From 5fd7807a8c5e5052681927364089f9e4cdc535ea Mon Sep 17 00:00:00 2001 From: linjiez Date: Fri, 13 Sep 2019 15:38:38 +0200 Subject: [PATCH] leran TexMaker --- paper_UAR.tex | 622 +------------------------------------------------- 1 file changed, 9 insertions(+), 613 deletions(-) diff --git a/paper_UAR.tex b/paper_UAR.tex index f87dbb2..51bbcf2 100644 --- a/paper_UAR.tex +++ b/paper_UAR.tex @@ -3,7 +3,7 @@ %% The document class accepts keyval options, which should include %% the target journal and optionally the manuscript type. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\documentclass[journal = jpcafh ,manuscript=article]{achemso} +\documentclass[journal = inoraj ,manuscript=article]{achemso} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Place any additional packages needed here. Only include packages @@ -107,644 +107,40 @@ %% require that it is printed as part of the abstract page. It will %% be automatically moved as appropriate. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{tocentry} -\includegraphics[scale=0.1]{TOC.png} -\end{tocentry} +%\begin{tocentry} +%\includegraphics[scale=0.1]{TOC.png} +%\end{tocentry} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% The abstract environment will automatically gobble the contents %% if an abstract is not used by the target journal. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{abstract} -The successive hydrogenation of CO is supposed to be the main mechanism leading -to the formation of complex oxygenated species in the interstellar medium, possibly -mediated by ice layers or ice grains. In order to simulate the dynamical influence -of a water environment on the first step of the hydrogenation process, we achieve -molecular dynamics simulations of the reactive collision of H with CO adsorbed on -water clusters in the framework of the self-consistent-charge density functional -based tight-binding approach (SCC-DFTB) to calculate Potential Energy Surfaces. The reaction -probabilities and the reactive cross sections are determined for water cluster sizes -up to ten water molecules. The collision results are analyzed in terms of different reaction pathways: -reactive or non-reactive, sticking or desorption of the products or reactants. We show that the -HCO radical, although potentially formed as an intermediate whatever the size of the -water cluster, is significantly stabilized for cluster sizes larger than one water molecule -and may remain adsorbed on water clusters with more than three molecules. This behavior -is shown to be linked to the dissipation of the collision energy into vibrational -excitation of the water cluster. + \end{abstract} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Start the main part of the manuscript here. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Introduction} -In recent decades, the chemical composition of the Universe has been continuously -investigated, essentially via absorption spectroscopy with background stars as lamps. -It was established that all chemical elements and molecules in the InterStellar Medium -(ISM) are concentrated in three main kind of clouds: diffuse, translucent and dense clouds. -The chemical composition of these clouds is dominated by the abundance of hydrogen, -the concentration of helium is about 10\%, and other elements such as carbon, nitrogen, -and oxygen are also present in the ratio $\sim$10$^{-3}$-10$^{-4}$ of the hydrogen -density \cite{Festou}. In addition to these elemental abundances, a large number of -simple (H$_{2}$, CH, CH$^{+}$, CN, C$_{2}$, OH, CO, HCO, HCO$^{+}$, HCN, C$_{3}$) -and more complex organic molecules (CH$_{3}$OH, C$_{2}$H$_{5}$OH, C$_{2}$H$_{5}$CN, -CH$_{3}$COCH$_{3}$, CH$_{4}$, NH$_{3}$, H$_{2}$O, \textit{etc.}) were -detected \cite{churchwell1,thompson1,schutte1,grim1,cordiner1,kaiser1,herbst1,herbst2}. -Although most of those detected compounds can form through gas-phase processes, -some of them, in particular H$_{2}$, H$_{2}$O and CH$_{3}$OH are assumed to form -through chemical reactions between atoms and molecules at the surface of grains.\cite{Horn2004,Oberg2016} -The composition and structure of the outer layers of these grains can be of different nature: organic, -ice-mineral mixture, pure water-ice and ice-dust mixture grains depending, for instance, -on the incidence of UV radiation and cosmic rays\cite{schulz1}, or the atomic densities of -the environment where they are present.\cite{Taquet2012} In 2015, a unique set of experimental data on the chemical -composition of the surface of the 67P/Churyumov-Gerasimenko comet were obtained through -various instruments of the Philae module \cite{wright1,goesmann1,spohn1}. For instance, -mass spectroscopy measurements performed by the Ptolemy instrument detected H$_{2}$O, -CO$_{2}$ and CO as main volatile species in a ratio of 10:2:$>$1 \cite{wright1}. -The COmetary SAmpling and Composition (COSAC) experiment also provided a picture of -the organic composition of the comet surface.\cite{goesmann1} Sixteen molecules, -belonging to two main molecular groups, were identified by the COSAC instrument. -The first group includes the H$_{2}$O and CO molecules and the subsequent oxygen-containing -organic species such as alcohols and carbonyls. The second group includes CH$_{4}$ -and NH$_{3}$ (although not confidently identified) that lead to the formation of -nitrogen-containing organic species (amines, nitriles, amides, and isocyanates) \cite{goesmann1}. -These results provide a rather accurate picture of the 67P chemical composition -(and potentially of other comets) but no accurate information is provided on the -mechanisms that lead to the formation of these complex organic compounds in the -ISM \cite{loomis1,kalvans1}. This is an important question to address for both -theoreticians and experimentalists in order to strengthen our understanding of -the ISM chemistry. -Currently, it is supposed that the main mechanism leading to the oxygenated -compound formation in grain mantles and comets is a process of successive -hydrogenation of CO, occurring by the consecutive addition of hydrogen -atoms:\cite{book1,tielens1,crovisier1,watanabe2,watanabe3,hidaka1} - -\begin{center} -CO $\xrightarrow{\text{H}}$ HCO $\xrightarrow{\text{H}}$ H$_{2}$CO $\xrightarrow{\text{H}}$ H$_{3}$CO $\xrightarrow{\text{H}}$ CH$_{3}$OH -\end{center} - -This mechanism has been the subject of various experimental studies. For instance, Hiraoka -and co-workers studied the reaction of H atoms with a solid CO thin film in the 10-25~K -temperature range.\cite{hiraoka1,hiraoka2} From these experiments, the authors -concluded that -(i)- H atoms do not diffuse into the CO matrix, the reaction proceeds only -at the surface -(ii)- the primary reaction product H$_{2}$CO is prone to polymerization -(iii)- the -rate constant for the first and second steps of this reaction is small at cryogenic temperature -(iv)- -formaldehyde and methanol were formed. Later, Pirim \textit{et al.} studied the same reaction -in two different ways, by simple hydrogenation of a CO surface and by co-injection of CO molecules -and H atoms \cite{pirim1}. In the former case, nothing was formed at 3~K whereas H$_{2}$CO and -CH$_{3}$OH were detected at 10~K by Fourier Transform InfraRed (FT-IR) spectroscopy. In contrast, -the co-injection at 10~K leads to the formation of both the HCO and H$_{3}$CO radicals as major -products. However, as mentioned above, the hydrogenation of CO in the ISM is likely to -occur at the surface of ice-coated grains. To understand such a situation, some groups also studied -the H addition on CO in a H$_{2}$O-CO ice \cite{watanabe1,watanabe2,pirim2}. They showed that -water molecules play two important roles in this process. On the one hand, they exhibit a catalytic -role by helping to overcome the activation barriers. On the other hand, water molecules create new -chemical pathways that enhance the reactivity. - -To complement these experimental measurements, theoretical studies were conducted on the different -steps of the sequential hydrogenation reaction of carbon monoxide, isolated or in the presence of -water molecules \cite{woon1,cao1,woon2,rimola1,peters1,Peters2013a}. In particular, the geometric and -energetic characteristics of reactants, transition states and products involved in this mechanism -have been the subject of various calculations at high levels of theory. For instance, Woon observed -that, at the QCISD$^{*}$ level of theory, the barrier of the H + H$_{2}$CO $\longrightarrow$ -CH$_{3}$O reaction is reduced from 5.04~kcal.mol$^{-1}$ for isolated CO to 4.18~kcal.mol$^{-1}$ -when adding four water molecules \cite{woon1}. The intermediates of this multi-step mechanism, -such as HCO and H$_{2}$CO, may also undergo isomerization under certain conditions and were -thus also investigated \cite{zanchet1,schreiner1,peters1}. - -However, it is certainly the first step of the sequential hydrogenation of CO that has deserved -the largest attention in the literature as it is a crucial step towards the formation of complex -oxygenated species \cite{woon1,cao1,woon2,rimola1,peters1,Peters2013a,adams1,bitter1,werner1,werner2,cho1,romanowski}. -For instance, Woon compared the structures and frequencies of CO and HCO as well as the energetics -of the H + CO $\longrightarrow$ HCO reaction (without water) with various high-accuracy schemes -such as Restricted Coupled Cluster RCCSD(T) or Davidson-corrected internally-contracted -MRCI+Q methods \cite{woon2}. The author showed that at the aug-cc-pVTZ level, MRCI+Q and -RCCSD(T) methods with ZPE correction slightly overestimate barrier heights, 4.1 and 4.2~kcal.mol$^{-1}$ -respectively, in comparison with the experimental value 2.0$\pm$0.4 kcal.mol$^{-1}$. In contrast, -the MRCI+Q and RCCSD(T) results for the reaction ergicity, -13.7 and -13.8 kcal.mol$^{-1}$, respectively, -are in a very good agreement with the experimental value of -14 kcal.mol$^{-1}$. Those calculations -were recently revisited by Peters \textit{et al.} using state-of-the-art multireference \textit{ab initio} -methods to study the energetics of the HCO/DCO formation and dissociation processes.\cite{Peters2013a} -In addition to their theoretical interest, the results of those and other \textit{ab initio} calculations -can be further used as input values for larger scale numerical simulations. For instance, the GRAINOBLE model -was used by Rimola \textit{et al.} \cite{rimola1} to describe the distribution of the H$_{2}$CO and CH$_{3}$OH -ice abundances. It leads to abundance values that are in a good agreement with the experimental data. -Although extremely informative, high-precision \textit{ab initio} wavefunction type calculations are only -achievable for very small systems. In a similar way, Density Functional Theory (DFT) can describe larger species -and has been applied to systems containing up to 32 water molecules but only in a static framework.\cite{rimola1} -Although a good description of the Potential Energy Surface (PES) of the various species -involved in the mechanism is of primary importance, a dynamical simulation of the hydrogenation -process at the molecular level is also desirable. Indeed, size and temperature effects of the water -substrate, influence of its morphology and diffusion of species at the surface of nanograins can -be important contributing factors that can hardly be included in highly accurate quantum chemical -calculations although they can have a strong impact. Furthermore, although reactions can occur at the -surface of grains between diffusing species \cite{Oberg2016}, they are also likely to occur during -collisions between molecules. This can hardly be described by static quantum chemical calculations -only and thus a more complete understanding of such a mechanism require the use of Molecular -Dynamics (MD) simulations. To the best of our knowledge, no MD study has been conducted to -explicitly simulate the reaction of H with CO in the presence of water molecules. - -In the present contribution, we present a MD study of the collision of H with CO at the surface -of water clusters, \textit{i.e.} CO-(H$_{2}$O)$_{n}$ (n=0-10), aiming at a statistical sampling of -the various possible pathways likely to occur between the two species. Such simulations are -made possible by the description of the PES at the Self-Consistent-Charge Density Functional -based Tight-Binding (SCC-DFTB) level of theory that allows to describe bond-forming and -bond-breaking at a limited computational cost. The outline of the article is as follows: the -computational model is described in Section II, the results of the simulations are presented in -Section III and the main outcomes and perspectives are summarized in the conclusion. +iuASDUKYSDFHFASDHDFASJHDASFJDHFS +SDFAKJGDFSGFSDAJGFSDASDFHGDSFA +JHASDFJSDFAGDFSHGSDFA \section{Computational Methods} \label{Comput_meth} -\textbf{Computation of the PES.} -We use the SCC-DFTB \cite{elstner,koskinen,frauenheim} approach implemented in the deMonNano code \cite{heine1} -to describe the PES of the CO-(H$_{2}$O)$_{n}$ clusters. Within the SCC-DFTB formalism, the electronic -energy is given by the following equation: -% -\begin{eqnarray}\label{enr} -E^{SCC-DFTB} = \sum\limits^{occ} \langle \psi_i | \hat{H_0} | \psi_i \rangle + \sum\limits_{\alpha \beta} U_{\alpha \beta} (R_{\alpha \beta}) -+ \frac{1}{2} \sum\limits_{\alpha \beta} \Delta q_{\alpha} \Delta q_{\beta} \gamma_{\alpha \beta} -- \sum\limits_{\alpha \beta} f_{damp} \frac{C_{6}^{\alpha \beta}}{R_{\alpha \beta}^{6}} -\end{eqnarray} -% -where the 1$^{\text{st}}$ term is a tight-binding term defined from parametrized integrals and -the 2$^{\text{nd}}$ term is a repulsive interaction expressed as a sum over all atomic pairs. -In the present study, we used the mio-set for Slater-Koster integrals \cite{elstner}. -The 3$^{\text{rd}}$ term is the second-order term of the Taylor expansion expressed as a function -of the atomic charge fluctuations $\Delta q_\alpha$ and the 4$^{\text{th}}$ term describes the -London dispersion interaction. Rapacioli and co-workers proposed to improve the description of -the electrostatic interaction in molecular systems by replacing the original Mulliken charges by -the Class IV - Charge Model 3 (CM3) charges \cite{DFTB_CM3,rapacioli2}, defined as: -% -\begin{equation}\label{cm3} -q_{\alpha}^{CM_3} = q_{\alpha}^{Mull} + \sum \limits_{\alpha' \neq \alpha}^{atoms} [D_{Z_{\alpha}Z_{\alpha'}}B_{\kappa \kappa'} + C_{Z_{\alpha}Z_{\alpha'}}B^{2}_{\kappa \kappa'}] -\end{equation} -% -where $B_{\kappa \kappa'}$ is the Mayer's bond order whereas $C_{Z_{\alpha}Z_{\alpha'}}$ and -$D_{Z_{\alpha}Z_{\alpha'}}$ are empirical parameters to define. We used the D$_{\text{OH}}$=0.129 -value previously proposed by Simon and Spiegelman in their study on water clusters \cite{simon1,simon2,simon3}. -We fitted the D$_{\text{CO}}$ parameter to reproduce the experimental dipole moment of CO which -leads to D$_{\text{OC}}$=0.012. We set D$_{\text{CH}}$=0.0. -A difficulty in the description of the H+CO reaction lies in the fact that it involves, -at small distances, a potential crossing between the $^{2}\Pi$ electronic ground-state -(which dissociates to ground state products H($^{2}S$) + CO($^{1}\Sigma^{+}$)) and a -$^{2}\Sigma^{+}$ excited state of the formyl radical correlated with H($^2S$)+CO($^3\Pi$). -Therefore, at the intersection of the electronic states, the treatment of the problem with -a mean-field single determinant scheme arises, and self-consistency convergence problems -occur. To solve this problem, we used a Fermi-Dirac orbital occupation defined by an -electronic temperature of 1000~K which allows to achieve a continuous switch from -one state to the other in the near vicinity of the crossing. - -\textbf{Exploration of the PES.} -Before performing the collisional trajectories between H and CO, we first optimized the -geometry of the considered CO-(H$_{2}$O)$_{n}$ clusters in order to start our trajectories -as close as possible to the equilibrium configurations at low temperature. To explore the -PES of the clusters in an exhaustive way, we used the Molecular Dynamics Parallel-Tempering -(MDPT) algorithm \cite{sugita1,sugita2,earl1}, which allows for replica -exchanges between trajectories at different temperatures. This scheme increases -the ergodicity of the MD simulations and thus speeds up the exploration of the PES at a determined -temperature. We used a temperature range going from 20 to 320~K by steps of 5~K which correspond -to 60 distinct temperatures. All the MD trajectories were 4~ns long with a timestep of 0.2 fs. -The PT replica exchanges were attempted every 400 fs. In order to achieve canonical simulations, -we used a Nos\'e-Hoover chain of five thermostats defined by a unique frequency of 800 cm$^{-1}$ \cite{nose,hoover}. - -In order to find the lowest-energy configurations on each PES, local geometry optimizations -of the CO-(H$_{2}$O)$_{n}$ clusters were subsequently performed using the following procedure: -for one out of four temperatures, \textit{i.e.} every 20~K, one thousand different geometries -were periodically selected and locally optimized using a conjugate gradient algorithm. This lead -to a total of 15000 geometry relaxations per CO-(H$_{2}$O)$_{n}$ cluster, from which the -lowest energy one was retained. - -\textbf{MD Collision Trajectories.} -The first step of the MD simulation consisted in the sampling of the initial conditions, namely --(i)- the initial positions and velocities of the CO-(H$_{2}$O)$_{n}$ clusters, -(ii)- the angular -orientations of the clusters and -(iii)- the impact parameter of the collision. In order to sample -the initial positions and velocities, we achieved thermalisation of the CO-(H$_{2}$O)$_{n}$ -clusters at 70~K via a 200~ps long MD simulation in the canonical ensemble using the previously -obtained lowest-energy -configuration as initial geometry. The last geometries and corresponding velocities were then taken -as initial conditions for subsequent collisional trajectories. These initial positions of the -CO-(H$_{2}$O)$_{n}$ clusters were further evenly rotated along the three Cartesian axes to obtain -64 initial angular conditions. For each orientation, the impact parameters -defining the initial position of the colliding hydrogen atom were randomly generated in a disk -of radius R (R$>$R$_{\text{cluster}}$) centered at 10 \AA \ from the center of mass of -the cluster. For the CO-(H$_{2}$O)$_{n}$ clusters with n=0-5, 53 different impact parameters -were generated per angular orientation leading to a sampling of 3392 initial conditions. -In the case of CO-(H$_{2}$O)$_{10}$, 2000 initial positions of the hydrogen atom were generated -opposite to the surface containing the CO molecule in order to describe quasi-frontal collisions only. -The initial velocity of the hydrogen atom was set to 0.01 \AA.fs$^{-1}$ which is consistent with -the temperature of the cluster at 70~K. The time length of each collision trajectory was set equal to 10~ps. - -\textbf{Wavefunction and DFT Calculations.} -In order to establish reference equilibrium geometries and intermolecular interaction energies -of the CO-H$_{2}$O isomers, we performed \textit{ab initio} MP2 and CCSD(T) calculations in -combination with the Pople-style 6-311++G(d,p) basis set \cite{krishnan1} and the aug-cc-pVTZ -basis set of Dunning and co-workers \cite{dunning1,kendall1}, respectively. To further check -the performances of the SCC-DFTB approach, we also carried out DFT calculations using the -B3LYP,\cite{becke1,lee1,vosko1} B3LYP-D3\cite{Grimme2010} and B97D\cite{Grimme2006} -exchange-correlation functional in combination with the 6-311++G(d,p) basis set. The latter -functional was tested as it was shown by Peters \textit{et al.} to provide a satisfactory value -for the formation barrier of the H + CO $\rightleftharpoons$ HCO reaction in vacuum.\cite{Peters2013a} -Basis set superposition errors (BSSE) were taken into account using the counterpoise method of Boys -and Bernardi.\cite{Boys2002} All DFT and wavefunction calculations were performed with the Gaussian -09 package \cite{g09}. - -All the binding energies between CO and the water clusters discussed in the text were defined as the energy of the -relaxed CO-(H$_{2}$O)$_{n}$ complex minus the energy of the water cluster minus the energy of CO both taken in -their geometry in the optimized complex. In the same way, formation energies for the H+CO-(H$_{2}$O)$_{n}$ reaction -were defined as the energy of the relaxed HCO-(H$_{2}$O)$_{n}$ complex minus the energy of one hydrogen minus the -energy CO-(H$_{2}$O)$_{n}$ considering its geometry in the optimized complex. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Results and Discussion} \label{resul_disc} -\subsection{Validation of SCC-DFTB Potential.} -The SCC-DFTB method is a parametrized approach. The D$_{\text{OH}}$ parameter involved in the -definition of the CM3 charges for the O--H pair was shown by Simon \textit{et al.} to yield -good results for the description of water clusters.\cite{simon1,simon2,simon3} -For instance, in the water dimer, it provides an oxygen-oxygen distance of 2.92 \AA \ to be -compared with the experimental value of 2.98 \AA \cite{odutola}. The validity of the -D$_{\text{CO}}$ and D$_{\text{CH}}$ parameters determined in the present work had to be -checked. For this purpose, we compared the structural and energetic characteristics of -the two well-known CO-H$_{2}$O isomers to fully \textit{ab initio} calculations. -Figure~\ref{str} shows the structure of these two CO-H$_{2}$O isomers. The first one -(C-structure) corresponds to a bonding between an H atom of water and the C atom of -CO while the second one (O-structure) corresponds to the interaction between an H atom -of water and the O atom of CO. - -\begin{figure}[h!] -\centering -\includegraphics[scale=0.40]{H2O_CO_OC.png} -\caption{MP2/6-311++G(d,p) geometries of the global (C-structure) and local (O-structure) minima of -CO-H$_{2}$O.} \label{str} -\end{figure} - -\begin{table}[h] -\small -\centering -\caption{Equilibrium geometries and intermolecular interaction energies of the C- and O-structures of -CO-H$_{2}$O obtained from SCC-DFTB, DFT/B3LYP, DFT/B3LYP-D3, DFT/B97D and MP2 with the 6-311++G(d,p) -basis set and CCSD(T) with the aug-cc-pVTZ basis set.} -\label{r_e} -\begin{tabular}{|c|c|c|c|c|} -\hline -\multirow{2}{*}{Method} & \multicolumn{2}{c|}{C-structure} & \multicolumn{2}{c|}{O-structure} \\ \cline{2-5} - & $r_{min}$, \AA & \begin{tabular}[c]{@{}c@{}}E$_{\text{int.}}$,\\ kcal.mol$^{-1}$\end{tabular} & $r_{min}$, \AA & \begin{tabular}[c]{@{}c@{}}E$_{\text{int.}}$,\\ kcal.mol$^{-1}$\end{tabular} \\ \hline -SCC-DFTB & 2.20 & -0.72 & 2.18 & -0.44 \\ \hline -MP2 & 2.45 & -1.84 & 2.41 & -1.02 \\ \hline -MP2/BSSE & 2.52 & -1.51 & 2.53 & -0.61 \\ \hline -B3LYP & 2.44 & -1.49 & 2.41 & -0.79 \\ \hline -B3LYP/BSSE & 2.42 & -1.36 & 2.40 & -0.66 \\ \hline -B3LYP-D3 & 2.38 & -2.03 & 2.33 & -1.47 \\ \hline -B3LYP-D3/BSSE & 2.40 & -1.89 & 2.36 & -1.28 \\ \hline -B97D & 2.51 & -1.82 & 2.50 & -1.06 \\ \hline -B97D/BSSE & 2.53 & -1.68 & 2.52 & -0.92 \\ \hline -CCSD(T)$^a$ & - & -2.05 & - & -1.21 \\ \hline -CCSD(T)/BSSE$^b$ & - & -1.65 & - & -0.90 \\ \hline -\end{tabular}\\ -$^a$ CCSD(T) energy calculations were performed using the MP2 optimized geometry\\ -$^b$ CCSD(T)/BSSE energy calculations were performed using the MP2/BSSE optimized geometry\\ -\end{table} - -The structural and energetic characteristics of these dimers are given in Table~\ref{r_e}. -The interaction distances calculated by the SCC-DFTB method are 2.20 and 2.18 \AA~for r(H$_{2}$-C) -and r(H$_{2}$-O$_{2}$), respectively, somewhat smaller than the data obtained from MP2/6-311++G(d,p) -calculations, namely 2.45 and 2.41 \AA, respectively. From an energy standpoint, the CO-H$_{2}$O is -a very weakly bound complex (both C- and O-structures), where the interaction energy includes about -40 \% of electrostatic, 35 \% of induction and 25 \% of dispersion contributions \cite{vilela1,wheatley1,yaron1,sadlej1}. -Referring to such a very small value of the interaction energy, an accurate description using -density functional or semi-empirical methods is a very difficult task. Thus, although the SCC-DFTB -correctly predicts the energetic ordering of the two isomers, the interaction energies are somewhat -underestimated, even-though it appears from Table~\ref{r_e} that the exact value of the interaction -energy is highly dependent on the method, basis set, and applied corrections. Indeed, the three -DFT calculations (B3LYP, B3LYP-D3 and B97D) leads to quite different values for the interaction energy. -Interestingly, the B97D functional in combination with the 6-311++G(d,p) basis set provides geometries -that are very close to MP2/BSSE structures, and interaction energies almost equal to CCSD(T)/BSSE ones. -This confirms the good performances of B97D to describe carbon monoxide.\cite{Peters2013a} -From the Table~\ref{r_e}, the SCC-DFTB results for CO-H$_{2}$O are thus qualitatively similar to \textit{ab initio} -data and one can expect that the observed differences will not affect too seriously the present dynamical simulations. -As shown in the Table~\ref{e_bind}, with increasing cluster size, the SCC-DFTB binding energies converge rather -quickly from 0.72 kcal.mol$^{-1}$ to 1.00 kcal.mol$^{-1}$ and reach convergence at n=4-5. A similar behavior is -obtained at the B97D and MP2 levels of theory while B3LYP-D3 values display larger fluctuations. Consequently, -although the SCC-DFTB binding energies are still underestimated for larger clusters with respect to DFT and MP2 values, -the rapid convergence trend is expected to be reliable and certainly important for the reactive collisional behavior -discussed in the next section. - -\subsection{Results} -\begin{figure}[h!] -\centering -\includegraphics[scale=0.45]{co_h2o_figures.png} -\caption{Geometries of the global SCC-DFTB minima of the -CO-(H$_{2}$O)$_{n}$ (n=1--5,10) clusters.} \label{str_2} -\end{figure} - -\begin{table}[] -\centering -\caption{Binding energies between the CO (second column) and HCO (third column) molecules and (H$_{2}$O)$_{n}$ -clusters obtained with SCC-DFTB as well as B3LYP-D3, B97D and MP2 in combination with the 6-311++G(d,p) -basis set. \textit{Ab initio} values are reported including BSSE corrections. -SCC-DFTB HCO formation energy for H+CO-(H$_{2}$O)$_{n}$ along with B97D results -obtained by Peters \textit{et al.}\cite{} (Fourth column). All energies are in kcal.mol$^{-1}$.} -\label{e_bind} -\begin{tabular}{|c|cccc|cccc|c|} -\hline - & \multicolumn{4}{c|}{CO-(H$_{2}$O)$_{n}$} & \multicolumn{4}{c|}{HCO-(H$_{2}$O)$_{n}$} & H+CO-(H$_{2}$O)$_{n}$ \\ - \multirow{-2}{*}{n} & DFTB & B3LYP-D3 & B97D & MP2 & DFTB & B3LYP-D3 & B97D & MP2 & DFTB \\ \hline -0 & - & - & - & - & - & - & - & - & -31.18 (\textit{-25.69}$^a$) \\ \hline -1 & -0.72 & -1.89 & -1.68 &-1.51 &-5.32 &-3.38 &-2.71 &-2.46 & - 26.25 \\ \hline -2 & -0.93 & -3.62 & -2.86 &-2.52 & -10.86 &-8.22 &-6.63 &-5.50 & - 33.43 \\ \hline -3 & -1.18 & -2.30 &-1.89 & -1.57 & -7.69 &-9.44 &-8.75 &-6.35 & - 27.95 (\textit{-26.76}$^a$) \\ \hline -4 & -1.00 & -2.43 & -1.74 &-1.45 & -11.96 &-10.21 &-8.58 &-6.84 & - 26.22 \\ \hline -5 & -1.00 & -1.99 & -1.78 & -1.53 &-4.77 &-5.87 &-4.62 &-3.47 & - 27.68 (\textit{-26.68}$^a$) \\ \hline -10 & -1.01 &-1.88 &-1.92 & -1.81 &-3.54 & -3.93 &-2.84 &-1.26 & - 26.57 \\ \hline -\end{tabular} \\ -$^a$ B97D results of Peters \textit{et al.}\cite{Peters2013a,Phillip2013}\\ -\end{table} - -To ensure that statistical convergence is reached, we checked the distributions of the initial -positions of the hydrogen atom with respect to the cluster in the 3392 starting configurations. -For visualisation, the distribution maps of the initial positions of hydrogen for CO-(H$_{2}$O)$_{n}$ (n=1,2,3) -are displayed in Figure~\ref{maps}. Similar data are obtained for CO-(H$_{2}$O)$_{n}$ (n=4,5). -From those pictures, it appears that the input geometries provide a reasonably uniform distribution -of hydrogen projectiles around the clusters. - -\begin{figure*} -\centering -\includegraphics[scale=0.45]{Maps_CO_H2O.png} -\caption{Distribution of the initial positions of the incident hydrogen atom around the CO-(H$_{2}$O)$_{n}$ - (n=1,2,3) clusters.} \label{maps} -\end{figure*} - -For each cluster size, we investigated and analyzed all trajectories according to seven -scenari (also called variants) characterizing the issue of the collision. A schematic -description of these mechanisms is shown in Figure~\ref{Variants}. - -\begin{figure*} -\centering -\includegraphics[scale=1.2]{Variants.png} -\caption{Possible pathways (variants) characterizing the issue of the H + CO collision.} \label{Variants} -\end{figure*} - -Variant 1 corresponds to the case where the two following conditions are fulfilled simultaneously: --(i)- during the collision, the reaction occurred and the HCO radical was formed, -and -(ii)- this radical remained connected to the cluster till the end of the simulation. -Geometric characteristics of the formyl radical such as R$_{\text{CO}}$ and R$_{\text{CH}}$ -were chosen to monitor the formation process. Recent studies by Adams and Purvis -provide the accurate equilibrium bond lengths of HCO using Many-Body Perturbation Theory -(MBPT) or Coupled-Cluster with Doubles excitations (CCD) calculations. The CCD values are -R$_{\text{CO}}$=1.188 \AA \ and R$_{\text{CH}}$=1.111 \AA~ \cite{adams1,marenich1}. -The present SCC-DFTB characteristics are R$_{\text{CO}}$=1.167 \AA \ and R$_{\text{CH}}$=1.197 \AA. -The criterion for HCO formation during the dynamics was thus chosen as follows: if during the simulation -the distances were fluctuating in the range 0.9-1.3 \AA~for C-O and 1.0-1.5 \AA~for C-H, -we assumed that HCO was formed. To ensure that the radical remains bonded to the surface, -we calculated the distances between the hydrogen atom of HCO and all oxygen atoms of the water -cluster (R$_{\text{H--O}}$), and the distances between the carbon atom of HCO and all oxygen atoms -of the water cluster (R$_{\text{C--O}}$). If at least one value of the R$_{\text{H--O}}$ -distance and one value of the R$_{\text{C--O}}$ distance were less than 4 \AA~at a given -MD step, the radical was assumed to be associated with the water cluster. - -The second variant describes the situation where the HCO radical was formed, but then desorbed from the -cluster (`Variant 2' in the Figure~\ref{Variants}). Similarly to CO, the binding energy between the formyl radical -and a water molecule is very small.Indeed, Cao \textit{et al.} calculated at the UCCSD(T)/aug-cc-pVTZ -level of theory, corrected for BSSE and vibrational zero-point energies, the interaction energies of three stable -isomers of HCO--H$_{2}$O. They obtained the three following values: -0.83, -1.70 and -1.61~kcal.mol$^{-1}$.\cite{cao1} -The corresponding values without vibrational zero-point energies are -2.24, -2.62 and -3.35~kcal.mol$^{-1}$. -This weak interaction energy confirms that Variant 2 is likely to occur if the incident hydrogen atom has enough -kinetic energy. It should also be noted that, similarly to CO, the HCO--(H$_{2}$O)$_{n}$ binding energies -are rather low and quite sensitive to the computational details. This is illustrated in the Table~\ref{e_bind} for -different DFT and MP2 calculations. Although the binding energies for HCO--(H$_{2}$O) and HCO--(H$_{2}$O)$_{2}$ -are somewhat overestimated, the DFTB values for larger species fall in the range of the DFT and MP2 values. -The next variant (`Variant 3' in the Figure~\ref{Variants}) -corresponds to the case where the reaction between H and CO did not occur while both reactants -remained stuck to the water cluster. The group of variants 4-6 may -occur whenever the kinetic energy of the incident hydrogen is above the energy required for -the formation of the radical. They can be briefly described as follows: Variant 4: the HCO -radical was not formed and H desorbed from the cluster while CO remained adsorbed; -Variant 5: the HCO radical was not formed, H was adsorbed while CO desorbed; Variant 6: - the HCO radical was not formed, both H and CO desorbed. It is worth pointing out that -those three variants can be encountered despite the transient formation of the HCO radical -if it dissociates during the trajectory. The last mechanism in our scheme (`Variant 7' in the Figure~\ref{Variants}) -is the situation where HCO is formed during some time of the simulation but finally dissociate -and both reactants remain bonded to the water cluster. The likelihood of each variant for clusters -CO-(H$_{2}$O)$_{n}$ (n=0-5,10) are listed in the Table~\ref{result_ratio}. - -\begin{table*} -\small -\centering -\caption{Probability (in percent) of each collisional pathway as a function of the cluster size.} -\label{result_ratio} -\begin{tabular}[t]{C{2.1cm} C{1.4cm} C{1.4cm} C{1.4cm} C{1.4cm} C{1.4cm} C{1.4cm} C{1.4cm}} -\hline \hline -\small{System} & \small{V.1 (\%)} & \small{V.2 (\%)} & \small{V.3 (\%)} & \small{V.4 (\%)} & \small{V.5 (\%)} & \small{V.6 (\%)} & \small{V.7 (\%)} \\ -\hline -\small{CO} & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \textbf{35.3} \\ -\small{CO-H$_{2}$O} & 0.0 & 3.1 & 0.0 & \textbf{63.2} & 9.1 & 10.2 & 7.5 \\ -\small{CO-(H$_{2}$O)$_{2}$} & 2.3 & \textbf{58.1} & 0.3 & 5.0 & 9.7 & 0.0 & \textbf{24.6} \\ -\small{CO-(H$_{2}$O)$_{3}$} & \textbf{10.1} & \textbf{50.9} & 1.3 & 0.9 & \textbf{31.4} & 0.0 & 5.4 \\ -\small{CO-(H$_{2}$O)$_{4}$} & \textbf{58.0} & 0.0 & \textbf{35.8} & 0.9 & \textbf{0.0} & 0.0 & 5.4 \\ -\small{CO-(H$_{2}$O)$_{5}$} & \textbf{61.4} & 0.0 & 7.4 & 1.1 & \textbf{26.9} & 0.1 & 0.8 \\ -\small{CO-(H$_{2}$O)$_{10}$} & \textbf{34.8} & 5.0 & \textbf{32.4} & 3.0 & \textbf{20.8} & 0.0 & 4.0 \\ -\hline \hline -\end{tabular} -\end{table*} - -In the gas phase conditions, \textit{i.e} without water molecule, the formation of the HCO radical with a favorable -geometry occurred in 35.3 \% of trajectories, while in other cases, the hydrogen atom flew away -from the collision area. However, even in the favorable cases, the HCO radical always dissociated -at some point of the simulations. Indeed, after a successful reaction, the kinetic energy of the incident -hydrogen distributes into the few vibrational modes of the radical which leads to its dissociation. -To support this point and to highlight the role of the water cluster, Figure~\ref{r_ch} displays -a typical example of the time-evolution of the C--H distance for the HCO and HCO-(H$_{2}$O)$_{5}$ -species. Immediately after the radical formation, the fluctuations of the C--H distance in the two -systems are of the same magnitude. However, after $\sim$1~ps, those fluctuations significantly -decrease for HCO-(H$_{2}$O)$_{5}$ highlighting the dissipation of kinetic energy towards the water -molecules. This leads to a stable HCO molecule. In contrast, the fluctuations are constant in the -simulation of pure HCO which can result in its dissociation. - -\begin{figure}[h!] -\centering -\includegraphics[scale=0.20]{rch_fluctuations.png} -\caption{Time-evolution of the C--H distance for HCO-(H$_{2}$O)$_{5}$ (top) and HCO (bottom) -immediately after the radical formation. $\Delta_{R_{C-H}}$ represents the amplitude of the -distance fluctuations.} \label{r_ch} -\end{figure} - -The same behavior is observed for CO-(H$_{2}$O). Indeed, $\sim$12 \% of the trajectories -lead to the formation of HCO although it is stable in only $\sim$3 \% of them. Variant -4, \textit{i.e.} with desorption of the hydrogen from the water molecule, is an important -pathway for this species as it encompasses $\sim$80 \% of the trajectories. For CO-(H$_{2}$O)$_{2}$ -and CO-(H$_{2}$O)$_{3}$, the HCO radical is obtained in more than 50 \% of cases. Due to the -small binding energy of HCO with water molecules (see discussion above), most of the -successfully formed radicals desorb from the cluster. This is demonstrated -by the predominance of the Variant 2 pathway. It is worth pointing out that the exact amount of -this latter pathway would be highly influenced by the level of theory used to describe the PES of -those systems. CO-(H$_{2}$O)$_{2}$ displays a significant amount -of dissociated radicals (24.6 \%) which supposes that two water molecules is not enough to -accommodate the excess kinetic energy of the hydrogen. In both CO-(H$_{2}$O)$_{2}$ and -CO-(H$_{2}$O)$_{3}$, only a few trajectories lead to a stable HCO radical adsorbed on the -water cluster, 2.3 and 10.1 \%, respectively. - -Things are completely different for CO-(H$_{2}$O)$_{4}$ and CO-(H$_{2}$O)$_{5}$. Indeed, -there is no desorption of HCO from the cluster and only a few cases of HCO dissociation, -5.4 and 0.8 \%, respectively. The majority of the simulations lead to a stable HCO radical -adsorbed on the water molecules. This allows us to assume that the second step of the -successive CO hydrogenation is likely to occur on complexes composed of four or more water -molecules. The main difference between those two species is the amount of Variant 3 and 5 -pathways that seems to be opposed. In particular, CO-(H$_{2}$O)$_{4}$ displays a 0.0 \% -amount of Variant 5, in contrast to the other species. This could likely be attributed to the -planar square conformation of (H$_{2}$O)$_{4}$. -Surprisingly, despite performing quasi-frontal collisions only, for CO-(H$_{2}$O)$_{10}$, -the probability for an adsorbed HCO radical to be formed (34.8 \%) is about twice as small as -for CO-(H$_{2}$O)$_{4}$ and CO-(H$_{2}$O)$_{5}$. However, this is also the only species -displaying a significant amount of both Variant 3 and 5, 32.4 \%~and 20.8 \%, respectively. -Furthermore, the likelihood of Variant 3 and 1 are equivalent as 32.4 \%~of the trajectories lead -to an H atom stuck on the water molecules. This results from the larger surface area -of CO-(H$_{2}$O)$_{10}$ as compared to the other aggregates. It should also be noted that -in those cases, the hydrogen does not diffuse to the CO molecule in the time length of the simulations. - -In order to get more dynamical, \textit{i.e.} time-dependent, insights into the H + CO -recombination mechanism, we calculated the probability for HCO formation along the MD simulations. -Two different functions, P1(t) and P2(t), were computed from all the trajectories, regardless of -the corresponding Variants. They are defined as follow: -(i)- P1(t) is the cumulative probability that -the HCO radical was formed for the first time at time \textit{t} during the simulation without considering -any further dissociation or recombination; -(ii)- P2(t) is the cumulative probability that HCO was -formed a time \textit{t} and remains stable till the end of the simulation. From these definitions, -P1(t) is mainly influenced by Variants 1, 2 and 7, at a lesser extent it is also influenced by the other -Variants, and P2(t) by trajectories belonging to Variants 1 and 2, only. Figure~\ref{time_func} displays -the P1(t) and P2(t) functions for CO-(H$_{2}$O)$_{n}$ (n=1, 3, 5 and 10). - -\begin{figure}[h!] -\includegraphics[scale=1.2]{new_time.png} -\caption{Cumulative probability of HCO formation as a function of time for the CO-(H$_{2}$O)$_{n}$ -(n=1, 3, 5 and 10) clusters.} \label{time_func} -\end{figure} - -We can see different dynamical pictures depending on the species. For CO-(H$_{2}$O), -formation of the HCO radical occurs very rapidly. The curve P1(t) reaches its maximum -during the first two picoseconds of simulation. Then, it retains a constant value of 11.6 \%. -This latter value correlates with the sum of the probabilities of Variants 2 and 7 in the -Table~\ref{result_ratio} (10.6 \%). It should be noted that the small difference between -these values results from the definition of both P1(t) and the Variants. Indeed, P1(t) does -not take into account the possible dissociation of HCO and subsequent disconnection of -the reactant from the water cluster. Those mechanisms correspond to Variants 4 to 6. Thus, -in 1\% \ of the trajectories, which belong to Variants 4, 5 or 6, there is the transient -formation of HCO before dissociation and desorption of one or both reactants. -P2(t) shows that a stable radical is formed only in 4.5 \% of cases. -However, this function increases only during the last picosecond of the trajectory. This -demonstrates that the HCO-(H$_{2}$O) aggregate is in a regime of successive formation-dissociation. -The increase of P2(t) at the end of the simulation thus results from the finite time length of the simulations. - -For CO-(H$_{2}$O)$_{3}$ and CO-(H$_{2}$O)$_{5}$, other behaviors are observed. Indeed, in the former case, -HCO formation occurs gradually from 0.5 to 6~ps. This strongly contrast with CO-(H$_{2}$O). The maximum -value of P1(t) (66.5 \%) corresponds to the sum of the probabilities of Variants 1, 2 and 7, which is equal to 66.4 \%. -Consequently, a negligible amount of trajectories where HCO is formed lead to its dissociation and the desorption -of the reactants. In addition, in contrast with CO-(H$_{2}$O), a large amount of the successfully formed HCO -remain stable -until the end of the trajectories. 61.5 \%~of them, corresponding to Variants 1 and 2, lead to a stable radical. Again, -the increase of the P2(t) curve during the last picosecond of simulation is only an artefact. -In CO-(H$_{2}$O)$_{5}$, a faster HCO formation is observed as revealed by the sharp rise of the P1(t) -curve between 0.5 and 1~ps. After 1~ps, it smoothly increases till 8~ps. The probability of HCO formation is -63 \%, which correlates with the corresponding Variants in the Table~\ref{result_ratio} (V.1+V.2+V.7 = 62.2 \%). -Similarly, the maximum of the P2(t) curve, 62.1 \%, correspond to the sum of the Variants 1 and 2 (61.4 \%). -Consequently, most of the radicals that are formed remain stable during the considered time length. -The curves for CO-(H$_{2}$O)$_{3}$ and CO-(H$_{2}$O)$_{5}$ in the Figure~\ref{time_func} display a -time lag between the increase of the P1(t) and P2(t) functions. The faster rise of P1(t) compared to P2(t) -shows that HCO is formed in a number of trajectories but immediately dissociates due to the excess -kinetic energy of the proton. This reveals that a small amount of time is needed to dissipate this energy, -which then allows for the formation of stable HCO and the rise of P2(t). This rise is faster for -CO-(H$_{2}$O)$_{5}$ due to the larger number of water molecules contributing to energy dissipation. -Finally, a plateau is observed for the P1(t) curve of CO-(H$_{2}$O)$_{5}$ at $\sim$1.2~ps. The subsequent -increase of P1(t) can be interpreted as the reaction of CO with hydrogen atoms initially stuck to -water molecules. A visual analysis of the trajectories reveal that only hydrogen atoms that are initially -very close to CO can lead to HCO formation as no diffusion over several water molecules is observed. -This is facilitated by the re-orientation of the CO molecule that allows for the hydrogen capture. -However, this process is rather long which explains the slow rise of the P1(t) and P2(t) curves for -CO-(H$_{2}$O)$_{5}$. The CO-(H$_{2}$O)$_{10}$ curves are very similar to the ones of CO-(H$_{2}$O)$_{5}$ -which suggests a similar behavior. The two main differences between those two species are: -a small time lag for the rise of P1(t) for CO-(H$_{2}$O)$_{10}$, which is attributed to a different initial -orientation of CO with respect to the colliding hydrogen, and a lower intensity of P1(t) and P2(t), attributed -to the larger amount of trajectories leading to the sticking of the hydrogen on the surface. - -Finally, we determined the reaction cross section for the investigated H + CO-(H$_{2}$O)$_{n}$ -(n=0-5, 10) reaction, defined as: - -\begin{eqnarray}\label{cross} -\Omega=\int_{0}^{b_{max}} p(b)2\pi bdb -\end{eqnarray} -where $b$ is the impact parameter and $p(b)$ the probability for a successful HCO formation at -impact parameter $b$. We considered as successful simulations corresponding to Variants 1 and 2, -only. Figure~\ref{size} shows the evolution of the reaction cross section $\Omega$ with increasing -cluster size from 0 to 10 water molecules. - -\begin{figure}[h!] -\includegraphics[scale=1.0]{cs_size.png} -\caption{Reaction cross section for H + CO formation as a function of water cluster size.} \label{size} -\end{figure} - -In the case of a single CO molecule, the reaction cross section is null, since a stable HCO radical -is never formed. When we go from one to two water molecules, although the size of CO-H$_{2}$O -and CO-(H$_{2}$O)$_{2}$ is similar (the distance between the two most distant atoms is 4.22 and -4.19 \AA, respectively), a significant increase of $\Omega$ is observed. Again, this shows that -the second water molecule assists the capture of the incident hydrogen and makes the -collision-induced reaction more effective. These data are consistent with the previous -analysis of the trajectories. -From two to four water molecules, the reaction cross section does not significantly change. For five -water molecules, a second small increase of $\Omega$ can be observed. Consequently, up to 5 -water molecules, the present results suggest that the reaction cross section increases with cluster -size, and hence, the probability of the HCO radical formation also increases. -In the case of CO-(H$_{2}$O)$_{10}$, as previously mentioned for the probabilities of -the collisional pathways, the surface area of (H$_{2}$O)$_{10}$ significantly increases and the probability -for a successful reaction between H and CO drastically decreases. Indeed, despite considering -frontal collisions only and no orientational sampling, $\Omega$ decreases to $\sim$3~\AA. -This precludes from calculating a cross section to be directly compared with the smaller clusters. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Conclusions} \label{Concl} -In the present study, a statistical analysis of the collision-induced reaction between hydrogen -and carbon monoxide on water clusters (H$_{2}$O)$_{n}$ (n=0-5,10) was achieved -using molecular dynamics simulation in combination with SCC-DFTB calculations of the energies -and forces. SCC-DFTB allows to describe covalent bonding in a quantum mechanical scheme -and charge relaxation along the dynamics and is thus well suited to study reactivity. -We show that the SCC-DFTB approach allows to satisfactorily describe the interaction between -the weakly bounded CO and H$_{2}$O molecules and can further be used to reaction study. -In a subsequent step, the classical collision-induced reaction of H with CO in CO-(H$_{2}$O)$_{n}$ -was investigated dynamically and the various pathways for the collision were analysed statistically. -We show that stable HCO radicals can be formed in species containing two or more water molecules. -Those water molecules play a key role in the collisional mechanism as they allow to dissipate the excess -kinetic energy of the colliding hydrogen. -However, in the case of (H$_{2}$O)$_{2}$ and (H$_{2}$O)$_{3}$, HCO returns to the gas phase in most cases -as dissociation between the radical and the water molecules is almost always observed. However, -starting from four water molecules, the successfully formed HCO remains associated -with the surface. This is an important feature for further hydrogenation steps that would lead to methanol. -For three water molecules and above, a large number of collisions lead to the sticking of the hydrogen -atom on the water molecules. In most cases, no subsequent HCO formation is observed in the simulation -time length. This suggests that the diffusion of H on the water cluster and its subsequent meeting with CO -(referred to as the Langmuir-Hinshelwood mechanism) either is damped by the cluster character of the -surface (with respect to perfect ice) or occurs at longer time than described by the present simulations. -In a few cases, when H is initially stuck close to CO, recombination can occur thanks to the -re-orientation of the CO molecule on the cluster allowing for the subsequent formation of HCO. This -process is observed mainly for (H$_{2}$O)$_{5}$ and (H$_{2}$O)$_{10}$. The recombination cross section -is of the order of $\approx$ 4 to 5~\AA \ for systems containing 3-5 water molecules. When increasing -the number of water molecules up to ten, this value drops drastically due to the sticking of H to the -cluster. Finally, it is worth point out that the size of the considered aggregates as well as the initial -conditions and length time of the trajectories favour the Eley-Rideal process with respect to the HCO -formation following the Langmuir-Hinshelwood mechanism, \textit{i.e.} the diffusion of hydrogen over the -water cluster. This latter would require a completely different set-up of the simulations to be properly -described. -Certainly, the present quantitative results are subject to the accuracy of the SCC-DFTB method and the -limitation of the dynamical parameters, such as the number of trajectories and their time length. -Nevertheless, we think that the present results are statistically meaningful and provide clear information -on the influence of water molecules on the H + CO reaction process in a dynamical picture. -The present work -could be extended in the following directions: -(i)- increase the CO coverage of the water clusters, -which would avoid the isolation of CO on a large nanodroplet, possibly with a factor dependence -of the surface area of the nanodroplet; -(ii)- perform simulations on real ice surface, ordered or -disordered, using periodic boundary conditions. We hope that the present work brings some -confirmation and new insights for the hydrogenation chain of CO up to methanol and contribute to -the understanding of the chemistry of the ISM. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% The "Acknowledgement" section can be given in all manuscript @@ -767,6 +163,6 @@ been no significant financial support for this work. %% Notice that the class file automatically sets \bibliographystyle %% and also names the section correctly. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\bibliography{Ref} +\bibliography{biblio} \end{document}