trunk/NPthiols/Sup_Info.tex

\documentclass[aps,jcp,preprint,showpacs,superscriptaddress,groupedaddress]{revtex4-1}
\usepackage{graphicx}  % needed for figures
\usepackage{dcolumn}   % needed for some tables
\usepackage{bm}        % for math
\usepackage{amssymb}   % for math
\usepackage{booktabs}
\usepackage[english]{babel}
\usepackage{multirow}
\usepackage{times}
\usepackage[version=3]{mhchem}
\usepackage{lineno}
\usepackage{gensymb}
\usepackage{multirow}

\begin{document}

\title{Supporting Information for: Interfacial Thermal Conductance of Thiolate-Protected
  Gold Nanospheres}
\author{Kelsey M. Stocker}
\author{Suzanne M. Neidhart}
\author{J. Daniel Gezelter}
\email{gezelter@nd.edu}
\affiliation{Department of Chemistry and Biochemistry, University of
  Notre Dame, Notre Dame, IN 46556}
\date{\today}

\begin{abstract}
  This document supplies force field parameters for the united-atom
  sites, bond, bend, and torsion parameters, as well as the cross
  interactions between the united-atom sites and the gold atoms. These
  parameters were used in the simulations presented in the main text.
\end{abstract}


\maketitle

Gold -- gold interactions were described by the quantum Sutton-Chen
(QSC) model.\cite{Qi:1999ph} The hexane solvent is described by the
TraPPE united atom model,\cite{TraPPE-UA.alkanes} where sites are
located at the carbon centers for alkyl groups. Bonding interactions
were used for intra-molecular sites closer than 3 bonds. Effective
Lennard-Jones potentials were used for non-bonded interactions.

\begin{table}[h]
\bibpunct{}{}{,}{n}{}{,}
\centering
\caption{Non-bonded interaction parameters (including cross interactions with Au atoms). \label{tab:atypes}}
\begin{tabular}{ c|cccccl }
 \toprule
Site & mass & $\sigma_{ii}$ & $\epsilon_{ii}$ & $\sigma_{\ce{Au}-i}$ & $\epsilon_{\ce{Au}-i}$  & source \\
     & (amu)& (\AA)        & (kcal/mol)     & (\AA)             &  (kcal/mol)          &  \\
 \colrule
 \ce{CH3}    & 15.04    & 3.75  & 0.1947 & 3.54   & 0.2146 & Refs. \protect\cite{TraPPE-UA.alkanes}, \protect\cite{vlugt:cpc2007154} and \protect\cite{landman:1998}\\
 \ce{CH2}    & 14.03    & 3.95  & 0.09141& 3.54   & 0.1749 & Refs. \protect\cite{TraPPE-UA.alkanes}, \protect\cite{vlugt:cpc2007154} and \protect\cite{landman:1998}\\
 CHene       & 13.02    & 3.73  & 0.09340& 3.4625 & 0.1680 & Refs. \protect\cite{TraPPE-UA.alkylbenzenes}, \protect\cite{vlugt:cpc2007154} and \protect\cite{landman:1998}\\
 S           & 32.0655  & 4.45  & 0.2504 & 2.40   & 8.465  & Refs. \protect\cite{landman:1998} ($\sigma$) and \protect\cite{vlugt:cpc2007154} ($\epsilon$) \\
 CHar        & 13.02    & 3.695 & 0.1004 & 3.4625 & 0.1680 & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{vlugt:cpc2007154}\\
 \ce{CH2ar}  & 14.03    & 3.695 & 0.1004 & 3.4625 & 0.1680 & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{vlugt:cpc2007154}\\
 \botrule
\end{tabular}
\bibpunct{[}{]}{,}{n}{,}{,}
\end{table}

The TraPPE-UA force field includes parameters for thiol
molecules\cite{TraPPE-UA.thiols} which were used for the
alkanethiolate molecules in our simulations.  To derive suitable
parameters for butanethiolate adsorbed on Au(111) surfaces, we adopted
the S parameters from Luedtke and Landman\cite{landman:1998} and
modified the parameters for the CTS atom to maintain charge neutrality
in the molecule.

Bonds are typically rigid in TraPPE-UA, so although we used
equilibrium bond distances from TraPPE-UA, for flexible bonds, we
adapted bond stretching spring constants from the OPLS-AA force
field.\cite{Jorgensen:1996sf}

\begin{table}[h]
\bibpunct{}{}{,}{n}{}{,}
\centering
\caption{Bond parameters. \label{tab:bond}}
\begin{tabular}{ cc|ccl }
 \toprule
 $i$&$j$ & $r_0$ & $k_\mathrm{bond}$ & source \\
    &    & (\AA) & $(\mathrm{~kcal/mole/\AA}^2)$ & \\
 \colrule
\ce{CH3}   & \ce{CH3} & 1.540   & 536  & Refs. \protect\cite{TraPPE-UA.alkanes} and \protect\cite{Jorgensen:1996sf}\\
\ce{CH3}   & \ce{CH2} & 1.540   & 536  & Refs. \protect\cite{TraPPE-UA.alkanes} and \protect\cite{Jorgensen:1996sf} \\
\ce{CH2}   & \ce{CH2} & 1.540   & 536  & Refs. \protect\cite{TraPPE-UA.alkanes} and \protect\cite{Jorgensen:1996sf} \\
CHene      & CHene    & 1.330   & 1098 & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{Jorgensen:1996sf}\\
\ce{CH3}   & CHene    & 1.540   & 634  & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{Jorgensen:1996sf} \\
\ce{CH2}   & CHene    & 1.540   & 634  & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{Jorgensen:1996sf} \\
S          & \ce{CH2} & 1.820   & 444  & Refs. \protect\cite{TraPPE-UA.thiols} and \protect\cite{Jorgensen:1996sf} \\
CHar       & CHar     & 1.40    & 938  & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{Jorgensen:1996sf} \\
CHar       & \ce{CH2} & 1.540   & 536  & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{Jorgensen:1996sf}\\
CHar       & \ce{CH3} & 1.540   & 536  & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{Jorgensen:1996sf}\\
\ce{CH2ar} & CHar     & 1.40    & 938  & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{Jorgensen:1996sf} \\
S          & CHar     & 1.80384 & 527.951 & This Work \\
 \botrule
\end{tabular}
\bibpunct{[}{]}{,}{n}{,}{,}
\end{table}

To describe the interactions between metal (Au) and non-metal atoms,
potential energy terms were adapted from an adsorption study of alkyl
thiols on gold surfaces by Vlugt, \textit{et
  al.}\cite{vlugt:cpc2007154} They fit an effective pair-wise
Lennard-Jones form of potential parameters for the interaction between
Au and pseudo-atoms CH$_x$ and S based on a well-established and
widely-used effective potential of Hautman and Klein for the Au(111)
surface.\cite{hautman:4994}

Parameters not found in the TraPPE-UA force field for the
intramolecular interactions of the conjugated and the penultimate
alkenethiolate ligands were calculated using constrained geometry
scans using the B3LYP functional~\cite{Becke:1993kq,Lee:1988qf} and
the 6-31G(d,p) basis set. Structures were scanned starting at the
minimum energy gas phase structure for small ($C_4$) ligands.  Only
one degree of freedom was constrained for any given scan -- all other
atoms were allowed to minimize subject to that constraint.  The
resulting potential energy surfaces were fit to a harmonic potential
for the bond stretching,
\begin{equation}
V_\mathrm{bond} = \frac{k_\mathrm{bond}}{2} \left( r - r_0 \right)^2,
\end{equation}
and angle bending potentials,
\begin{equation}
V_\mathrm{bend} = \frac{k_\mathrm{bend}}{2} \left(\theta - \theta_0\right)^2.
\end{equation}
Torsional potentials were fit to the TraPPE torsional function,
\begin{equation}
V_\mathrm{tor} = c_0 + c_1  \left(1 + \cos\phi \right) + c_2  \left(1 - \cos 2\phi \right) + c_3  \left(1 + \cos 3 \phi \right).
\end{equation}

For the penultimate thiolate ligands, the model molecule used was
2-Butene-1-thiol, for which one bend angle (\ce{S-CH2-CHene}) was
scanned to fit an equilibrium angle and force constant, as well as one
torsion (\ce{S-CH2-CHene-CHene}).  The parameters for these two
potentials also served as model for the longer conjugated thiolate
ligands which require bend angle parameters for (\ce{S-CH2-CHar}) and
torsion parameters for (\ce{S-CH2-CHar-CHar}).

For the $C_4$ conjugated thiolate ligands, the model molecule for the
quantum mechanical calculations was 1,3-Butadiene-1-thiol.  This
ligand required fitting one bond (\ce{S-CHar}), and one bend angle
(\ce{S-CHar-CHar}).

The geometries of the model molecules were optimized prior to
performing the constrained angle scans, and the fit values for the
bond, bend, and torsional parameters were in relatively good agreement
with similar parameters already present in TraPPE.


\begin{table}[h]
\bibpunct{}{}{,}{n}{,}{,}
\centering
\caption{Bend angle parameters. The central atom in the bend is atom $j$.\label{tab:bend}}
\begin{tabular}{ ccc|ccl }
\toprule
 $i$&$j$&$k$ & $\theta_0$ & $k_\mathrm{bend}$ & source\\
    &   &    & ($\degree$) & (kcal/mol/rad\textsuperscript{2}) & \\
 \colrule
\ce{CH2} & \ce{CH2} & S         & 114.0   &   124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ 
\ce{CH3} & \ce{CH2} & \ce{CH2}  & 114.0   &   124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ 
\ce{CH2} & \ce{CH2} & \ce{CH2}  & 114.0   &   124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ 
CHene    & CHene    & \ce{CH3}  & 119.7   &   139.94& Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ 
CHene    & CHene    & \ce{CH2}  & 119.7   &   139.94& Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ 
\ce{CH2} & \ce{CH2} & CHene     & 114.0   &   124.20& Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ 
CHar     & CHar     & CHar      & 120.0   &   126.0 & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{Jorgensen:1996sf}\\ 
CHar     & CHar     & \ce{CH2}  & 120.0   &   140.0 & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{Jorgensen:1996sf}\\
CHar     & CHar     & \ce{CH3}  & 120.0   &   140.0 & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{Jorgensen:1996sf}\\
CHar     & CHar     & \ce{CH2ar}& 120.0   &   126.0 & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{Jorgensen:1996sf}\\
S        & \ce{CH2} & CHene     & 109.97  &  127.37 & This work  \\
S        & \ce{CH2} & CHar      & 109.97  &  127.37 & This work  \\
S        & CHar     & CHar      & 123.911 & 138.093 & This work  \\
 \botrule
\end{tabular}
\bibpunct{[}{]}{,}{n}{,}{,}
\end{table}

\begin{table}[h]
\bibpunct{}{}{,}{n}{,}{,}
\centering
\caption{Torsion parameters. The central atoms for each torsion are atoms $j$ and $k$,
  and wildcard atom types are denoted by ``X''.  All $c_n$ parameters
  have units of kcal/mol. The torsions around carbon-carbon double bonds
  are harmonic and assume a trans (180$\degree$) geometry.  The force
  constant for this torsion is given in $\mathrm{kcal~mol~}^{-1}\mathrm{degrees}^{-2}$.  \label{tab:torsion}}
\begin{tabular}{ cccc|ccccl }
\toprule
 $i$&$j$&$k$&$l$& $c_0$&$c_1$& $c_2$ & $c_3$ & source\\
 \colrule
\ce{CH3} & \ce{CH2} & \ce{CH2} & \ce{CH2} & 0.0     & 0.7055   & -0.13551 &  1.5725    & Ref. \protect\cite{TraPPE-UA.alkanes}\\
\ce{CH2} & \ce{CH2} & \ce{CH2} & \ce{CH2} & 0.0     & 0.7055   & -0.13551 &  1.5725    & Ref. \protect\cite{TraPPE-UA.alkanes}\\
\ce{CH2} & \ce{CH2} & \ce{CH2} & S        & 0.0     & 0.7055   & -0.13551 &  1.5725    & Ref. \protect\cite{TraPPE-UA.thiols}\\ \colrule
X        & CHene    & CHene    & X        & \multicolumn{4}{c}{\multirow{2}{*}{$V = \frac{0.008112}{2} (\phi - 180.0)^2$}} & \multirow{2}{*}{Ref. \protect\cite{TraPPE-UA.alkylbenzenes}} \\
X        & CHar     & CHar     & X        &         & & & & \\ \colrule
\ce{CH2} & \ce{CH2} & CHene    & CHene    & 1.368   & 0.1716   & -0.2181  &  -0.56081  & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\
\ce{CH2} & \ce{CH2} & \ce{CH2} & CHene    & 0.0     & 0.7055   & -0.13551 &   1.5725   & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\
CHene    & CHene    & \ce{CH2} & S        & 3.20753 & 0.207417 & -0.912929&  -0.958538 & This work \\
CHar     & CHar     & \ce{CH2} & S        & 3.20753 & 0.207417 & -0.912929&  -0.958538 & This work \\
 \botrule
\end{tabular}
\bibpunct{[}{]}{,}{n}{,}{,}
\end{table}

\newpage
\bibliographystyle{aip}
\bibliography{NPthiols}
\end{document}
Revision:	4388
Committed:	Wed Oct 28 17:17:56 2015 UTC (9 years, 10 months ago) by gezelter
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#	User	Rev	Content
1	gezelter	4387	\documentclass[aps,jcp,preprint,showpacs,superscriptaddress,groupedaddress]{revtex4-1}
2	skucera	4375	\usepackage{graphicx} % needed for figures
3			\usepackage{dcolumn} % needed for some tables
4			\usepackage{bm} % for math
5			\usepackage{amssymb} % for math
6	gezelter	4384	\usepackage{booktabs}
7	skucera	4375	\usepackage[english]{babel}
8			\usepackage{multirow}
9			\usepackage{times}
10			\usepackage[version=3]{mhchem}
11			\usepackage{lineno}
12			\usepackage{gensymb}
13	gezelter	4376	\usepackage{multirow}
14	skucera	4375
15			\begin{document}
16
17			\title{Supporting Information for: Interfacial Thermal Conductance of Thiolate-Protected
18			Gold Nanospheres}
19			\author{Kelsey M. Stocker}
20			\author{Suzanne M. Neidhart}
21			\author{J. Daniel Gezelter}
22			\email{gezelter@nd.edu}
23			\affiliation{Department of Chemistry and Biochemistry, University of
24			Notre Dame, Notre Dame, IN 46556}
25	gezelter	4384	\date{\today}
26	skucera	4375
27	gezelter	4384	\begin{abstract}
28			This document supplies force field parameters for the united-atom
29			sites, bond, bend, and torsion parameters, as well as the cross
30			interactions between the united-atom sites and the gold atoms. These
31			parameters were used in the simulations presented in the main text.
32			\end{abstract}
33
34
35	skucera	4375	\maketitle
36	gezelter	4384
37	gezelter	4379	Gold -- gold interactions were described by the quantum Sutton-Chen
38			(QSC) model.\cite{Qi:1999ph} The hexane solvent is described by the
39			TraPPE united atom model,\cite{TraPPE-UA.alkanes} where sites are
40			located at the carbon centers for alkyl groups. Bonding interactions
41			were used for intra-molecular sites closer than 3 bonds. Effective
42			Lennard-Jones potentials were used for non-bonded interactions.
43
44	gezelter	4381	\begin{table}[h]
45	gezelter	4384	\bibpunct{}{}{,}{n}{}{,}
46	gezelter	4381	\centering
47	gezelter	4387	\caption{Non-bonded interaction parameters (including cross interactions with Au atoms). \label{tab:atypes}}
48	gezelter	4388	\begin{tabular}{ c\|cccccl }
49	gezelter	4381	\toprule
50	gezelter	4387	Site & mass & $\sigma_{ii}$ & $\epsilon_{ii}$ & $\sigma_{\ce{Au}-i}$ & $\epsilon_{\ce{Au}-i}$ & source \\
51			& (amu)& (\AA) & (kcal/mol) & (\AA) & (kcal/mol) & \\
52	gezelter	4381	\colrule
53	gezelter	4388	\ce{CH3} & 15.04 & 3.75 & 0.1947 & 3.54 & 0.2146 & Refs. \protect\cite{TraPPE-UA.alkanes}, \protect\cite{vlugt:cpc2007154} and \protect\cite{landman:1998}\\
54			\ce{CH2} & 14.03 & 3.95 & 0.09141& 3.54 & 0.1749 & Refs. \protect\cite{TraPPE-UA.alkanes}, \protect\cite{vlugt:cpc2007154} and \protect\cite{landman:1998}\\
55			CHene & 13.02 & 3.73 & 0.09340& 3.4625 & 0.1680 & Refs. \protect\cite{TraPPE-UA.alkylbenzenes}, \protect\cite{vlugt:cpc2007154} and \protect\cite{landman:1998}\\
56	gezelter	4387	S & 32.0655 & 4.45 & 0.2504 & 2.40 & 8.465 & Refs. \protect\cite{landman:1998} ($\sigma$) and \protect\cite{vlugt:cpc2007154} ($\epsilon$) \\
57			CHar & 13.02 & 3.695 & 0.1004 & 3.4625 & 0.1680 & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{vlugt:cpc2007154}\\
58	gezelter	4388	\ce{CH2ar} & 14.03 & 3.695 & 0.1004 & 3.4625 & 0.1680 & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{vlugt:cpc2007154}\\
59	gezelter	4381	\botrule
60			\end{tabular}
61	gezelter	4384	\bibpunct{[}{]}{,}{n}{,}{,}
62	gezelter	4381	\end{table}
63
64	gezelter	4379	The TraPPE-UA force field includes parameters for thiol
65			molecules\cite{TraPPE-UA.thiols} which were used for the
66			alkanethiolate molecules in our simulations. To derive suitable
67			parameters for butanethiolate adsorbed on Au(111) surfaces, we adopted
68			the S parameters from Luedtke and Landman\cite{landman:1998} and
69			modified the parameters for the CTS atom to maintain charge neutrality
70			in the molecule.
71
72	gezelter	4383	Bonds are typically rigid in TraPPE-UA, so although we used
73			equilibrium bond distances from TraPPE-UA, for flexible bonds, we
74			adapted bond stretching spring constants from the OPLS-AA force
75			field.\cite{Jorgensen:1996sf}
76	gezelter	4381
77			\begin{table}[h]
78	gezelter	4384	\bibpunct{}{}{,}{n}{}{,}
79	gezelter	4381	\centering
80			\caption{Bond parameters. \label{tab:bond}}
81	gezelter	4388	\begin{tabular}{ cc\|ccl }
82	gezelter	4381	\toprule
83	gezelter	4388	$i$&$j$ & $r_0$ & $k_\mathrm{bond}$ & source \\
84			& & (\AA) & $(\mathrm{~kcal/mole/\AA}^2)$ & \\
85	gezelter	4381	\colrule
86	gezelter	4388	\ce{CH3} & \ce{CH3} & 1.540 & 536 & Refs. \protect\cite{TraPPE-UA.alkanes} and \protect\cite{Jorgensen:1996sf}\\
87			\ce{CH3} & \ce{CH2} & 1.540 & 536 & Refs. \protect\cite{TraPPE-UA.alkanes} and \protect\cite{Jorgensen:1996sf} \\
88			\ce{CH2} & \ce{CH2} & 1.540 & 536 & Refs. \protect\cite{TraPPE-UA.alkanes} and \protect\cite{Jorgensen:1996sf} \\
89			CHene & CHene & 1.330 & 1098 & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{Jorgensen:1996sf}\\
90			\ce{CH3} & CHene & 1.540 & 634 & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{Jorgensen:1996sf} \\
91			\ce{CH2} & CHene & 1.540 & 634 & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{Jorgensen:1996sf} \\
92			S & \ce{CH2} & 1.820 & 444 & Refs. \protect\cite{TraPPE-UA.thiols} and \protect\cite{Jorgensen:1996sf} \\
93			CHar & CHar & 1.40 & 938 & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{Jorgensen:1996sf} \\
94			CHar & \ce{CH2} & 1.540 & 536 & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{Jorgensen:1996sf}\\
95			CHar & \ce{CH3} & 1.540 & 536 & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{Jorgensen:1996sf}\\
96			\ce{CH2ar} & CHar & 1.40 & 938 & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{Jorgensen:1996sf} \\
97			S & CHar & 1.80384 & 527.951 & This Work \\
98	gezelter	4381	\botrule
99			\end{tabular}
100	gezelter	4384	\bibpunct{[}{]}{,}{n}{,}{,}
101	gezelter	4381	\end{table}
102
103	gezelter	4379	To describe the interactions between metal (Au) and non-metal atoms,
104			potential energy terms were adapted from an adsorption study of alkyl
105			thiols on gold surfaces by Vlugt, \textit{et
106			al.}\cite{vlugt:cpc2007154} They fit an effective pair-wise
107			Lennard-Jones form of potential parameters for the interaction between
108			Au and pseudo-atoms CH$_x$ and S based on a well-established and
109			widely-used effective potential of Hautman and Klein for the Au(111)
110			surface.\cite{hautman:4994}
111
112			Parameters not found in the TraPPE-UA force field for the
113			intramolecular interactions of the conjugated and the penultimate
114			alkenethiolate ligands were calculated using constrained geometry
115			scans using the B3LYP functional~\cite{Becke:1993kq,Lee:1988qf} and
116			the 6-31G(d,p) basis set. Structures were scanned starting at the
117			minimum energy gas phase structure for small ($C_4$) ligands. Only
118			one degree of freedom was constrained for any given scan -- all other
119			atoms were allowed to minimize subject to that constraint. The
120			resulting potential energy surfaces were fit to a harmonic potential
121			for the bond stretching,
122			\begin{equation}
123			V_\mathrm{bond} = \frac{k_\mathrm{bond}}{2} \left( r - r_0 \right)^2,
124			\end{equation}
125			and angle bending potentials,
126			\begin{equation}
127			V_\mathrm{bend} = \frac{k_\mathrm{bend}}{2} \left(\theta - \theta_0\right)^2.
128			\end{equation}
129			Torsional potentials were fit to the TraPPE torsional function,
130			\begin{equation}
131			V_\mathrm{tor} = c_0 + c_1 \left(1 + \cos\phi \right) + c_2 \left(1 - \cos 2\phi \right) + c_3 \left(1 + \cos 3 \phi \right).
132			\end{equation}
133	skucera	4375
134	gezelter	4381	For the penultimate thiolate ligands, the model molecule used was
135			2-Butene-1-thiol, for which one bend angle (\ce{S-CH2-CHene}) was
136			scanned to fit an equilibrium angle and force constant, as well as one
137			torsion (\ce{S-CH2-CHene-CHene}). The parameters for these two
138			potentials also served as model for the longer conjugated thiolate
139			ligands which require bend angle parameters for (\ce{S-CH2-CHar}) and
140			torsion parameters for (\ce{S-CH2-CHar-CHar}).
141	gezelter	4379
142	gezelter	4381	For the $C_4$ conjugated thiolate ligands, the model molecule for the
143			quantum mechanical calculations was 1,3-Butadiene-1-thiol. This
144			ligand required fitting one bond (\ce{S-CHar}), and one bend angle
145			(\ce{S-CHar-CHar}).
146	gezelter	4379
147	gezelter	4381	The geometries of the model molecules were optimized prior to
148			performing the constrained angle scans, and the fit values for the
149			bond, bend, and torsional parameters were in relatively good agreement
150			with similar parameters already present in TraPPE.
151	gezelter	4379
152
153			\begin{table}[h]
154	gezelter	4384	\bibpunct{}{}{,}{n}{,}{,}
155	gezelter	4379	\centering
156			\caption{Bend angle parameters. The central atom in the bend is atom $j$.\label{tab:bend}}
157	gezelter	4388	\begin{tabular}{ ccc\|ccl }
158	gezelter	4379	\toprule
159	gezelter	4388	$i$&$j$&$k$ & $\theta_0$ & $k_\mathrm{bend}$ & source\\
160			& & & ($\degree$) & (kcal/mol/rad\textsuperscript{2}) & \\
161	gezelter	4379	\colrule
162	gezelter	4388	\ce{CH2} & \ce{CH2} & S & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\
163			\ce{CH3} & \ce{CH2} & \ce{CH2} & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\
164			\ce{CH2} & \ce{CH2} & \ce{CH2} & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\
165			CHene & CHene & \ce{CH3} & 119.7 & 139.94& Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\
166			CHene & CHene & \ce{CH2} & 119.7 & 139.94& Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\
167			\ce{CH2} & \ce{CH2} & CHene & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\
168			CHar & CHar & CHar & 120.0 & 126.0 & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{Jorgensen:1996sf}\\
169			CHar & CHar & \ce{CH2} & 120.0 & 140.0 & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{Jorgensen:1996sf}\\
170			CHar & CHar & \ce{CH3} & 120.0 & 140.0 & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{Jorgensen:1996sf}\\
171			CHar & CHar & \ce{CH2ar}& 120.0 & 126.0 & Refs. \protect\cite{TraPPE-UA.alkylbenzenes} and \protect\cite{Jorgensen:1996sf}\\
172			S & \ce{CH2} & CHene & 109.97 & 127.37 & This work \\
173			S & \ce{CH2} & CHar & 109.97 & 127.37 & This work \\
174			S & CHar & CHar & 123.911 & 138.093 & This work \\
175	gezelter	4379	\botrule
176	skucera	4375	\end{tabular}
177	gezelter	4384	\bibpunct{[}{]}{,}{n}{,}{,}
178	gezelter	4379	\end{table}
179
180			\begin{table}[h]
181	gezelter	4384	\bibpunct{}{}{,}{n}{,}{,}
182	gezelter	4379	\centering
183	gezelter	4381	\caption{Torsion parameters. The central atoms for each torsion are atoms $j$ and $k$,
184			and wildcard atom types are denoted by ``X''. All $c_n$ parameters
185	gezelter	4383	have units of kcal/mol. The torsions around carbon-carbon double bonds
186	gezelter	4381	are harmonic and assume a trans (180$\degree$) geometry. The force
187			constant for this torsion is given in $\mathrm{kcal~mol~}^{-1}\mathrm{degrees}^{-2}$. \label{tab:torsion}}
188	gezelter	4388	\begin{tabular}{ cccc\|ccccl }
189	gezelter	4379	\toprule
190			$i$&$j$&$k$&$l$& $c_0$&$c_1$& $c_2$ & $c_3$ & source\\
191			\colrule
192	gezelter	4388	\ce{CH3} & \ce{CH2} & \ce{CH2} & \ce{CH2} & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkanes}\\
193			\ce{CH2} & \ce{CH2} & \ce{CH2} & \ce{CH2} & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkanes}\\
194			\ce{CH2} & \ce{CH2} & \ce{CH2} & S & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.thiols}\\ \colrule
195			X & CHene & CHene & X & \multicolumn{4}{c}{\multirow{2}{}{$V = \frac{0.008112}{2} (\phi - 180.0)^2$}} & \multirow{2}{}{Ref. \protect\cite{TraPPE-UA.alkylbenzenes}} \\
196			X & CHar & CHar & X & & & & & \\ \colrule
197			\ce{CH2} & \ce{CH2} & CHene & CHene & 1.368 & 0.1716 & -0.2181 & -0.56081 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\
198			\ce{CH2} & \ce{CH2} & \ce{CH2} & CHene & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\
199			CHene & CHene & \ce{CH2} & S & 3.20753 & 0.207417 & -0.912929& -0.958538 & This work \\
200			CHar & CHar & \ce{CH2} & S & 3.20753 & 0.207417 & -0.912929& -0.958538 & This work \\
201	gezelter	4379	\botrule
202	skucera	4375	\end{tabular}
203	gezelter	4384	\bibpunct{[}{]}{,}{n}{,}{,}
204	gezelter	4379	\end{table}
205	skucera	4378
206	gezelter	4376	\newpage
207			\bibliographystyle{aip}
208			\bibliography{NPthiols}
209	skucera	4375	\end{document}