated Structures of Protonated Uracil Water Clusters}{84}{subsubsection.3.3.2.2}%
\contentsline {subsection}{\numberline {3.3.3}Conclusions on (H$_2$O)$_{n}$UH$^+$ clusters}{94}{subsection.3.3.3}%
\contentsline {chapter}{\numberline {4}Dynamical Simulation of Collision-Induced Dissociation}{99}{chapter.4}%
\contentsline {section}{\numberline {4.1}Experimental Methods}{99}{section.4.1}%
\contentsline {subsection}{\numberline {4.1.1}Principle of TCID}{101}{subsection.4.1.1}%
\contentsline {subsection}{\numberline {4.1.2}Experimental Setup}{102}{subsection.4.1.2}%
\contentsline {section}{\numberline {4.2}Computational Details}{104}{section.4.2}%
\contentsline {subsection}{\numberline {4.2.1}SCC-DFTB Potential}{104}{subsection.4.2.1}%
\contentsline {subsection}{\numberline {4.2.2}Collision Trajectories}{105}{subsection.4.2.2}%
\contentsline {subsection}{\numberline {4.2.3}Trajectory Analysis}{106}{subsection.4.2.3}%
\contentsline {section}{\numberline {4.3}Dynamical Simulation of Collision-Induced Dissociation of Protonated Uracil Water Clusters}{107}{section.4.3}%
\contentsline {subsection}{\numberline {4.3.1}Introduction}{107}{subsection.4.3.1}%
\contentsline {subsection}{\numberline {4.3.2}Results and Discussion}{108}{subsection.4.3.2}%
\contentsline {subsubsection}{\numberline {4.3.2.1}Statistical Convergence}{108}{subsubsection.4.3.2.1}%
\contentsline {subsection}{\numberline {4.3.3}Time-Dependent Proportion of Fragments}{111}{subsection.4.3.3}%
\contentsline {subsection}{\numberline {4.3.4}Proportion of Neutral Uracil Loss and Total Fragmentation Cross Sections for Small Clusters}{114}{subsection.4.3.4}%
\contentsline {subsection}{\numberline {4.3.5}Behaviour at Larger Sizes, the Cases of (H$_2$O)$_{11, 12}$UH$^+$}{124}{subsection.4.3.5}%
\contentsline {subsection}{\numberline {4.3.6}Mass Spectra of Fragments with Excess Proton}{128}{subsection.4.3.6}%
\contentsline {subsection}{\numberline {4.3.7}Conclusions about CID of (H$_2$O)$_{n}$UH$^+$}{131}{subsection.4.3.7}%
\contentsline {section}{\numberline {4.4}Dynamical Simulation of Collision-Induced Dissociation for Pyrene Dimer Cation}{133}{section.4.4}%
\contentsline {subsection}{\numberline {4.4.1}Introduction}{133}{subsection.4.4.1}%
\contentsline {subsection}{\numberline {4.4.2}Calculation of Energies}{135}{subsection.4.4.2}%
\contentsline {subsection}{\numberline {4.4.3}Simulation of the Experimental TOFMS}{137}{subsection.4.4.3}%
\contentsline {subsection}{\numberline {4.4.4}Results and Discussion}{139}{subsection.4.4.4}%
\contentsline {subsubsection}{\numberline {4.4.4.1}TOFMS Comparison}{139}{subsubsection.4.4.4.1}%
\contentsline {subsubsection}{\numberline {4.4.4.2}Molecular Dynamics Analysis}{140}{subsubsection.4.4.4.2}%
\contentsline {subsection}{\numberline {4.4.5}Conclusions about CID of Py$_2^+$}{156}{subsection.4.4.5}%
\contentsline {chapter}{\numberline {5}General Conclusions and Perspectives}{159}{chapter.5}%
\contentsline {section}{\numberline {5.1}General Conclusions}{159}{section.5.1}%
\contentsline {section}{\numberline {5.2}Perspectives}{162}{section.5.2}%
\contentsline {chapter}{References}{165}{chapter*.83}%

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