ajout partie NH
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|
||||
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|
||||
\newlabel{1a-f-b3lyp}{{3.18}{86}{Lowest-energy structures of (H$_2$O)UH$^+$ obtained at the B3LYP/6-311++G(3df,2p) level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. The corresponding values with ZPVE corrections are provided in brackets. Important hydrogen-bond distances are indicated in bold and are given in \AA }{figure.caption.29}{}}
|
||||
\citation{Zundel1968}
|
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|
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\newlabel{2a-f}{{3.11}{71}{Lowest-energy structures of (H$_2$O)$_2$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA }{figure.caption.20}{}}
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|
||||
\newlabel{3a-f}{{3.12}{72}{(H$_2$O)$_3$UH$^+$ lowest-energy structures obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA }{figure.caption.21}{}}
|
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|
||||
\newlabel{4a-f}{{3.13}{73}{Lowest-energy structures of (H$_2$O)$_4$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA }{figure.caption.22}{}}
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||||
\newlabel{5a-f}{{3.14}{74}{Lowest-energy structures of (H$_2$O)$_5$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA }{figure.caption.23}{}}
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\newlabel{2a-f}{{3.19}{87}{Lowest-energy structures of (H$_2$O)$_2$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA }{figure.caption.30}{}}
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\newlabel{3a-f}{{3.20}{88}{(H$_2$O)$_3$UH$^+$ lowest-energy structures obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA }{figure.caption.31}{}}
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|
||||
\newlabel{4a-f}{{3.21}{89}{Lowest-energy structures of (H$_2$O)$_4$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA }{figure.caption.32}{}}
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|
||||
\newlabel{5a-f}{{3.22}{90}{Lowest-energy structures of (H$_2$O)$_5$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA }{figure.caption.33}{}}
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\citation{Molina2015,Molina2016}
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|
||||
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\@writefile{toc}{\contentsline {subsection}{\numberline {3.3.3}Conclusions on (H$_2$O)$_{n}$UH$^+$ clusters}{76}{subsection.3.3.3}}
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|
||||
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|
||||
\newlabel{7a-f}{{3.16}{77}{Lowest-energy structures of (H$_2$O)$_7$UH$^+$ obtained at the MP2/Def2TZVP level of theory. Relative ($E_\textrm {rel}$) and binding energies ($E_\textrm {bind}$) are given in kcal.mol$^{-1}$. Important hydrogen-bond distances are indicated in bold and are given in \AA }{figure.caption.25}{}}
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|
||||
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|
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|
||||
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|
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@ -222,58 +222,309 @@ ammonium/ammonia was shifted along the N--O vector, all other geometrical parame
|
||||
\end{figure}
|
||||
|
||||
From Figure~\ref{fig:E_nh4}, the five curves display the same trends with a minimum located at almost the same N---O distance. At the curve minimum,
|
||||
binding energies vary between XX and XX~kcal.mol$^{-1}$ at the original SCC-DFTB and SCC-DFTB 0.14/1.28 levels, respectively. The binding energy
|
||||
obtained at the SCC-DFTB 0.12/1.16 level is the closest to that obtained at MP2/Def2TZVP level with BSSE correction with a binding energy difference of
|
||||
only XX~kcal.mol$^{-1}$. The SCC-DFTB 0.14/1.28 curve is also very close with a difference in binding energy only XX~kcal.mol$^{-1}$ higher. It is
|
||||
binding energies vary between -25.57 and -21,07~kcal.mol$^{-1}$ at the original SCC-DFTB and SCC-DFTB 0.14/1.28 levels, respectively. The binding
|
||||
energy obtained at the SCC-DFTB 0.12/1.16 level is the closest to that obtained at MP2/Def2TZVP level with BSSE correction with a binding energy difference of
|
||||
only 0.47~kcal.mol$^{-1}$. The SCC-DFTB 0.14/1.28 curve is also very close with a difference in binding energy only 0.16~kcal.mol$^{-1}$ higher. It is
|
||||
worth mentioning that both sets of corrections lead to improved results as compared to the original SCC-DFTB parameters which leads to a too low
|
||||
binding energy as compared to MP2/Def2TZVP level with BSSE correction. Also the position of the minimum is more shifted at the original SCC-DFTB
|
||||
level than with corrections. So from structural and energetic point of views, both sets of corrections are satisfactory.
|
||||
level (2.64~\AA) than with corrections (2.73~\AA). So from structural and energetic point of views, both sets of corrections are satisfactory.
|
||||
|
||||
From Figure~\ref{fig:E_nh3}, the five curves display significant differences. This effect is accentuated by smaller binding energy values: they
|
||||
vary from XX to XX~kcal.mol$^{-1}$ at the original SCC-DFTB and MP2/Def2TZVP levels, respectively, at the minimum of the curves. The binding
|
||||
energy obtained at the SCC-DFTB 0.14/1.28 level is the closest to that obtained at MP2/Def2TZVP level with BSSE correction with a binding energy
|
||||
difference of only XX~kcal.mol$^{-1}$. The SCC-DFTB 0.12/1.16 curve is also rather close with a difference in binding energy only XX~kcal.mol$^{-1}$
|
||||
vary from -3.82 to -7,39~kcal.mol$^{-1}$ at the original SCC-DFTB and MP2/Def2TZVP levels, respectively, at the minimum of the curves. The binding
|
||||
energy obtained at the SCC-DFTB 0.12/1.16 level is the closest to that obtained at MP2/Def2TZVP level with BSSE correction with a binding energy
|
||||
difference of only 0.01~kcal.mol$^{-1}$. The SCC-DFTB 0.14/1.28 curve is also rather close with a difference in binding energy only 1.3~kcal.mol$^{-1}$
|
||||
higher. Here also, both sets of corrections lead to improved results as compared to the original SCC-DFTB parameters. The position of the minimum
|
||||
is also better reproduced by the the corrected potentials than by the original SCC-DFTB. It is worth mentioning that the rather difference in binding
|
||||
energy between (H$_2$O){NH$_4$}$^+$ and (H$_2$O)NH$_3$ was expected owing to a stronger electrostatic contribution of {NH$_4$}$^+$ to the
|
||||
is also well reproduced by the corrected potentials. In contrast to (H$_2$O){NH$_4$}$^+$, the shape of the curves for (H$_2$O){NH$_3$} obtained
|
||||
at the SCC-DFTB level differs significantly from those obtained at MP2 level. Vibrational frequencies calculated at the SCC-DFTB level for this systems
|
||||
are therefore expected to be inacurate. It is worth mentioning that the large difference in binding energy between
|
||||
(H$_2$O){NH$_4$}$^+$ and (H$_2$O)NH$_3$ was expected owing to a stronger electrostatic contribution of {NH$_4$}$^+$ to the
|
||||
binding energy.
|
||||
|
||||
Another very important point when comparing the original SCC-DFTB potential and the corrected potentials, is the structure obtained for the
|
||||
(H$_2$O){NH$_4$}$^+$ dimer. Figure~\ref{dimers} compares the structure obtained from geometry optimization at the SCC-DFTB 0.14/1.28
|
||||
and original SCC-DFTB levels. The N-H covalent bond involved in the hydrogen bond is significantly longer with the original potential while
|
||||
the N---O distance is XXX. This is reminiscent of the too low proton affinity of {NH$_4$}$^+$ predicted by the original SCC-DFTB potential.
|
||||
and original SCC-DFTB levels. The N-H covalent bond involved in the hydrogen bond is longer with the original potential while the N---O
|
||||
distance is smaller by 0.14~\AA. This is reminiscent of the too low proton affinity of {NH$_4$}$^+$ predicted by the original SCC-DFTB potential.
|
||||
This discrepancy has been previously highlighted in other studies,\cite{Winget2003,Gaus2013para} and makes this potential unusable in any
|
||||
realistic molecular dynamics simulation as it leads to a spurious deprotonation. Both sets of corrections are free of this error. \red{An additional
|
||||
proof of this assertion is presented in Figure~\ref{XX} that displays the energy barrier for the proton transfer at constant N---O distance obtained
|
||||
from different methods.}
|
||||
realistic molecular dynamics simulation as it leads to a spurious deprotonation. Both sets of corrections are free of this error.
|
||||
%\red{An additional
|
||||
%proof of this assertion is presented in Figure~\ref{XX} that displays the energy barrier for the proton transfer at constant N---O distance obtained
|
||||
%from different methods.}
|
||||
|
||||
%\begin{figure}[H]
|
||||
\begin{figure}
|
||||
\begin{figure}[h!]
|
||||
\includegraphics[width=0.3\linewidth]{dimers.png}
|
||||
\centering
|
||||
\caption{Structure of (H$_2$O){NH$_4$}$^+$ obtained from geometry optimization at the SCC-DFTB 0.14/1.28 (right) and original SCC-DFTB (left) levels.}
|
||||
\label{dimers}
|
||||
\end{figure}
|
||||
|
||||
Figures~\ref{fig:E_nh4} and ~\ref{fig:E_nh3} show that SCC-DFTB 0.14/1.28 better describe (H$_2$O){NH$_3$} dissociation curve while SCC-DFTB 0.12/1.16
|
||||
better describe (H$_2$O){NH$_4$}$^+$. As one looks for a unique potential to describe both ammonium and ammonia water clusters, we choose SCC-DFTB
|
||||
0.14/1.28 for the present study. Indeed, as (H$_2$O){NH$_3$} is characterized by a much lower binding energy than (H$_2$O){NH$_4$}$^+$, an error of
|
||||
the of order of XX~kcal.mol$^{-1}$ is more likely to play a significant role for ammonia than ammonium containing species. All the following discussion therefore
|
||||
involve the SCC-DFTB 0.14/1.28 potential.
|
||||
Figures~\ref{fig:E_nh4} and ~\ref{fig:E_nh3} show that SCC-DFTB 0.12/1.16 better describe both (H$_2$O){NH$_3$} and
|
||||
(H$_2$O){NH$_4$}$^+$ dissociation curves. Furthermore, as (H$_2$O){NH$_3$} is characterized by a much lower
|
||||
binding energy than (H$_2$O){NH$_4$}$^+$, an error of the order of $\sim$1.0~kcal.mol$^{-1}$ is more likely to play
|
||||
a significant role for ammonia than ammonium containing species. All the following discussion therefore involve the
|
||||
SCC-DFTB 0.12/1.16 potential.
|
||||
|
||||
|
||||
\subsubsection{Small Species: (H$_2$O)$_{1-3}${NH$_4$}$^+$ and (H$_2$O)$_{1-3}${NH$_3$}}
|
||||
|
||||
As a first test case for the application of the SCC-DFTB 0.14/1.28 potential is the study of small ammonium and ammonia water clusters:
|
||||
(H$_2$O)$_{1-3}${NH$_4$}$^+$ and (H$_2$O)$_{1-3}${NH$_3$}. Due to the limited number of low-energy isomers for these species, we
|
||||
only consider the lowest-energy isomer of (H$_2$O)$_{1-2}${NH$_4$}$^+$ and (H$_2$O)$_{1-3}${NH$_3$} and the two lowest-energy
|
||||
isomers for (H$_2$O)$_{3}${NH$_4$}$^+$.
|
||||
As displayed in Figure~\ref{fig:nh3-nh4-1w} and\ref{fig:nh3-nh4-2-3w}, the reported low-energy isomers 1-a, 1$^\prime$-a, 2-a, 2$^\prime$-a, 3-a, 3-b, and
|
||||
3$^\prime$ display a structure very similar to those obtained at the MP2/Def2TZVP level (1-a$^*$, 1$^\prime$-a$^*$, 2-a$^*$, 2$^\prime$-a$^*$, 3-a$^*$,
|
||||
3-b$^*$ and 3$^\prime$-a$^*$). Indeed, although differences in bond lengths are observed, they are rather small.
|
||||
In terms of energetics,
|
||||
|
||||
From en energetic point of view, it is interesting to first look at the relative energy between the two reported isomers of
|
||||
(H$_2$O)$_{3}${NH$_4$}$^+$. Isomer 3-b is 2.12~kcal·mol\textsuperscript{-1} higher than 3-a at the SCC-DFTB level.
|
||||
At the MP2/Def2TZVP level, 3-b is 0.30~kcal·mol\textsuperscript{-1} lower than 3-a when ZPVE is not considered while
|
||||
it is 1.21 kcal·mol\textsuperscript{-1} higher when it is considered. In comparison, in the experimental results by
|
||||
Chang and co-workers, 3-a is more stable than 3-b.\cite{Wang1998, Jiang1999} The aauhors also complemented their
|
||||
measurements by theoretical calculations that show that at the B3LYP/6-31+G(d) level, 3-a is higher than 3-b but. In
|
||||
contrast, at the MP2/6-31+G(d) level corrected with ZPVE, the energy of 3-a is lower than that of 3-b while it is inverted
|
||||
if ZPVE is taken into account.\cite{Wang1998, Jiang1999} Additionally, Spiegelman and co-workers, conducted a
|
||||
global Monte Carlo optimizations with an intermolecular polarizable potential that lead to 3-a as lowest-energy isomer.\cite{Douady2008}
|
||||
All these results show that for the specific question of lowest-energy isomer of (H$_2$O)$_{3}${NH$_4$}$^+$, SCC-DFTB
|
||||
has an accuracy close to other \textit{ab initio} methods which confirms its applicability.
|
||||
|
||||
\begin{figure}[h!]
|
||||
\includegraphics[width=0.2\linewidth]{nh3-nh4-1w.png}
|
||||
\centering
|
||||
\caption{Structure of 1-a and 1$^\prime$-a isomers obtained at the SCC-DFTB level and corresponding
|
||||
structures obtained at MP2/Def2TZVP level (1-a$^*$ and 1$^\prime$-a$^*$ isomers). Selected bond
|
||||
lengths are in \AA.}
|
||||
\label{fig:nh3-nh4-1w}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}[h!]
|
||||
\includegraphics[width=0.5\linewidth]{nh3-nh4-2w.png}
|
||||
\centering
|
||||
\caption{Structure of 2-a and 2$^\prime$-a isomers obtained at the SCC-DFTB level and corresponding
|
||||
structures obtained at MP2/Def2TZVP level (2-a$^*$, 2$^\prime$-a$^*$ isomers). Selected bond
|
||||
lengths are in \AA.}
|
||||
\label{fig:nh3-nh4-2-3w}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}[h!]
|
||||
\includegraphics[width=0.5\linewidth]{nh3-nh4-3w.png}
|
||||
\centering
|
||||
\caption{Structure of 3-a, 3-b and 3$^\prime$-a isomers obtained at the SCC-DFTB level and corresponding
|
||||
structures obtained at MP2/Def2TZVP level (3-a$^*$, 3-b$^*$ and 3$^\prime$-a$^*$ isomers). Selected bond
|
||||
lengths are in \AA.}
|
||||
\label{fig:nh3-nh4-3w}
|
||||
\end{figure}
|
||||
|
||||
\begin{table*}
|
||||
\begin{center}
|
||||
\caption{Relative binding energies $\Delta E_{bind.}^{whole}$ and $\Delta E_{bind.}^{sep.}$
|
||||
of the low-energy isomers of (H$_2$O)$_{1-3}${NH$_4$}$^+$ and (H$_2$O)$_{1-3}${NH$_3$} clusters.
|
||||
Values are given in kcal.mol$^{-1}$.} \label{reBindE-small}
|
||||
\begin{tabular}{c|c|c|c|c|c}
|
||||
\hline
|
||||
(H$_2$O)$_{n}$NH$_4^+$ & $\Delta E_{bind.}^{whole}$ & $\Delta E_{bind.}^{sep.}$ & (H$_2$O)$_{n}${NH$_3$} & $\Delta E_{bind.}^{whole}$ & $\Delta E_{bind.}^{sep.}$\\
|
||||
\hline
|
||||
\rowcolor{lightgray} 1-a & 1.21 & 1.21 & 1$^\prime$-a & -1.17 & -1.17 \\
|
||||
2-a & 0.82 & 0.91 & 2$^\prime$-a & 0.57 & 0.28 \\
|
||||
\rowcolor{lightgray} 3-a & -0.25 & 0.11 & 3$^\prime$-a & 0.91 & 0.01 \\
|
||||
\rowcolor{lightgray} 3-b & 1.21 & -0.15 & - & - & - \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
\end{table*}
|
||||
|
||||
As listed in Table~\ref{reBindE-small}, the relative binding energies $\Delta E_{bind.}^{whole}$ or $\Delta E_{bind.}^{sep.}$ of
|
||||
(H$_2$O){NH$_4$}$^+$ and (H$_2$O){NH$_3$} are 1.21 and -1.17 kcal·mol\textsuperscript{-1}, respectively, which again
|
||||
highlights that SCC-DFTB is in agreement with MP2/Def2TZVP. For (H$_2$O){NH$_3$}, the negative value
|
||||
show that MP2/Def2TZVP binding energy is smaller than the SCC-DFTB value. This is inverse to what is shown in Figure~\ref{fig:E_nh3}
|
||||
and results from structural reorganization after optimization. All other values of Table~\ref{reBindE-small} are equal of smaller than these
|
||||
values, whether considering $\Delta E_{bind.}^{whole}$ or $\Delta E_{bind.}^{sep.}$, which again demonstrates that the presently proposed
|
||||
SCC-DFTB potential provides results in line with reference MP2/Def2TZVP calculations.
|
||||
|
||||
(H$_2$O)$_{4-10}${NH$_4$}$^+$ clusters have been studied by molecular dynamic and Monte Carlo simulations in combination with
|
||||
DFT and MP2 approaches although these latter are computationally expensive.\cite{Wang1998, Jiang1999, Douady2008, Lee2004, Douady2009, Morrell2010}
|
||||
In contrast, to the best of our knowledge, no theoretical calculation about (H$_2$O)$_{5-10}${NH$_3$} clusters have been conducted.
|
||||
The low computational cost of SCC-DFTB and its seemingly good performances on small clusters provide an appealing opportunity
|
||||
to thoroughly explore the PES of both large ammonium and ammonia containing water clusters. In the following section, the five lowest-energy
|
||||
isomers of clusters (H$_2$O)$_{4-10}${NH$_4$}$^+$ and (H$_2$O)$_{4-10}$NH$_3$ are presented and discussed in details.
|
||||
|
||||
\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
|
||||
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 Chang and co-workers.\cite{Chang1998, Wang1998} Isomer 4-a diplays four hydrogen bonds around the ionic
|
||||
center which lead to no dangling N-H bonds. Other isomers of comparable stability are displayed in Figure~\ref{fig:nh4-4-6w}
|
||||
The energy ordering of 4-a to 4-e at SCC-DFTB level is consistent with that at MP2/Def2TZVP level with ZPVE correction, although they
|
||||
are slightly higher by$\sim$2.0 kcal.mol$^{-1}$. Isomer 4-c was not reported in Chang’s study,\cite{Jiang1999} and the corresponding
|
||||
energy ordering of the five lowest-energy isomers was the same as ours which certainly results from the use of a different basis set.
|
||||
|
||||
\begin{figure}[h!]
|
||||
\includegraphics[width=0.9\linewidth]{nh4-4-6w.png}
|
||||
\centering
|
||||
\caption{Five lowest-energy isomers of (H$_2$O)$_{4-6}${NH$_4$}$^+$ and corresponding relative energies at MP2/Def2TZVP level with (bold) and without ZPVE (roman)
|
||||
correction and SCC-DFTB level (italic).
|
||||
Relative energies are given in kcal·mol\textsuperscript{-1}.}
|
||||
\label{fig:nh4-4-6w}
|
||||
\end{figure}
|
||||
|
||||
\begin{table*}
|
||||
\begin{center}
|
||||
\caption{Relative binding energies $\Delta E_{bind.}^{whole}$ and $\Delta E_{bind.}^{sep.}$ of the five
|
||||
lowest-energy isomers of (H$_2$O)$_{4-10}${NH$_4$}$^+$ and (H$_2$O)$_{4-10}${NH$_3$}.
|
||||
Binding energies are given in kcal·mol\textsuperscript{-1}.} \label{reBindE}
|
||||
\begin{tabular}{c|c|c|c|c|c}
|
||||
\hline
|
||||
(H$_2$O)$_{n}$NH$_4^+$ & $\Delta E_{bind.}^{whole}$ & $\Delta E_{bind.}^{sep.}$ & (H$_2$O)$_{n}${NH$_3$} & $\Delta E_{bind.}^{whole}$ & $\Delta E_{bind.}^{sep.}$\\
|
||||
\hline
|
||||
\rowcolor{lightgray} 4-a & -1.67 & -0.87 & 4$^\prime$-a & -1.11 & -1.76 \\
|
||||
\rowcolor{lightgray} 4-b & 0.00 & 0.61 & 4$^\prime$-b & -0.29 & -1.62 \\
|
||||
\rowcolor{lightgray} 4-c & 0.77 & 0.44 & 4$^\prime$-c & -0.29 & -1.38 \\
|
||||
\rowcolor{lightgray} 4-d & 0.77 & 0.42 & 4$^\prime$-d & 1.08 & -0.49 \\
|
||||
\rowcolor{lightgray} 4-e & -4.04 & 0.69 & 4$^\prime$-e & 1.02 & -1.07 \\
|
||||
5-a & -1.62 & 0.56 & 5$^\prime$-a & 0.82 & -1.78 \\
|
||||
5-b & 0.72 & 0.48 & 5$^\prime$-b & -0.23 & -2.26 \\
|
||||
5-c & 0.69 & 0.55 & 5$^\prime$-c & -0.34 & -2.50 \\
|
||||
5-d & -1.08 & -0.78 & 5$^\prime$-d & -0.59 & -1.84 \\
|
||||
5-e & -2.08 & 0.88 & 5$^\prime$-e & -0.38 & -2.60 \\
|
||||
\rowcolor{lightgray} 6-a & -1.71 & -0.38 & 6$^\prime$-a & -0.27 & -3.05 \\
|
||||
\rowcolor{lightgray} 6-b & -1.14 & -0.76 & 6$^\prime$-b & -0.31 & -3.55 \\
|
||||
\rowcolor{lightgray} 6-c & -2.06 & 0.27 & 6$^\prime$-c & -1.11 & -4.67 \\
|
||||
\rowcolor{lightgray} 6-d & -2.90 & -1.06 & 6$^\prime$-d & -0.05 & -4.44 \\
|
||||
\rowcolor{lightgray} 6-e & -1.18 & -0.60 & 6$^\prime$-e & 0.55 & -1.96 \\
|
||||
7-a & -2.95 & -0.39 & 7$^\prime$-a & 1.09 & -2.02 \\
|
||||
7-b & -2.92 & -0.38 & 7$^\prime$-b & -0.02 & -4.07 \\
|
||||
7-c & -2.17 & 0.09 & 7$^\prime$-c & -0.40 & -4.15 \\
|
||||
7-d & -1.28 & -1.35 & 7$^\prime$-d & -0.14 & -3.10 \\
|
||||
7-e & -3.22 & -2.27 & 7$^\prime$-e & -1.11 & -4.32 \\
|
||||
\rowcolor{lightgray} 8-a & -2.20 & -1.63 & 8$^\prime$-a & -1.12 & -4.41 \\
|
||||
\rowcolor{lightgray} 8-b & -1.61 & -2.01 & 8$^\prime$-b & -0.10 & -3.04 \\
|
||||
\rowcolor{lightgray} 8-c & -3.71 & -1.17 & 8$^\prime$-c & -0.41 & -4.46 \\
|
||||
\rowcolor{lightgray} 8-d & -2.43 & -0.36 & 8$^\prime$-d & 0.20 & -3.68 \\
|
||||
\rowcolor{lightgray} 8-e & -0.55 & 0.35 & 8$^\prime$-e & -1.28 & -4.75 \\
|
||||
9-a & -2.02 & -1.39 & 9$^\prime$-a & -0.15 & -4.47 \\
|
||||
9-b & 0.51 & -0.84 & 9$^\prime$-b & -1.01 & -4.45 \\
|
||||
9-c & -3.31 & -0.85 & 9$^\prime$-c & -1.04 & -4.42 \\
|
||||
9-d & -1.58 & -1.78 & 9$^\prime$-d & -1.09 & -5.14 \\
|
||||
9-e & -2.39 & -0.91 & 9$^\prime$-e & 0.41 & -2.57 \\
|
||||
\rowcolor{lightgray} 10-a & -2.64 & -1.94 & 10$^\prime$-a & -0.03 & -4.80 \\
|
||||
\rowcolor{lightgray} 10-b & -5.79 & -4.35 & 10$^\prime$-b & 0.13 & -5.61 \\
|
||||
\rowcolor{lightgray} 10-c & -1.26 & -2.36 & 10$^\prime$-c & -0.62 & -6.50 \\
|
||||
\rowcolor{lightgray} 10-d & -1.98 & -1.42 & 10$^\prime$-d & -1.10 & -6.30 \\
|
||||
\rowcolor{lightgray} 10-e & -7.17 & -1.54 & 10$^\prime$-e & 0.23 & -8.36 \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
\end{table*}
|
||||
|
||||
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 first 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 Spiegelman’s result using the global MC optimization and 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 first five low-energy isomers, the energy order of our results are not exactly the same with Chang’s calculation results at MP2/6-31+G(d)level with ZPVE correction.\cite{Jiang1999} In Chang’s results, 5-d is the first 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 first 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 first 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 MC 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 Chang’s study, 6-b with a three-coordinated H2O 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.
|
||||
|
||||
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 energy 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 first 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 Spiegelman’s study, 7-a is also the first low-energy isomer using the MC 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 H2O molecules at MP2/aug-cc-pVDZ level in 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 iosmer 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.
|
||||
|
||||
\begin{figure}[h!]
|
||||
\includegraphics[width=1.0\linewidth]{nh4-7-10w.png}
|
||||
\centering
|
||||
\caption{The first five low-energy isomers of clusters (H$_2$O)$_{7-10}${NH$_4$}$^+$ and the associated relative energies (in kcal·mol\textsuperscript{-1}) at MP2/Def2TZVP level with (bold) and without ZPVE correction and SCC-DFTB level (italic).}
|
||||
\label{fig:nh4-7-10w}
|
||||
\end{figure}
|
||||
|
||||
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 first 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 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 Spiegelman’s results obtained using MC 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 first 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 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 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 first 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 H2O 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 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 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 first 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 0.20 and 0.07 kcal·mol\textsuperscript{-1} at SCC-DFTB and MP2/Def2TZVP with ZPVE correction 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 Novoa et al\cite{Lee1996} 4$^\prime$-d is also the first low-energy isomer in 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 first five low-energy isomers in 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}
|
||||
\centering
|
||||
\caption{The first five low-energy isomers of cluster (H$_2$O)$_{4-7}${NH$_3$} and the associated relative energies (in kcal·mol\textsuperscript{-1}) at MP2/Def2TZVP level with (bold) and without ZPVE correction and SCC-DFTB level (italic).}
|
||||
\label{fig:nh3-4-7w}
|
||||
\end{figure}
|
||||
|
||||
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 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 first 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 SCC-DFTB and MP2/Def2TZVP with ZPVE correction 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 0.05 and 0.44 kcal·mol\textsuperscript{-1} at SCC-DFTB level and MP2/Def2TZVP with ZPVE correction 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 SCC-DFTB and MP2/Def2TZVP with ZPVE correction levels. 5$^\prime$-e with four three-coordinated water molecules is the fifth low-energy structure at both SCC-DFTB and MP2/Def2TZVP with ZPVE correction 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 first 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 0.05 and 0.42 kcal·mol\textsuperscript{-1} higher than the ones of 6$^\prime$-a at SCC-DFTB level and MP2/Def2TZVP with ZPVE correction 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 SCC-DFTB and MP2/Def2TZVP with ZPVE correction levels that it is difficult to keep the energy order when different methods or basis sets are applied. This also shown the SCC-DFTB method we 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 first 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 SCC-DFTB and MP2/Def2TZVP with ZPVE correction levels. 7$^\prime$-b is the second low-energy structure at both SCC-DFTB and MP2/Def2TZVP with ZPVE correction 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 SCC-DFTB and MP2/Def2TZVP with ZPVE correction levels. The results of SCC-DFTB method agree well with those of MP2/Def2TZVP with ZPVE correction for the first 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 first 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 0.93 an 0.30 kcal·mol\textsuperscript{-1} at SCC-DFTB and MP2/Def2TZVP with ZPVE correction levels. From Figure \ref{fig:nh3-8-10w}, the fifth low-energy isomer 8$^\prime$-e includes less number of 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}
|
||||
\centering
|
||||
\caption{The first five low-energy isomers of clusters (H$_2$O)$_{8-10}${NH$_3$} and the associated relative energies (in kcal·mol\textsuperscript{-1}) at MP2/Def2TZVP level with (bold) and without ZPVE correction and SCC-DFTB level (italic).}
|
||||
\label{fig:nh3-8-10w}
|
||||
\end{figure}
|
||||
|
||||
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 first 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$_3$}.
|
||||
|
||||
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 first five low-energy structures illustrated in Figure \ref{fig:nh3-8-10w}. The energy order for the first 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 first 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.
|
||||
|
||||
\subsubsection{Properties of (H$_2$O)$_{20}${NH$_4$}$^+$ Clusters}
|
||||
|
||||
For cluster (H$_2$O)$_{20}${NH$_4$}$^+$, the lowest-energy structure shown in Figure \ref{fig:nh3-nh4-20w} (a) was obtained with the combination of SCC-DFTB and PTMD which is consistent with that of previous study.\cite{Kazimirski2003, Douady2009, Bandow2006}
|
||||
Microcanonical and canonical caloric curves were obtained using exchange Monte Carlo simulations by Spiegelman’s group.\cite{Douady2009}
|
||||
We also calculated the canonical heat capacities of cluster (H$_2$O)$_{20}${NH$_4$}$^+$ using the combination of SCC-DFTB and PTMD depicted in Figure.
|
||||
|
||||
\begin{figure}[h!]
|
||||
\includegraphics[width=0.6\linewidth]{nh3-nh4-20w.jpeg}
|
||||
\centering
|
||||
\caption{The first five low-energy isomers of cluster (H$_2$O)$_{20}${NH$_4$}$^{+}$ (a) and (H$_2$O)$_{20}${NH$_3$} (b) at SCC-DFTB level.}
|
||||
\label{fig:nh3-nh4-20w}
|
||||
\end{figure}
|
||||
|
||||
\subsection{Conclusions for Ammonium/Ammonia Including Water Clusters}
|
||||
|
||||
The low-energy isomers reported for (H$_2$O)$_{1-10, 20}${NH$_4$}$^+$ and (H$_2$O)$_{1-10, 20}$NH$_3$ clusters are obtained with a combination of
|
||||
SCC-DFTB (0.12/1.16) and PTMD. Binding energies as a function of the N---O distance in (H$_2$O){NH$_4$}$^+$ and (H$_2$O)NH$_3$ demonstrate
|
||||
that the improve parameters we propose are in much better agreement with reference calculations than the original SCC-DFTB parameters.
|
||||
The low-energy isomers of clusters (H$_2$O)$_{1-10}${NH$_4$}$^+$ and (H$_2$O)$_{1-10}$NH$_3$ at the SCC-DFTB (0.12/1.16) level
|
||||
agree well with those at MP2/Def2TZVP level and the corresponding results in the literature. The SCC-DFTB binding energies also agree well
|
||||
with those calculated with MP2/Def2TZVP method with BSSE correction. This demonstrate that SCC-DFTB (0.12/1.16) approach is good
|
||||
enough to model ammonium and ammonia containing water clusters.
|
||||
|
||||
Among the five lowest-energy structures of (H$_2$O)$_{4}${NH$_4$}$^+$, four of them display a dangling N-H bond. Among the five lowest-energy
|
||||
structures of (H$_2$O)$_{5}${NH$_4$}$^+$, only two structures display a dangling N-H bond. Among the five lowest-energy isomers of (H$_2$O)$_{6-10}${NH$_4$}$^+$,
|
||||
all the structures, except 8-e, display a ion core {NH$_4$}$^+$ that has a complete solvation shell but it is not located at the center of the water cluster.
|
||||
In the most stable structures of (H$_2$O)$_{20}${NH$_4$}$^+$, the ion core {NH$_4$}$^+$ has a complete solvation shell and it is in the center of the
|
||||
water cluster. In contrast, in the low-energy isomers of (H$_2$O)$_{1-10}$NH$_3$ clusters, NH$_3$ is never fully solvated by the water cluster.
|
||||
|
||||
The present study demonstrate thet ability of SCC-DFTB to model small size ammonium and ammonia containing water clusters, which is less
|
||||
expensive than \textit{ab initio} methods. It is possible for SCC-DFTB to describe the larger scaled ammonium and ammonia containing water clusters.
|
||||
|
||||
\section{Structural and Energetic Properties of Protonated Uracil Water Clusters} \label{structureUH}
|
||||
|
||||
|
||||
@ -5,16 +5,16 @@
|
||||
\citation{Wong2004,Bush2008}
|
||||
\citation{Holm2010,Gatchell2014,Gatchell2017}
|
||||
\citation{Boering1992,Wells2005,Zamith2019thermal}
|
||||
\@writefile{toc}{\contentsline {chapter}{\numberline {4}Dynamical Simulation of Collision-Induced Dissociation}{81}{chapter.4}}
|
||||
\@writefile{toc}{\contentsline {chapter}{\numberline {4}Dynamical Simulation of Collision-Induced Dissociation}{97}{chapter.4}}
|
||||
\@writefile{lof}{\addvspace {10\p@ }}
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\@writefile{brf}{\backcite{Brechignac1989}{{81}{4.1}{section.4.1}}}
|
||||
\@writefile{brf}{\backcite{Brechignac1994}{{81}{4.1}{section.4.1}}}
|
||||
\@writefile{brf}{\backcite{Wong2004}{{81}{4.1}{section.4.1}}}
|
||||
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|
||||
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||||
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||||
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|
||||
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|
||||
\citation{Ma1997,Chowdhury2009}
|
||||
\citation{Nelson1994,Molina2015}
|
||||
\citation{Carl2007}
|
||||
@ -31,80 +31,80 @@
|
||||
\citation{Dawson1982,Bakker2008,Mcquinn2009,Zamith2012}
|
||||
\citation{Liu2006}
|
||||
\citation{Carl2013,Hofstetter2013,Coates2018}
|
||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
\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
|
||||
\BOOKMARK [3][]{subsubsection.3.2.2.3}{3.2.2.3 Properties of \(H2O\)4-10NH4+ Clusters}{subsection.3.2.2}% 27
|
||||
\BOOKMARK [2][]{subsection.3.2.3}{3.2.3 Conclusions for Ammonium/Ammonia Including Water Clusters}{section.3.2}% 28
|
||||
\BOOKMARK [1][]{section.3.3}{3.3 Structural and Energetic Properties of Protonated Uracil Water Clusters}{chapter.3}% 29
|
||||
\BOOKMARK [2][]{subsection.3.3.1}{3.3.1 General introduction}{section.3.3}% 30
|
||||
\BOOKMARK [2][]{subsection.3.3.2}{3.3.2 Results and Discussion}{section.3.3}% 31
|
||||
\BOOKMARK [3][]{subsubsection.3.3.2.1}{3.3.2.1 Experimental Results}{subsection.3.3.2}% 32
|
||||
\BOOKMARK [3][]{subsubsection.3.3.2.2}{3.3.2.2 Calculated Structures of Protonated Uracil Water Clusters}{subsection.3.3.2}% 33
|
||||
\BOOKMARK [2][]{subsection.3.3.3}{3.3.3 Conclusions on \(H2O\)nUH+ clusters}{section.3.3}% 34
|
||||
\BOOKMARK [0][]{chapter.4}{4 Dynamical Simulation of Collision-Induced Dissociation}{}% 35
|
||||
\BOOKMARK [1][]{section.4.1}{4.1 Experimental Methods}{chapter.4}% 36
|
||||
\BOOKMARK [2][]{subsection.4.1.1}{4.1.1 Principle of TCID}{section.4.1}% 37
|
||||
\BOOKMARK [2][]{subsection.4.1.2}{4.1.2 Experimental Setup}{section.4.1}% 38
|
||||
\BOOKMARK [1][]{section.4.2}{4.2 Computational Details}{chapter.4}% 39
|
||||
\BOOKMARK [2][]{subsection.4.2.1}{4.2.1 SCC-DFTB Potential}{section.4.2}% 40
|
||||
\BOOKMARK [2][]{subsection.4.2.2}{4.2.2 Collision Trajectories}{section.4.2}% 41
|
||||
\BOOKMARK [2][]{subsection.4.2.3}{4.2.3 Trajectory Analysis}{section.4.2}% 42
|
||||
\BOOKMARK [1][]{section.4.3}{4.3 Dynamical Simulation of Collision-Induced Dissociation of Protonated Uracil Water Clusters}{chapter.4}% 43
|
||||
\BOOKMARK [2][]{subsection.4.3.1}{4.3.1 Introduction}{section.4.3}% 44
|
||||
\BOOKMARK [2][]{subsection.4.3.2}{4.3.2 Results and Discussion}{section.4.3}% 45
|
||||
\BOOKMARK [3][]{subsubsection.4.3.2.1}{4.3.2.1 Statistical Convergence}{subsection.4.3.2}% 46
|
||||
\BOOKMARK [2][]{subsection.4.3.3}{4.3.3 Time-Dependent Proportion of Fragments}{section.4.3}% 47
|
||||
\BOOKMARK [2][]{subsection.4.3.4}{4.3.4 Proportion of Neutral Uracil Loss and Total Fragmentation Cross Sections for Small Clusters}{section.4.3}% 48
|
||||
\BOOKMARK [2][]{subsection.4.3.5}{4.3.5 Behaviour at Larger Sizes, the Cases of \(H2O\)11, 12UH+}{section.4.3}% 49
|
||||
\BOOKMARK [2][]{subsection.4.3.6}{4.3.6 Mass Spectra of Fragments with Excess Proton}{section.4.3}% 50
|
||||
\BOOKMARK [2][]{subsection.4.3.7}{4.3.7 Conclusions about CID of \(H2O\)nUH+}{section.4.3}% 51
|
||||
\BOOKMARK [1][]{section.4.4}{4.4 Dynamical Simulation of Collision-Induced Dissociation for Pyrene Dimer Cation}{chapter.4}% 52
|
||||
\BOOKMARK [2][]{subsection.4.4.1}{4.4.1 Introduction}{section.4.4}% 53
|
||||
\BOOKMARK [2][]{subsection.4.4.2}{4.4.2 Calculation of Energies}{section.4.4}% 54
|
||||
\BOOKMARK [2][]{subsection.4.4.3}{4.4.3 Simulation of the Experimental TOFMS}{section.4.4}% 55
|
||||
\BOOKMARK [2][]{subsection.4.4.4}{4.4.4 Results and Discussion}{section.4.4}% 56
|
||||
\BOOKMARK [3][]{subsubsection.4.4.4.1}{4.4.4.1 TOFMS Comparison}{subsection.4.4.4}% 57
|
||||
\BOOKMARK [3][]{subsubsection.4.4.4.2}{4.4.4.2 Molecular Dynamics Analysis}{subsection.4.4.4}% 58
|
||||
\BOOKMARK [2][]{subsection.4.4.5}{4.4.5 Conclusions about CID of Py2+}{section.4.4}% 59
|
||||
\BOOKMARK [0][]{chapter.5}{5 General Conclusions and Perspectives}{}% 60
|
||||
\BOOKMARK [1][]{section.5.1}{5.1 General Conclusions}{chapter.5}% 61
|
||||
\BOOKMARK [1][]{section.5.2}{5.2 Perspectives}{chapter.5}% 62
|
||||
\BOOKMARK [0][]{chapter*.71}{References}{}% 63
|
||||
\BOOKMARK [3][]{subsubsection.3.2.2.4}{3.2.2.4 Properties of \(H2O\)4-10NH3 Clusters}{subsection.3.2.2}% 28
|
||||
\BOOKMARK [3][]{subsubsection.3.2.2.5}{3.2.2.5 Properties of \(H2O\)20NH4+ Clusters}{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.3.3.2}{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
|
||||
\BOOKMARK [2][]{subsection.3.3.3}{3.3.3 Conclusions on \(H2O\)nUH+ clusters}{section.3.3}% 36
|
||||
\BOOKMARK [0][]{chapter.4}{4 Dynamical Simulation of Collision-Induced Dissociation}{}% 37
|
||||
\BOOKMARK [1][]{section.4.1}{4.1 Experimental Methods}{chapter.4}% 38
|
||||
\BOOKMARK [2][]{subsection.4.1.1}{4.1.1 Principle of TCID}{section.4.1}% 39
|
||||
\BOOKMARK [2][]{subsection.4.1.2}{4.1.2 Experimental Setup}{section.4.1}% 40
|
||||
\BOOKMARK [1][]{section.4.2}{4.2 Computational Details}{chapter.4}% 41
|
||||
\BOOKMARK [2][]{subsection.4.2.1}{4.2.1 SCC-DFTB Potential}{section.4.2}% 42
|
||||
\BOOKMARK [2][]{subsection.4.2.2}{4.2.2 Collision Trajectories}{section.4.2}% 43
|
||||
\BOOKMARK [2][]{subsection.4.2.3}{4.2.3 Trajectory Analysis}{section.4.2}% 44
|
||||
\BOOKMARK [1][]{section.4.3}{4.3 Dynamical Simulation of Collision-Induced Dissociation of Protonated Uracil Water Clusters}{chapter.4}% 45
|
||||
\BOOKMARK [2][]{subsection.4.3.1}{4.3.1 Introduction}{section.4.3}% 46
|
||||
\BOOKMARK [2][]{subsection.4.3.2}{4.3.2 Results and Discussion}{section.4.3}% 47
|
||||
\BOOKMARK [3][]{subsubsection.4.3.2.1}{4.3.2.1 Statistical Convergence}{subsection.4.3.2}% 48
|
||||
\BOOKMARK [2][]{subsection.4.3.3}{4.3.3 Time-Dependent Proportion of Fragments}{section.4.3}% 49
|
||||
\BOOKMARK [2][]{subsection.4.3.4}{4.3.4 Proportion of Neutral Uracil Loss and Total Fragmentation Cross Sections for Small Clusters}{section.4.3}% 50
|
||||
\BOOKMARK [2][]{subsection.4.3.5}{4.3.5 Behaviour at Larger Sizes, the Cases of \(H2O\)11, 12UH+}{section.4.3}% 51
|
||||
\BOOKMARK [2][]{subsection.4.3.6}{4.3.6 Mass Spectra of Fragments with Excess Proton}{section.4.3}% 52
|
||||
\BOOKMARK [2][]{subsection.4.3.7}{4.3.7 Conclusions about CID of \(H2O\)nUH+}{section.4.3}% 53
|
||||
\BOOKMARK [1][]{section.4.4}{4.4 Dynamical Simulation of Collision-Induced Dissociation for Pyrene Dimer Cation}{chapter.4}% 54
|
||||
\BOOKMARK [2][]{subsection.4.4.1}{4.4.1 Introduction}{section.4.4}% 55
|
||||
\BOOKMARK [2][]{subsection.4.4.2}{4.4.2 Calculation of Energies}{section.4.4}% 56
|
||||
\BOOKMARK [2][]{subsection.4.4.3}{4.4.3 Simulation of the Experimental TOFMS}{section.4.4}% 57
|
||||
\BOOKMARK [2][]{subsection.4.4.4}{4.4.4 Results and Discussion}{section.4.4}% 58
|
||||
\BOOKMARK [3][]{subsubsection.4.4.4.1}{4.4.4.1 TOFMS Comparison}{subsection.4.4.4}% 59
|
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\BOOKMARK [3][]{subsubsection.4.4.4.2}{4.4.4.2 Molecular Dynamics Analysis}{subsection.4.4.4}% 60
|
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\BOOKMARK [2][]{subsection.4.4.5}{4.4.5 Conclusions about CID of Py2+}{section.4.4}% 61
|
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\BOOKMARK [0][]{chapter.5}{5 General Conclusions and Perspectives}{}% 62
|
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\BOOKMARK [1][]{section.5.1}{5.1 General Conclusions}{chapter.5}% 63
|
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\BOOKMARK [1][]{section.5.2}{5.2 Perspectives}{chapter.5}% 64
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\BOOKMARK [0][]{chapter*.81}{References}{}% 65
|
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\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$_3$}}{59}{subsubsection.3.2.2.2}
|
||||
\contentsline {subsubsection}{\numberline {3.2.2.3}Properties of (H$_2$O)$_{4-10}${NH$_4$}$^+$ Clusters}{59}{subsubsection.3.2.2.3}
|
||||
\contentsline {subsection}{\numberline {3.2.3}Conclusions for Ammonium/Ammonia Including Water Clusters}{59}{subsection.3.2.3}
|
||||
\contentsline {section}{\numberline {3.3}Structural and Energetic Properties of Protonated Uracil Water Clusters}{59}{section.3.3}
|
||||
\contentsline {subsection}{\numberline {3.3.1}General introduction}{59}{subsection.3.3.1}
|
||||
\contentsline {subsection}{\numberline {3.3.2}Results and Discussion}{61}{subsection.3.3.2}
|
||||
\contentsline {subsubsection}{\numberline {3.3.2.1}Experimental Results}{61}{subsubsection.3.3.2.1}
|
||||
\contentsline {subsubsection}{\numberline {3.3.2.2}Calculated Structures of Protonated Uracil Water Clusters}{67}{subsubsection.3.3.2.2}
|
||||
\contentsline {subsection}{\numberline {3.3.3}Conclusions on (H$_2$O)$_{n}$UH$^+$ clusters}{76}{subsection.3.3.3}
|
||||
\contentsline {chapter}{\numberline {4}Dynamical Simulation of Collision-Induced Dissociation}{81}{chapter.4}
|
||||
\contentsline {section}{\numberline {4.1}Experimental Methods}{81}{section.4.1}
|
||||
\contentsline {subsection}{\numberline {4.1.1}Principle of TCID}{83}{subsection.4.1.1}
|
||||
\contentsline {subsection}{\numberline {4.1.2}Experimental Setup}{84}{subsection.4.1.2}
|
||||
\contentsline {section}{\numberline {4.2}Computational Details}{86}{section.4.2}
|
||||
\contentsline {subsection}{\numberline {4.2.1}SCC-DFTB Potential}{86}{subsection.4.2.1}
|
||||
\contentsline {subsection}{\numberline {4.2.2}Collision Trajectories}{87}{subsection.4.2.2}
|
||||
\contentsline {subsection}{\numberline {4.2.3}Trajectory Analysis}{88}{subsection.4.2.3}
|
||||
\contentsline {section}{\numberline {4.3}Dynamical Simulation of Collision-Induced Dissociation of Protonated Uracil Water Clusters}{89}{section.4.3}
|
||||
\contentsline {subsection}{\numberline {4.3.1}Introduction}{89}{subsection.4.3.1}
|
||||
\contentsline {subsection}{\numberline {4.3.2}Results and Discussion}{90}{subsection.4.3.2}
|
||||
\contentsline {subsubsection}{\numberline {4.3.2.1}Statistical Convergence}{90}{subsubsection.4.3.2.1}
|
||||
\contentsline {subsection}{\numberline {4.3.3}Time-Dependent Proportion of Fragments}{93}{subsection.4.3.3}
|
||||
\contentsline {subsection}{\numberline {4.3.4}Proportion of Neutral Uracil Loss and Total Fragmentation Cross Sections for Small Clusters}{96}{subsection.4.3.4}
|
||||
\contentsline {subsection}{\numberline {4.3.5}Behaviour at Larger Sizes, the Cases of (H$_2$O)$_{11, 12}$UH$^+$}{106}{subsection.4.3.5}
|
||||
\contentsline {subsection}{\numberline {4.3.6}Mass Spectra of Fragments with Excess Proton}{110}{subsection.4.3.6}
|
||||
\contentsline {subsection}{\numberline {4.3.7}Conclusions about CID of (H$_2$O)$_{n}$UH$^+$}{113}{subsection.4.3.7}
|
||||
\contentsline {section}{\numberline {4.4}Dynamical Simulation of Collision-Induced Dissociation for Pyrene Dimer Cation}{115}{section.4.4}
|
||||
\contentsline {subsection}{\numberline {4.4.1}Introduction}{115}{subsection.4.4.1}
|
||||
\contentsline {subsection}{\numberline {4.4.2}Calculation of Energies}{117}{subsection.4.4.2}
|
||||
\contentsline {subsection}{\numberline {4.4.3}Simulation of the Experimental TOFMS}{119}{subsection.4.4.3}
|
||||
\contentsline {subsection}{\numberline {4.4.4}Results and Discussion}{121}{subsection.4.4.4}
|
||||
\contentsline {subsubsection}{\numberline {4.4.4.1}TOFMS Comparison}{121}{subsubsection.4.4.4.1}
|
||||
\contentsline {subsubsection}{\numberline {4.4.4.2}Molecular Dynamics Analysis}{122}{subsubsection.4.4.4.2}
|
||||
\contentsline {subsection}{\numberline {4.4.5}Conclusions about CID of Py$_2^+$}{138}{subsection.4.4.5}
|
||||
\contentsline {chapter}{\numberline {5}General Conclusions and Perspectives}{141}{chapter.5}
|
||||
\contentsline {section}{\numberline {5.1}General Conclusions}{141}{section.5.1}
|
||||
\contentsline {section}{\numberline {5.2}Perspectives}{144}{section.5.2}
|
||||
\contentsline {chapter}{References}{145}{chapter*.71}
|
||||
\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$_4$}$^+$ Clusters}{73}{subsubsection.3.2.2.5}
|
||||
\contentsline {subsection}{\numberline {3.2.3}Conclusions for Ammonium/Ammonia Including Water Clusters}{74}{subsection.3.2.3}
|
||||
\contentsline {section}{\numberline {3.3}Structural and Energetic Properties of Protonated Uracil Water Clusters}{75}{section.3.3}
|
||||
\contentsline {subsection}{\numberline {3.3.1}General introduction}{75}{subsection.3.3.1}
|
||||
\contentsline {subsection}{\numberline {3.3.2}Results and Discussion}{77}{subsection.3.3.2}
|
||||
\contentsline {subsubsection}{\numberline {3.3.2.1}Experimental Results}{77}{subsubsection.3.3.2.1}
|
||||
\contentsline {subsubsection}{\numberline {3.3.2.2}Calculated Structures of Protonated Uracil Water Clusters}{83}{subsubsection.3.3.2.2}
|
||||
\contentsline {subsection}{\numberline {3.3.3}Conclusions on (H$_2$O)$_{n}$UH$^+$ clusters}{92}{subsection.3.3.3}
|
||||
\contentsline {chapter}{\numberline {4}Dynamical Simulation of Collision-Induced Dissociation}{97}{chapter.4}
|
||||
\contentsline {section}{\numberline {4.1}Experimental Methods}{97}{section.4.1}
|
||||
\contentsline {subsection}{\numberline {4.1.1}Principle of TCID}{99}{subsection.4.1.1}
|
||||
\contentsline {subsection}{\numberline {4.1.2}Experimental Setup}{100}{subsection.4.1.2}
|
||||
\contentsline {section}{\numberline {4.2}Computational Details}{102}{section.4.2}
|
||||
\contentsline {subsection}{\numberline {4.2.1}SCC-DFTB Potential}{102}{subsection.4.2.1}
|
||||
\contentsline {subsection}{\numberline {4.2.2}Collision Trajectories}{103}{subsection.4.2.2}
|
||||
\contentsline {subsection}{\numberline {4.2.3}Trajectory Analysis}{104}{subsection.4.2.3}
|
||||
\contentsline {section}{\numberline {4.3}Dynamical Simulation of Collision-Induced Dissociation of Protonated Uracil Water Clusters}{105}{section.4.3}
|
||||
\contentsline {subsection}{\numberline {4.3.1}Introduction}{105}{subsection.4.3.1}
|
||||
\contentsline {subsection}{\numberline {4.3.2}Results and Discussion}{106}{subsection.4.3.2}
|
||||
\contentsline {subsubsection}{\numberline {4.3.2.1}Statistical Convergence}{106}{subsubsection.4.3.2.1}
|
||||
\contentsline {subsection}{\numberline {4.3.3}Time-Dependent Proportion of Fragments}{109}{subsection.4.3.3}
|
||||
\contentsline {subsection}{\numberline {4.3.4}Proportion of Neutral Uracil Loss and Total Fragmentation Cross Sections for Small Clusters}{112}{subsection.4.3.4}
|
||||
\contentsline {subsection}{\numberline {4.3.5}Behaviour at Larger Sizes, the Cases of (H$_2$O)$_{11, 12}$UH$^+$}{122}{subsection.4.3.5}
|
||||
\contentsline {subsection}{\numberline {4.3.6}Mass Spectra of Fragments with Excess Proton}{126}{subsection.4.3.6}
|
||||
\contentsline {subsection}{\numberline {4.3.7}Conclusions about CID of (H$_2$O)$_{n}$UH$^+$}{129}{subsection.4.3.7}
|
||||
\contentsline {section}{\numberline {4.4}Dynamical Simulation of Collision-Induced Dissociation for Pyrene Dimer Cation}{131}{section.4.4}
|
||||
\contentsline {subsection}{\numberline {4.4.1}Introduction}{131}{subsection.4.4.1}
|
||||
\contentsline {subsection}{\numberline {4.4.2}Calculation of Energies}{133}{subsection.4.4.2}
|
||||
\contentsline {subsection}{\numberline {4.4.3}Simulation of the Experimental TOFMS}{135}{subsection.4.4.3}
|
||||
\contentsline {subsection}{\numberline {4.4.4}Results and Discussion}{137}{subsection.4.4.4}
|
||||
\contentsline {subsubsection}{\numberline {4.4.4.1}TOFMS Comparison}{137}{subsubsection.4.4.4.1}
|
||||
\contentsline {subsubsection}{\numberline {4.4.4.2}Molecular Dynamics Analysis}{138}{subsubsection.4.4.4.2}
|
||||
\contentsline {subsection}{\numberline {4.4.5}Conclusions about CID of Py$_2^+$}{154}{subsection.4.4.5}
|
||||
\contentsline {chapter}{\numberline {5}General Conclusions and Perspectives}{157}{chapter.5}
|
||||
\contentsline {section}{\numberline {5.1}General Conclusions}{157}{section.5.1}
|
||||
\contentsline {section}{\numberline {5.2}Perspectives}{160}{section.5.2}
|
||||
\contentsline {chapter}{References}{161}{chapter*.81}
|
||||
|
||||
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