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This commit is contained in:
linjie zheng
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%%
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%% This is file `achemso.sty',
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%% generated with the docstrip utility.
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||||
%%
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||||
%% The original source files were:
|
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%%
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||||
%% achemso.dtx (with options: `package')
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||||
%% ----------------------------------------------------------------
|
||||
%% achemso --- Support for submissions to American Chemical Society
|
||||
%% journals
|
||||
%% E-mail: joseph.wright@morningstar2.co.uk
|
||||
%% Released under the LaTeX Project Public License v1.3c or later
|
||||
%% See http://www.latex-project.org/lppl.txt
|
||||
%% ----------------------------------------------------------------
|
||||
%%
|
||||
\NeedsTeXFormat{LaTeX2e}
|
||||
|
||||
\ProvidesPackage{achemso}
|
||||
[2014/08/18 v3.8k Support for ACS journals]
|
||||
\@ifclassloaded{achemso}{%
|
||||
\PackageInfo{achemso}{%
|
||||
You have already loaded the `achemso' class:\MessageBreak
|
||||
loading the package will abort%
|
||||
}%
|
||||
\endinput
|
||||
}{%
|
||||
\PackageInfo{achemso}{%
|
||||
When writing a submission to an ACS journal, please\MessageBreak
|
||||
use the achemso document class%
|
||||
}%
|
||||
}
|
||||
\newcommand*\acs@warning{\PackageWarning{achemso}}
|
||||
\newcommand*\acs@ifundefined[1]{%
|
||||
\begingroup\expandafter\expandafter\expandafter\endgroup
|
||||
\expandafter\ifx\csname #1\endcsname\relax
|
||||
\expandafter\@firstoftwo
|
||||
\else
|
||||
\expandafter\@secondoftwo
|
||||
\fi
|
||||
}
|
||||
\RequirePackage{xkeyval}
|
||||
\newcommand*\acs@keyval@bool[2]{%
|
||||
\acs@ifundefined{acs@#1#2}{%
|
||||
\acs@warning{Unknown option `#2' for key #1}%
|
||||
}{%
|
||||
\@nameuse{acs@#1#2}%
|
||||
}%
|
||||
}
|
||||
\newif\ifacs@abbreviations
|
||||
\newif\ifacs@articletitle
|
||||
\newif\ifacs@biochem
|
||||
\newif\ifacs@chaptertitle
|
||||
\newif\ifacs@email
|
||||
\newif\ifacs@hyperref
|
||||
\newif\ifacs@keywords
|
||||
\newif\ifacs@super
|
||||
\define@key{acs}{abbreviations}[true]{%
|
||||
\acs@keyval@bool{abbreviations}{#1}%
|
||||
}
|
||||
\define@key{acs}{articletitle}[true]{%
|
||||
\acs@keyval@bool{articletitle}{#1}%
|
||||
}
|
||||
\define@key{acs}{biochem}[true]{%
|
||||
\acs@keyval@bool{biochem}{#1}%
|
||||
}
|
||||
\define@key{acs}{chaptertitle}[true]{%
|
||||
\acs@keyval@bool{chaptertitle}{#1}%
|
||||
}
|
||||
\define@key{acs}{email}[true]{%
|
||||
\acs@keyval@bool{email}{#1}%
|
||||
}
|
||||
\define@key{acs}{hyperref}[true]{%
|
||||
\acs@keyval@bool{hyperref}{#1}%
|
||||
}
|
||||
\define@key{acs}{keywords}[true]{%
|
||||
\acs@keyval@bool{keywords}{#1}%
|
||||
}
|
||||
\define@key{acs}{super}[true]{%
|
||||
\acs@keyval@bool{super}{#1}%
|
||||
}
|
||||
\define@key{acs}{usetitle}[true]{%
|
||||
\acs@keyval@bool{articletitle}{#1}%
|
||||
}
|
||||
\newcommand*\acs@journal{jacsat}
|
||||
\newcommand*\acs@layout{traditional}
|
||||
\newcommand*\acs@manuscript{article}
|
||||
\newcommand*\acs@maxauthors{15}
|
||||
\define@key{acs}{journal}{%
|
||||
\def\acs@journal{#1}%
|
||||
}
|
||||
\define@key{acs}{layout}{%
|
||||
\def\acs@layout{#1}%
|
||||
}
|
||||
\define@key{acs}{manuscript}{%
|
||||
\def\acs@manuscript{#1}%
|
||||
}
|
||||
\define@key{acs}{maxauthors}{%
|
||||
\def\acs@maxauthors{#1}%
|
||||
}
|
||||
\newif\ifacs@etal@truncate
|
||||
\define@key{acs}{etalmode}{%
|
||||
\acs@ifundefined{acs@etal@#1}{%
|
||||
\acs@warning{%
|
||||
Unknown value `#1' for\MessageBreak etalmode option%
|
||||
}%
|
||||
}{%
|
||||
\@nameuse{acs@etal@#1}%
|
||||
}%
|
||||
}
|
||||
\newcommand*\acs@etal@firstonly{\acs@etal@truncatefalse}
|
||||
\newcommand*\acs@etal@truncate{\acs@etal@truncatetrue}
|
||||
\define@key{acs}{biochemistry}{%
|
||||
\setkeys{acs}{biochem = #1}%
|
||||
}
|
||||
\define@key{acs}{biblabel}{%
|
||||
\acs@ifundefined{acs@biblabel@#1}{%
|
||||
\acs@warning{%
|
||||
Unknown value `#1' for\MessageBreak biblabel option%
|
||||
}%
|
||||
}{%
|
||||
\acs@activate@biblabel{\@nameuse{acs@biblabel@#1}}%
|
||||
}%
|
||||
}
|
||||
\newcommand*\acs@activate@biblabel{}
|
||||
\let\acs@activate@biblabel\AtEndOfPackage
|
||||
\AtEndOfPackage{\let\acs@activate@biblabel\@firstofone}
|
||||
\newcommand*\acs@biblabel@brackets{\def\bibnumfmt##1{(##1)}}
|
||||
\newcommand*\acs@biblabel@fullstop{\def\bibnumfmt##1{##1.}}
|
||||
\newcommand*\acs@biblabel@period{\def\bibnumfmt##1{##1.}}
|
||||
\newcommand*\acs@biblabel@plain{\def\bibnumfmt##1{##1}}
|
||||
\setkeys{acs}{
|
||||
email = true,
|
||||
super = true
|
||||
}
|
||||
\ProcessOptionsX*<acs>
|
||||
\newcommand*\acs@manuscript@communication{communication}
|
||||
\newcommand*\acs@manuscript@letter{letter}
|
||||
\newcommand*\acs@manuscript@note{note}
|
||||
\newcommand*\acs@manuscript@review{review}
|
||||
\newcommand*\acs@manuscript@suppinfo{suppinfo}
|
||||
\newcommand*\acs@niib@create{%
|
||||
\@namedef{ver@notes2bib.sty}{%
|
||||
2009/04/20 v1.6a Integrating notes into the bibliography (achemso
|
||||
version)
|
||||
}%
|
||||
\@ifundefined{c@bibnote}{\newcounter{bibnote}}{}
|
||||
\def\thebibnote{%
|
||||
Note-\the\value{bibnote}%
|
||||
}%
|
||||
\DeclareRobustCommand*{\bibnote}[1][\thebibnote]{%
|
||||
\stepcounter{bibnote}%
|
||||
\def\acs@niib@after@text{\cite{##1}}%
|
||||
\acs@niib@text{##1}%
|
||||
}%
|
||||
\DeclareRobustCommand*{\bibnotemark}[1][\thebibnote]{%
|
||||
\stepcounter{bibnote}%
|
||||
\cite{##1}%
|
||||
}%
|
||||
\DeclareRobustCommand*{\bibnotetext}[1][\thebibnote]{%
|
||||
\let\acs@niib@after@text\relax
|
||||
\acs@niib@text{##1}%
|
||||
}%
|
||||
\newcommand*\printbibnotes{%
|
||||
\ifnum\the\value{bibnote}>\z@\relax
|
||||
\nocite{achemso-control}%
|
||||
\acs@bibliography{acs-\jobname}%
|
||||
\fi
|
||||
}%
|
||||
}
|
||||
\newcommand*\acs@niib@after@text{}
|
||||
\newcommand*\acs@niib@text{%
|
||||
\@bsphack
|
||||
\if@filesw
|
||||
\expandafter\acs@niib@write
|
||||
\else
|
||||
\expandafter\acs@niib@no@write
|
||||
\fi
|
||||
}
|
||||
\newcommand*\acs@niib@write[1]{%
|
||||
\begingroup
|
||||
\let\do\@makeother
|
||||
\dospecials
|
||||
\catcode`\{ 1\relax
|
||||
\catcode`\} 2\relax
|
||||
\acs@niib@write@aux@i{#1}%
|
||||
}
|
||||
\newcommand*\acs@niib@write@aux@i[1]{%
|
||||
\long\def\@tempa##1{%
|
||||
\def\@tempa{##1}%
|
||||
\@onelevel@sanitize\@tempa
|
||||
\expandafter\endgroup
|
||||
\expandafter\def\expandafter\@tempa\expandafter{\@tempa}%
|
||||
\acs@niib@write@aux@ii{#1}%
|
||||
}%
|
||||
\catcode`\^^M 10\relax
|
||||
\@tempa
|
||||
}
|
||||
\newcommand*\acs@niib@write@aux@ii[1]{%
|
||||
\immediate\write\acs@bib@file{%
|
||||
@Misc\string{#1,^^J%
|
||||
\space\space note = \string{\@tempa\string},^^J%
|
||||
\string}^^J%
|
||||
}%
|
||||
\@esphack
|
||||
\acs@niib@after@text
|
||||
}
|
||||
\newcommand\acs@niib@no@write[2]{%
|
||||
\@esphack
|
||||
\acs@niib@after@text
|
||||
}
|
||||
\AtBeginDocument{
|
||||
\def\nmv@natbib@detect{%
|
||||
\ifNAT@super
|
||||
\expandafter\acs@nmv@activate
|
||||
\else
|
||||
\expandafter\acs@autonote
|
||||
\fi
|
||||
}
|
||||
}
|
||||
\newcommand*\acs@nmv@activate{%
|
||||
\let\nmv@citex@nat\@citex
|
||||
\let\@citex\nmv@citex
|
||||
\let\nmv@cite\cite
|
||||
\renewcommand*{\cite}[2][]{%
|
||||
\nmv@ifmtarg{##1}{%
|
||||
\nmv@citetrue
|
||||
\nmv@cite{##2}%
|
||||
}{%
|
||||
\nocite{##2}%
|
||||
\bibnote{Ref.~\citenum{##2}, ##1}%
|
||||
}%
|
||||
}%
|
||||
}
|
||||
\newcommand*\acs@autonote{%
|
||||
\let\nmv@cite\cite
|
||||
\renewcommand*{\cite}[2][]{%
|
||||
\nmv@ifmtarg{##1}{%
|
||||
\nmv@cite{##2}%
|
||||
}{%
|
||||
\nocite{##2}%
|
||||
\bibnote{Ref.~\citenum{##2}, ##1}%
|
||||
}%
|
||||
}%
|
||||
}
|
||||
\newwrite\acs@bib@file
|
||||
\newcommand*\acs@bib@message{%
|
||||
This is an auxiliary file used by the `achemso' bundle.^^J%
|
||||
This file may safely be deleted. It will be recreated as required.^^J
|
||||
}
|
||||
\newcommand*\acs@bib@name{acs-\jobname.bib}
|
||||
\newcommand*\acs@bib@write{%
|
||||
\if@filesw
|
||||
\expandafter\acs@bib@write@aux
|
||||
\fi
|
||||
}
|
||||
\AtBeginDocument{\acs@bib@write}
|
||||
\newcommand*\acs@bib@write@aux{%
|
||||
\immediate\openout\acs@bib@file\acs@bib@name\relax
|
||||
\immediate\write\acs@bib@file{\acs@bib@message}%
|
||||
\edef\@tempa##1##2{%
|
||||
\space\space##1\space = "##2",^^J%
|
||||
}%
|
||||
\immediate\write\acs@bib@file{%
|
||||
@Control\string{%
|
||||
achemso-control,^^J%
|
||||
\@tempa{ctrl-article-title\space}{%
|
||||
\ifacs@articletitle yes\else no\fi
|
||||
}%
|
||||
\@tempa{ctrl-chapter-title\space}{%
|
||||
\ifacs@chaptertitle yes\else no\fi
|
||||
}%
|
||||
\@tempa{ctrl-etal-number\space\space\space}{\acs@maxauthors}%
|
||||
\@tempa{ctrl-etal-firstonly}{%
|
||||
\ifacs@etal@truncate no\else yes\fi
|
||||
}%
|
||||
\string}^^J%
|
||||
}%
|
||||
\immediate\write\@auxout{%
|
||||
\string\citation\string{achemso-control\string}%
|
||||
}%
|
||||
\AtEndDocument{%
|
||||
\immediate\closeout\acs@bib@file\relax
|
||||
}%
|
||||
}
|
||||
\AtBeginDocument{%
|
||||
\let\acs@bibliography\bibliography
|
||||
\def\bibliography#1{%
|
||||
\acs@bibliography{acs-\jobname,#1}%
|
||||
}%
|
||||
}
|
||||
\AtBeginDocument{
|
||||
\providecommand{\latin}[1]{#1}
|
||||
}
|
||||
\ifacs@super
|
||||
\RequirePackage[sort&compress,numbers,super]{natbib}
|
||||
\else
|
||||
\RequirePackage[sort&compress,numbers,round]{natbib}
|
||||
\def\citenumfont{\textit}
|
||||
\fi
|
||||
\RequirePackage{natmove}
|
||||
\IfFileExists{mciteplus.sty}{%
|
||||
\RequirePackage{mciteplus}
|
||||
\providecommand*{\@mciteNatbibCiteCmdList}{}%
|
||||
\edef\@tempa{\noexpand\in@{citenum}{\@mciteNatbibCiteCmdList}}%
|
||||
\@tempa
|
||||
\ifin@
|
||||
\else
|
||||
\edef\@mciteNatbibCiteCmdList{\@mciteNatbibCiteCmdList,citenum}%
|
||||
\fi
|
||||
}{}
|
||||
\newcommand*\acs@bibstyle{achemso}
|
||||
\ifacs@biochem
|
||||
\def\acs@bibstyle{biochem}
|
||||
\bibliographystyle{biochem}
|
||||
\else
|
||||
\bibliographystyle{achemso}
|
||||
\fi
|
||||
\newcommand*\acs@bibliographystyle{}
|
||||
\let\acs@bibliographystyle\bibliographystyle
|
||||
\def\bibliographystyle#1{%
|
||||
\acs@warning{\string\bibliographystyle\space ignored}%
|
||||
\expandafter\acs@bibliographystyle\expandafter{\acs@bibstyle}%
|
||||
}
|
||||
\AtBeginDocument{%
|
||||
\@ifpackageloaded{notes2bib}{}{%
|
||||
\acs@niib@create
|
||||
}%
|
||||
}
|
||||
%%
|
||||
%% Originally developed by Mats Dahlgren
|
||||
%% Copyright (C) 1996-1998 by Mats Dahlgren
|
||||
%% Copyright (C) 2008-2014 by
|
||||
%% Joseph Wright <joseph.wright@morningstar2.co.uk>
|
||||
%%
|
||||
%% Part of this bundle is derived from cite.sty, to which the
|
||||
%% following license applies:
|
||||
%% Copyright (C) 1989-2009 by Donald Arseneau
|
||||
%% These macros may be freely transmitted, reproduced, or
|
||||
%% modified provided that this notice is left intact.
|
||||
%%
|
||||
%% It may be distributed and/or modified under the conditions of
|
||||
%% the LaTeX Project Public License (LPPL), either version 1.3c of
|
||||
%% this license or (at your option) any later version. The latest
|
||||
%% version of this license is in the file:
|
||||
%%
|
||||
%% http://www.latex-project.org/lppl.txt
|
||||
%%
|
||||
%% This work is "maintained" (as per LPPL maintenance status) by
|
||||
%% Joseph Wright.
|
||||
%%
|
||||
%% This work consists of the file achemso.dtx
|
||||
%% and the derived files achemso.cls,
|
||||
%% achemso.ins,
|
||||
%% achemso.pdf,
|
||||
%% achemso.sty,
|
||||
%% achemso-demo.bib,
|
||||
%% achemso-demo.tex,
|
||||
%% natmove.sty and
|
||||
%% a number of configuration files.
|
||||
%%
|
||||
%%
|
||||
%% End of file `achemso.sty'.
|
||||
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@ -0,0 +1,62 @@
|
|||
%%
|
||||
%% This is file `jpcbfk.cfg',
|
||||
%% generated with the docstrip utility.
|
||||
%%
|
||||
%% The original source files were:
|
||||
%%
|
||||
%% achemso.dtx (with options: `jpcbfk')
|
||||
%% ----------------------------------------------------------------
|
||||
%% achemso --- Support for submissions to American Chemical Society
|
||||
%% journals
|
||||
%% E-mail: joseph.wright@morningstar2.co.uk
|
||||
%% Released under the LaTeX Project Public License v1.3c or later
|
||||
%% See http://www.latex-project.org/lppl.txt
|
||||
%% ----------------------------------------------------------------
|
||||
%%
|
||||
|
||||
\ProvidesFile{jpcbfk.cfg}
|
||||
[2014/08/18 v3.8k achemso configuration: J. Phys. Chem. B]
|
||||
\def\acs@type@list{article,suppinfo}
|
||||
\setkeys{acs}{
|
||||
articletitle = true,
|
||||
etalmode = truncate,
|
||||
maxauthors = 10,
|
||||
keywords = true
|
||||
}
|
||||
\SectionNumbersOff
|
||||
\captionsetup[table]{labelfont=bf,textfont=bf}
|
||||
\g@addto@macro{\maketitle}{\newpage}
|
||||
%%
|
||||
%% Originally developed by Mats Dahlgren
|
||||
%% Copyright (C) 1996-1998 by Mats Dahlgren
|
||||
%% Copyright (C) 2008-2014 by
|
||||
%% Joseph Wright <joseph.wright@morningstar2.co.uk>
|
||||
%%
|
||||
%% Part of this bundle is derived from cite.sty, to which the
|
||||
%% following license applies:
|
||||
%% Copyright (C) 1989-2009 by Donald Arseneau
|
||||
%% These macros may be freely transmitted, reproduced, or
|
||||
%% modified provided that this notice is left intact.
|
||||
%%
|
||||
%% It may be distributed and/or modified under the conditions of
|
||||
%% the LaTeX Project Public License (LPPL), either version 1.3c of
|
||||
%% this license or (at your option) any later version. The latest
|
||||
%% version of this license is in the file:
|
||||
%%
|
||||
%% http://www.latex-project.org/lppl.txt
|
||||
%%
|
||||
%% This work is "maintained" (as per LPPL maintenance status) by
|
||||
%% Joseph Wright.
|
||||
%%
|
||||
%% This work consists of the file achemso.dtx
|
||||
%% and the derived files achemso.cls,
|
||||
%% achemso.ins,
|
||||
%% achemso.pdf,
|
||||
%% achemso.sty,
|
||||
%% achemso-demo.bib,
|
||||
%% achemso-demo.tex,
|
||||
%% natmove.sty and
|
||||
%% a number of configuration files.
|
||||
%%
|
||||
%%
|
||||
%% End of file `jpcbfk.cfg'.
|
||||
|
|
@ -0,0 +1,152 @@
|
|||
%%
|
||||
%% This is file `natmove.sty',
|
||||
%% generated with the docstrip utility.
|
||||
%%
|
||||
%% The original source files were:
|
||||
%%
|
||||
%% achemso.dtx (with options: `natmove')
|
||||
%% ----------------------------------------------------------------
|
||||
%% achemso --- Support for submissions to American Chemical Society
|
||||
%% journals
|
||||
%% E-mail: joseph.wright@morningstar2.co.uk
|
||||
%% Released under the LaTeX Project Public License v1.3c or later
|
||||
%% See http://www.latex-project.org/lppl.txt
|
||||
%% ----------------------------------------------------------------
|
||||
%%
|
||||
\NeedsTeXFormat{LaTeX2e}
|
||||
|
||||
\ProvidesPackage{natmove}
|
||||
[2010/01/15 v1.1a Automatic citation moving with natbib]
|
||||
\RequirePackage{natbib}
|
||||
\newcommand*\nmv@ifmtarg{}
|
||||
\newcommand*\nmv@xifmtarg{}
|
||||
\begingroup
|
||||
\catcode`\Q 3\relax
|
||||
\long\gdef\nmv@ifmtarg#1{%
|
||||
\nmv@xifmtarg#1QQ\@secondoftwo\@firstoftwo\@nil
|
||||
}
|
||||
\long\gdef\nmv@xifmtarg#1#2Q#3#4#5\@nil{#4}
|
||||
\endgroup
|
||||
\newif\ifnmv@cite
|
||||
\newcommand*\nmv@citex{%
|
||||
\ifnmv@cite
|
||||
\expandafter\nmv@citex@moving
|
||||
\else
|
||||
\expandafter\nmv@citex@nat
|
||||
\fi
|
||||
}
|
||||
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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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|
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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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|
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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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|
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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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|
||||
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|
||||
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|
||||
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|
||||
The natbib package is not loaded.\MessageBreak
|
||||
Loading natmove will do nothing
|
||||
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|
||||
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|
||||
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|
||||
\AtBeginDocument{\nmv@natbib@detect}
|
||||
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|
||||
%%
|
||||
%% Originally developed by Mats Dahlgren
|
||||
%% Copyright (C) 1996-1998 by Mats Dahlgren
|
||||
%% Copyright (C) 2008-2014 by
|
||||
%% Joseph Wright <joseph.wright@morningstar2.co.uk>
|
||||
%%
|
||||
%% Part of this bundle is derived from cite.sty, to which the
|
||||
%% following license applies:
|
||||
%% Copyright (C) 1989-2009 by Donald Arseneau
|
||||
%% These macros may be freely transmitted, reproduced, or
|
||||
%% modified provided that this notice is left intact.
|
||||
%%
|
||||
%% It may be distributed and/or modified under the conditions of
|
||||
%% the LaTeX Project Public License (LPPL), either version 1.3c of
|
||||
%% this license or (at your option) any later version. The latest
|
||||
%% version of this license is in the file:
|
||||
%%
|
||||
%% http://www.latex-project.org/lppl.txt
|
||||
%%
|
||||
%% This work is "maintained" (as per LPPL maintenance status) by
|
||||
%% Joseph Wright.
|
||||
%%
|
||||
%% This work consists of the file achemso.dtx
|
||||
%% and the derived files achemso.cls,
|
||||
%% achemso.ins,
|
||||
%% achemso.pdf,
|
||||
%% achemso.sty,
|
||||
%% achemso-demo.bib,
|
||||
%% achemso-demo.tex,
|
||||
%% natmove.sty and
|
||||
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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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|
||||
%% The document class accepts keyval options, which should include
|
||||
%% the target journal and optionally the manuscript type.
|
||||
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|
||||
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|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%% Place any additional packages needed here. Only include packages
|
||||
%% which are essential, to avoid problems later. Do NOT use any
|
||||
%% packages which require e-TeX (for example etoolbox): the e-TeX
|
||||
%% extensions are not currently available on the ACS conversion
|
||||
%% servers.
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\usepackage[version=3]{mhchem} % Formula subscripts using \ce{}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%% If issues arise when submitting your manuscript, you may want to
|
||||
%% un-comment the next line. This provides information on the
|
||||
%% version of every file you have used.
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%\listfiles
|
||||
|
||||
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|
||||
%% Place any additional macros here. Please use \newcommand* where
|
||||
%% possible, and avoid layout-changing macros (which are not used
|
||||
%% when typesetting).
|
||||
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|
||||
\newcommand*\mycommand[1]{\texttt{\emph{#1}}}
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%% Added by author
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\usepackage{graphicx}
|
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\usepackage{tikz}
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|
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|
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%% Meta-data block
|
||||
%% ---------------
|
||||
%% Each author should be given as a separate \author command.
|
||||
%%
|
||||
%% Corresponding authors should have an e-mail given after the author
|
||||
%% name as an \email command. Phone and fax numbers can be given
|
||||
%% using \phone and \fax, respectively; this information is optional.
|
||||
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|
||||
%% The affiliation of authors is given after the authors; each
|
||||
%% \affiliation command applies to all preceding authors not already
|
||||
%% assigned an affiliation.
|
||||
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|
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|
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|
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|
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%% The \altaffiliation macro should be used for new address, etc.
|
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%% On the other hand, \alsoaffiliation is used on a per author basis
|
||||
%% when authors are associated with multiple institutions.
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\author{Kseniia A. Korchagina}
|
||||
\affiliation[Universit\'{e} de Toulouse (UPS) and CNRS]{Laboratoire de Chimie et Physique Quantiques LCPQ/IRSAMC, Université\'e de Toulouse (UPS) and CNRS, 118 Route de Narbonne, F-31062 Toulouse, France}
|
||||
\author{Fernand Spiegelman}
|
||||
\affiliation[Universit\'{e} de Toulouse (UPS) and CNRS]{Laboratoire de Chimie et Physique Quantiques LCPQ/IRSAMC, Université\'e de Toulouse (UPS) and CNRS, 118 Route de Narbonne, F-31062 Toulouse, France}
|
||||
\author{J\'er\^ome Cuny}
|
||||
\affiliation[Universit\'{e} de Toulouse (UPS) and CNRS]{Laboratoire de Chimie et Physique Quantiques LCPQ/IRSAMC, Université\'e de Toulouse (UPS) and CNRS, 118 Route de Narbonne, F-31062 Toulouse, France}
|
||||
\email{jerome.cuny@irsamc.ups-tlse.fr}
|
||||
\phone{+33 (0)5 61 55 68 36}
|
||||
\fax{+33 (0)5 61 55 60 65}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%% The document title should be given as usual. Some journals require
|
||||
%% a running title from the author: this should be supplied as an
|
||||
%% optional argument to \title.
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\title[An \textsf{achemso} demo]
|
||||
{Molecular Dynamics Study of the Collision-Induced Reaction of H with CO on Small Water Clusters\footnote{Molecular Dynamics Study of the Collision-Induced Reaction of H with CO on Small Water Clusters}}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%% Some journals require a list of abbreviations or keywords to be
|
||||
%% supplied. These should be set up here, and will be printed after
|
||||
%% the title and author information, if needed.
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%\abbreviations{PES,ISM,COSAC,FT-IR,MRCI+Q,CCD,CCSD(T),RCCSD(T),UCCSD(T),MP2, MBPT, BSSE, ZPE, DFT, SCC-DFTB, CM3, MD, MDPT}
|
||||
\keywords{Molecular Dynamics, SCC-DFTB, HCO Radical, Collision-Induced Reaction, Water Clusters}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%% The manuscript does not need to include \maketitle, which is
|
||||
%% executed automatically.
|
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|
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\begin{document}
|
||||
|
||||
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|
||||
%% The "tocentry" environment can be used to create an entry for the
|
||||
%% graphical table of contents. It is given here as some journals
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||||
%% 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}
|
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|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%% 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.
|
||||
|
||||
\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
|
||||
%% classes. This should be given within the "acknowledgement"
|
||||
%% environment, which will make the correct section or running title.
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{acknowledgement}
|
||||
The authors acknowledge the supercomputing facility of CALMIP for generous allocation
|
||||
of computer resources (projects P1320 and P0059). The authors declare that there has
|
||||
been no significant financial support for this work.
|
||||
\end{acknowledgement}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%% The same is true for Supporting Information, which should use the
|
||||
%% suppinfo environment.
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%% The appropriate \bibliography command should be placed here.
|
||||
%% Notice that the class file automatically sets \bibliographystyle
|
||||
%% and also names the section correctly.
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\bibliography{Ref}
|
||||
|
||||
\end{document}
|
||||
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Reference in New Issue