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\chapter{General Introduction}

%The work of this thesis is focused on two aspects.  First, to obtain the low-lying energy isomers of ammonium/ammonia water clusters and protonated uracil water clusters through exploring the potential energy surfaces using the combination of global and local optimizations. Then the structural, solvation, thermodynamics properties of the low-lying energy isomers were characterized. Second, the molecular dynamics simulations of collision-induced dissociation of protonated uracil water clusters and pyrene dimer cation were carried out to explore the collision trajectories, dissociation mechanism, energy partition, mass spectra, cross-section and do on.

%\section{Molecular Clusters}

The term cluster was coined by Cotton in the early 1960s to refer to compounds containing metal–metal bonds such as [Re$_2$Cl$_8$]$^{2-}$
and [Re$_2$Br$_8$]$^{2-}$.\cite{Cotton1964} More generally, in chemistry, the term cluster refers to an ensemble of bound atoms or molecules,
that can be isolated or incorporated in a larger chemical compounds, for instance in a material. A cluster is intermediate in size between a single
molecule or atom and a nanoparticle  which can be composed of up to a few nanometers in diameter. Clusters are also intermediate in terms of
properties between a single molecule or atom and the corresponding bulk compound. Although there is no strict definition of the size range
for a species to be referred to as a cluster, a rule of thumb is that a cluster can be composed of 3 to 3$\times$10$^7$ components. \cite{Cluster} 
%Two-atom particle is sometimes also considered as a cluster. 

Cluster chemistry developed contemporaneously along several independent research lines and several families of compounds can be referred to as
clusters.  Among them, one can mention \textbf{ transition metal carbonyl clusters},\cite{Dahl1963} \textbf{transition metal halide clusters},\cite{Fucugauchi1994}
\textbf{transition metal organic carbon clusters} (organometallic),\cite{Sutton2016} \textbf{metalloid clusters},\cite{Schnepf2002}
\textbf{intermetalloid clusters},\cite{Fassler2004, Stegmaier2011} as well as \textbf{atomic clusters} composed of non-metal atoms \cite{Farges1981, Kroto1991c60, Blase2008, Siedschlag2004}
and \textbf{molecular clusters}. \cite{Rapacioli2005stacked, Zhen2018}.
%The cluster can be either pure formed (from a single atomic species) or mixed (formed from different atomic species). 
%It can classified according to the nature of predominantly bond (metallic, covalent or ionic bond). 

\blue{\textbf{Transition metal carbonyl cluster} is a compound containing a core that consists of two or more metal atoms linked in part by metal-metal bonds and embraced by carbon monoxide (CO) ligand groups exclusively or predominantly. 
\textbf{Transition metal halide cluster} is a compound that contains two or more metal atoms (prevalent for the heavy metals) linked in part by metal-metal bonds and embraced by halide ligand. Some representative species for transition metal carbonyl and halide clusters are Mn$_2$(CO)$_{10}$,\cite{Dahl1963} Ni(CO)$_4$,\cite{Braga1993}
Fe(CO)$_5$,\cite{Braga1993} Re$_3$Cl$_{12}^{3-}$,\cite{Colton1965} (Mo$_6$Cl$_8$)Cl$_4$,\cite{Fucugauchi1994} Nb$_3$Cl$_8$,\cite{Yoon2020}}
\sout{\textbf{Transition metal carbonyl} and \textbf{halide clusters}, among which some representative species are Mn$_2$(CO)$_{10}$,\cite{Dahl1963} Ni(CO)$_4$,\cite{Braga1993}
Fe(CO)$_5$,\cite{Braga1993} Re$_3$Cl$_{12}^{3-}$,\cite{Colton1965} (Mo$_6$Cl$_8$)Cl$_4$,\cite{Fucugauchi1994} Nb$_3$Cl$_8$.\cite{Yoon2020}
have benefited from single-crystal X-ray diffraction} \red{because .... In this paragraph you are giving some randum facts about clusters but
it is not clear why, if you want to give details OK, but be precis and give more context For the other one you describe what are they main charactyeristic,
but not for these ones, why}. \textbf{Organometallic clusters} contain metal-metal bonds as well as at least an organic ligand directly bonded to a
metal atom. It can be neutral or ionic. One typical representative for the organometallic cluster is [Co$_3$(CCH$_3$)(CO)$_9$].\cite{Sutton2016}
\textbf{Metalloid cluster} are ligand-stabilized clusters that metal atoms possess more direct element-element than element-ligand contacts such
as [Al$_{69}$(N(SiMe$_3$)$_2$)$_{18}$]$^{3-}$ and [Ga$_{84}$(N(SiMe$_3$)$_2$)$_{20}$]$^{4-}$.\cite{Schnepf2002} The suffix ``oid" designates
such cluster possesses atom arrangements that appear in bulk intermetallic compounds with high coordination numbers of the atoms at a molecular
scale. \textbf{Intermetalloid} clusters consisting in at least two different (semi) metallic elements, and possess more direct metal-metal contacts
than metal-ligand contacts. This kind of cluster often appears as discrete units in intermetallic compounds separated from each other by electropositive
atoms for instance $[$Sn@Cu$_{12}$@Sn$_{20}]^{12-}$.\cite{Stegmaier2011, Fassler2004} 
%Clusters can also be observed in the gas-phase by means of mass spectrometry but usually they are not stable. 
Finally, \textbf{clusters composed of non-metal atoms or molecules} are usually found in gas-phase for instance \textbf{fullerenes}, \cite{Kroto1991c60}  \red{citation} \textbf{rare-gas clusters},\cite{Farges1981, Siedschlag2004} \red{citation}  \textbf{water cluster},\cite{Berden1996, Buck2000} \red{citation} and \textbf{PAHs cluster}.\cite{Rapacioli2005stacked, Zhen2018} 

%\cite{Farges1981, Kroto1991c60, Blase2008, Siedschlag2004, Rapacioli2005stacked, Zhen2018, Berden1996, Buck2000} \

These various kinds of clusters, which list has no mean to be non-exhaustive, can be differentiated by the bounding mode, \textit{i.e.} the interaction,
between the cluster constituents. They can be of different natures:

\begin{itemize}
\item[$\bullet$] \textbf{Van der Waals interactions.} %rises from attraction between induced electric dipoles and repulsion between electron cores of closed electronic configurations.
This is the main interaction in the rare-gas clusters such as argon clusters.\red{citations}

\item[$\bullet$] \textbf{Hydrogen-bond interaction,} which is of paramount important in a variety of molecular clusters,
in particular those containing water molecules.

\item[$\bullet$] \textbf{Covalent interaction,} as found in fullerenes\red{citation}, or more generally pure carbonaceous aggregates, and other atomic aggregates
made of non-metallic atoms.
%which is from the stable balance of attractive and repulsive forces between atoms, when they share electron pairs. 

\item[$\bullet$] \textbf{Electrostatic interaction.} as found in \red{Linjie found in the litterature some clusters held together by electrostatic interaction}
%that stems from the valence electrons which almost entirely transferred among closest neighbors to yield two equal but opposite electric charge distributions that mutually attract. 

\item[$\bullet$] Electrostatic attractive force. For instance, the metal clusters are together by electrostatic attractive force. \red{LMinjie, do not know what is this
 Electrostatic attractive force, I want reference here to metalic bound or metalic interecatiuon and some examples.}
%rising from long range valence electron sharing (over many successive adjacent atoms) and partially directional.
\end{itemize}

%Fullerene is a cluster composed of 60 carbon atoms arranged as the vertices of a truncated icosahedron.\cite{Kroto1991c60}
%Rare-gas clusters are ideal microclusters, for which a reliable theoretical treatment may be reached due to the applicability of a simple pair potential. \cite{Farges1981, Siedschlag}
%such as the Lennard-Jones potential. 

%Such naked clusters that are not stabilized by ligands are usually produced by ablation of a bulk metal or metal-containing compound or laser induced evaporation. These approaches produce a broad size distributed clusters. Their reactivity, ionization potential and HOMO-LUMO gap usually show a pronounced size dependence such as certain aluminium clusters and gold clusters. The laser ablation experiments can also generate isolated compounds, and the premier cases are the clusters of carbon \textit{i.e.}, the fullerenes for instance C$_{60}$ and C$_{84}$. 

Properties of clusters stem from both their size and composition. Clusters can thus exhibit very specific physical and chemical properties
that are strongly influence by their structure, which them self are strongly determined by the number of atoms or molecules they are made of.
In particular, the properties of a given clusters can be significantly different from the properties of the corresponding bulk material.\red{citation + exemple here}
Furthermore, when a given cluster of a well defined composition  switches between different stable configurations, chemical and physical
properties can also be strongly impacted.\red{here also, citation + example} This becomes all the more true as the chemical complexity of the cluster
increases, \textit{i.e.} when its is constituted of more than one chemical element, for instance several types of molecules for a molecular clusters or
different atoms for an atomic cluster. Depending on the cluster type, see above,  intermolecular interactions can be rather weak.\red{citation}
This is true for atomic or molecular clusters which cohesion is governed by Van der Waals and/or hydrogen-bond interactions. In that case, its
potential energy surface (PES), or energy landscape, can be extremely complex and a very large variety of local minima displaying equivalent stabilities.
In that case, the structural properties of such an aggregate result from a fine equilibrium between different contributions such as \red{which ones}.
Although properties of clusters generally differ from those of the corresponding bulk materials, a gradual transition occurs between the properties
of the clusters and those of the corresponding bulk as cluster size increases increase.\red{citation} This transition can be rough or continuous depending
on the considered species and properties.\red{citation + exemple} Consequently, the study of clusters allow to bridge the gap between single
molecule or atom properties and bulk materials, which can be of help to reveal microscopic aspects which are hardly observable in the bulk only.

The field of cluster research can be traced back to 1857 when Faraday gave his lecture entitled ``Experimental Relation of (Colloidal) Gold to Light"  which paved the way for modern work on both metal clusters and the interaction of photons with clusters.\cite{Faraday1857} Clusters research have drawn interest and undergone a dramatic growth for several reasons. One is the matter of technique. Now some techniques made it possible for the investigation of clusters both experimentally and theoretically in several scientific fields, for instance the astrophysics, atmospheric physico-chemistry, biochemistry, environmental science.
With the help of mass spectrometer, the well-defined clusters were observed in a supersonic expansion.
The advent of the laser provided a new dimension, enabling detailed spectroscopic observations through probing the systems of different size and degree of solvation.
Others are reasons of purpose. Clusters may offer ways to make new kinds of materials together, to carry out chemical reactions in new ways and to get new kinds of understanding of bulk matter by learning how the bulk properties emerge from properties of clusters as the cluster grow larger and larger.
The behavior study of clusters has been giving new insights into phase transition, e.g. the adsorption to the surface, condensation of gas mixtures and evaporation, precipitation, solidification of liquid mixtures and melting of solids, which makes it a big interest standpoint.\cite{Galvez2019, Xu2020, Tian2018, Deng2018, Rapacioli2019}
The study of clusters helps to understand the nucleation phenomena, for instance the formation of nanoscale materials and aerocolloids, ultrafine particles.\cite{Castleman1978, Castleman1978the, Zhong2000, Pinkard2018}
Cluster in gas-phase state study can provide detailed structural, energetic, and spectroscopic information which is hard to extract from the bulk measurement.\cite{Asuka2013, Luo2016, Wang2016, Jiang2019}
Clusters containing organic/inorganic molecules and some water molecules can be viewed as an intermediate state of matter between the dilute gas phase and solution and the study of them allows the effects of solvation on the chemistry of gas-phase molecules and ions to be explored.\cite{Meot1984, Castleman1994, Castleman1996, Farrar1988, Mayer2002} 

%\subsection{Water clusters with impurities}
\textbf{Water clusters}

Water is ubiquitous in our environment. In view of the importance of water to all life and its complex properties, a significant amount of experimental \cite{Woutersen1997, Ruan2004, Brubach2005, Bergmann2007, Pokapanich2009, Sun2010, Harada2017, Yamazoe2019} and theoretical \cite{Silvestrelli1999, Laage2006, Bryantsev2009, Silvestrelli2017} studies have been performed about this fundamental substance since the first realistic interaction potential of water was proposed in 1933. \cite{Bernal1933, Shields2010} Water clusters are intermediate systems between gas phase and condensed phases. The study of water clusters is of fundamental importance to understand properties of liquid water and ice and offers the opportunity to understand how the properties of bulk water emerge and how the properties of water change with size.\cite{Gregory1996} The research about water clusters focusing on the determination of the most stable structures, the corresponding stabilization energies, and the harmonic vibrational frequencies etc has been done.\cite{Teeter1984, Pedulla1998, James2005, Prell2009, Brown2017, Malloum2021}  There have been many $ab initio$ studies of small water clusters, and the global potential energy minima of (H$_2$O)$_{1-5}$ are not in doub. \cite{Wales1998}
The water complexes are plentiful in the atmosphere, which plays a crucial role in the evolution of climate. \cite{Bigg1975, Vaida2000, Aloisio2000, Ramanathan2001, Mccurdy2002, Hartt2008, Vaida2011}
It is known that water clusters can absorb significant amounts of energy,\cite{Kjaergaard2003} and these clusters are not yet included in climate models due to the lack of data about their formation. \cite{Vaida2003} Detailed computational thermodynamics can be useful in modeling the aerosol growth by determining the equilibrium constants for cluster formation.\cite{Morrell2010}

Hydrogen bonding is arguably the most extensively studied among all the noncovalent interactions. Hydrogen bonding governs many chemical
and biological processes in nature and living organisms.\cite{Pimentel1960, Jeffrey1997}
The hydrogen bonding has been known for about one hundred years, \cite{Latimer1920} but new researches involving hydrogen bonding species continues to generate interesting results.
An important property of water is its ability to form
hydrogen bonds.
Commonly it is asserted that each hydrogen bond between water molecules stabilizes a structure by about 5 kcal.mol$^{-1}$. \cite{Eisenberg2005} Therefore, water clusters that differ only by the direction of hydrogen bonds, but otherwise have the same number of H-bonds and placement of oxygen atoms should have approximately the same energy. \cite{Kuo2003} The stability of water clusters, based on the arrangement of individual molecules in different phases has been widely explored. \cite{Ludwig2001, Buckingham2008} A lot of theoretical studies have focused on understanding hydrogen bonding in small water clusters (H$_2$O)$_{2-6}$. \cite{Lee2000, Maheshwary2001, Santra2008, Buckingham2008, Hanninen2009, Neela2010} In one of the carefully conducted computational studies, it was shown that the most stable geometries of water clusters H$_2$O)$_{8-20}$ arise from a fusion of tetrameric or pentameric rings. \cite{Maheshwary2001, Neela2010}

Molecular clusters with a controlled number of solvent molecules are ideal model systems for providing a  fundamental understanding of solute-solvent and  solvent-solvent interactions at the molecular level.\cite{Wang2010}
The study of the stability of water clusters containing inorganic/organic ions or neutral molecules for instance the Cl$^{-}$(H$_2$O)$_n$, Na$^+$(H$_2$O)$_n$, H$_2$PO$_4^{-}$, NH$_4^+$(H$_2$O)$_n$, NH$_3$(H$_2$O)$_n$, C$_6$H$_6$O(H$_2$O)$_n$, H$_2$SO$_4$(H$_2$O)$_n$,
HSO$_4^{-}$(H$_2$O)$_n$, (CO)$_m$(H$_2$O)$_n$, ((CH$_3$)$_2$NH$_2^+$)$_m$(HSO$_4^{-}$)$_m$(H$_2$O)$_n$, C$_4$H$_5$N$_2$O$_2^+$(H$_2$O)$_n$, (C$_5$H$_5$N)$_m$H$^+$(H$_2$O)$_n$, and so on is the foundation for the study of other properties of these systems such as the spectroscopic study. \cite{Berden1996, Buck2000, Huneycutt2003, Schermann2007, Caleman2007, Rozenberg2009, Ryding2011, Depalma2014, Korchagina2016, Korchagina2017M, Korchagina2017, Braud2019}

Many significant efforts have been devoted to the experimental characterization of the chemical composition and behavior of atmospheric particles 
since 1970s. \cite{Hogan1975, Arnold1977, Arnold1982, Heymsfield1986} Among these studies, the ion composition measurements demonstrated the existence of charged molecular aggregates in the stratosphere,\cite{Arnold1977, Arnold1982} especially the negatively charged species such as nitrate- and sulfate-containing water clusters.
These grown atmospheric particles initiate the process of acid cloud formation and participate in reactions leading to the destruction of the ozone layers in polar regions, \cite{Koop1996, Carslaw1997} which makes it meaningful to study the corresponding charged water clusters. \cite{Korchagina2016}
In addition, charged clusters can be sorted easily by electrostatic, magnetic or time-of-flight mass analysis to yield mass spectra, which contributes to the exploration of charged clusters.  
Understanding the hydrated proton is of paramount importance for the knowledge of fundamental processes in biology and chemistry, and the investigation of protonated water clusters has been proven to be essential for understanding the nature of protons in solution. \cite{Kunst1980, Torrent2011}
In the work of this thesis, the stability of ammonium/ammonia water clusters and protonated uracil water clusters were explored.

%\subsection{PAHs Clusters}
\textbf{PAHs clusters}

Polycyclic aromatic hydrocarbon clusters are abundant in the interstellar medium, which lock up about 10\% - 20\% of the carbon element in the universe and are considered as the possible starting material for the earliest forms of life. \cite{Hoover2014, Tielens2008} They are one of the main pollutants in the environment. They act as part of the soot particles in combustion science. In addition, they act as the prototypes for the design of new organic solar cell devices. PAHs can be transformed, through hydrogenation, oxygenation, and hydroxylation, to become more complex organic compounds, which makes it an interesting choice to study the PAH clusters.

In order to characterize the stability of polycyclic aromatic hydrocarbons, the involution of them has been explored a lot in experiment after absorption of photons, collision with high or low energetic particles or in a very high pressure environment. The collision details of polycyclic aromatic hydrocarbon cluster with projectile are always not possible to obtain from the experimental data. In addition, the experimental studies are complicated and associated facilities are expensive, which sometimes prevent all desired measurements to be carried out. Therefore, further theoretical studies should be conducted to bring us to make a deeper interpretation of the experimental measurements and complement the experiments. 

%\section{CID of molecular clusters}
\textbf{CID of molecular clusters}

The structure, energetics and reactivity of a variety of molecular cluster can be explored by collision-induced dissociation. \cite{Dawson1982, Graul1989, Wei1991, Liu2006, Goebbert2006, Coates2018}. By colliding a molecule, or a molecular cluster with a non-reactive noble gas atom or a small molecule such as N$_2$, it is possible to monitor the parent ions and collision products then the spectra of the parent and product ions can provide a wealth of information about the structure from which one can infer, for instance, dissociation mechanisms \cite{Nelson1994, Molina2015} or bond and hydration enthalpies \cite{Carl2007}. The collision-induced dissociation also has been used to understand the impact of high-energy radiations on living cells and DNA or RNA \cite{Liu2006, Nguyen2011, Shuck2014}, as well as low-energy collisions on  of biological molecules. \cite{Castrovilli2017,Bera2018}.

Extracting energetics or collision process from collision-induced dissociation is not an easy task and it often requires the theoretical calculations to complement. Two main methodologies can be conducted. The first one is to make an exhaustive description of the potential energy surface connecting both parent ions and products. 
%Energetic information on both minima and transition states can then be introduced in Rice-Ramsperger-Kassel-Marcus \cite{Klippenstein1992, Baer1996} and/or Kinetic Monte Carlo simulations \cite{Metropolis1949, Voter2007}.
The second approach is to perform molecular dynamics simulations to explicitly model the collision trajectory of the target ion and the projectile, the energy redistribution, the subsequent reorganizations and fragmentations. 
A potential is needed to correctly describe the potential energy surface of the system and its reactivity. The method chosen need to reach a balance between the desired precision and the computational cost.
%The question appeared during the theoretical study of molecular clusters is to chose the calculation method. 

For the dynamical simulations of system composed of several tens of atoms, the full configuration interaction and wave function based methods allow to calculate the energy, but do not allow to achieve sufficient simulations to describe their dynamic behavior at finite temperature.
It is difficult for the exhaustive exploration of potential energy surfaces of system with tens of atoms or for carrying out dynamical simulations for several hundred picoseconds using DFT method.
The density-functional based tight-binding method (DFTB) method can perform molecular dynamical simulations of systems containing several tens of atoms for simulation time of several hundred picoseconds.
The force field methods can achieve dynamical simulations of system with tens of atoms for several hundred nanoseconds, but it can poorly describe the formation or breaking of covalent bonds. 
Therefore, the DFTB approach seems to be well suited to the study of molecular clusters investigated in this thesis work.

For the work of this thesis, it is concentrated on the structure, solvation, thermodynamics study of ammonia containing water clusters, ammonium containing water clusters, which help to understand the nucleation phenomena and the formation of aerosols. The uracil included water clusters were also studied, which can provide a benchmark to observe how the properties of biological molecules change from isolated gas-phase to hydrated species. The polycyclic aromatic hydrocarbon (PAH) clusters are abundant in the universe.\cite{Carey2005, Hudgins2005, Clavin2015}
The dynamics study of the dissociation of the simplest pyrene aggregates, pyrene dimer, to interpret the CID experiments of PAHs with noble gas to have a better understanding of the physics of this kind of cluster.

The first chapter introduces the object of this thesis work. A generality about clusters and the clusters studied in this thesis are introduced. Then the collision-induced dissociation of molecular clusters is  briefly described. 

The second chapter is devoted to the introduction the fundamental concepts used in theoretical chemistry for the solution of the electronic problem, which describes the main approaches traditionally employed. 
The method, density functional based tight binding (DFTB), applied in this thesis work is also described. The different methods to explore the potential energy surface are presented in this chapter.

In the third chapter, the study on the structure and stability of ammonium/ammonia water clusters, 
%mixed ammonium/ammonia and sulfate containing water clusters, 
and protonated uracil water clusters were presented. 
Comparing the results calculated using DFTB method with the corresponding ones using MP2 method or the ones in  the literature, it shows the DFTB method can provide a quite good result for the optimization of these  clusters. 

The fourth chapter presents the study on the molecular dynamics simulations of collision-induced dissociation of protonated uracil water clusters. The theoretical proportion of formed neutral uracil molecule \textit{vs.} protonated water cluster as well as total fragmentation cross sections are consistent with
the experimental data which highlights the accuracy of the simulations. The molecular dynamic simulations allow to probe which fragments are formed on the short time scale and rationalize the location of the excess proton on these fragments. We demonstrate that the location of the excess proton is highly influenced by the nature of the aggregate undergoing the collision. The analyses show that, up to seven water molecules in the cluster, a shattering mechanism occurs after collision whereas for the cluster with twelve water molecules has a chance to rearrange prior to complete dissociation. In addition, the dymical simulations of the collision-induced dissociation of pyrene dimer cation at different collision energies are described in this chapter. It appears that most of the dissociation occurs on a short timescale (less than 3 ps). The dynamical simulations allow to visualise the dissociation processes.
At low collision energies, the dissociation cross section increases with collision energies whereas it remains almost constant for collision energies greater than 10-15~eV. The analysis of the kinetic energy partition is used to get insights into the collision/dissociation processes at the atomic scale.
The simulated time of flight mass spectra of parent and dissociated products are obtained from the combination of molecular dynamics simulations and phase space theory to address the short and long timescales dissociation, respectively. The agreement between the simulated and measured mass spectra suggests that the main processes are captured by this approach.  

Finally, the conclusions of the work of this thesis as well as a number of perspectives are displayed in chapter 5.
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