trunk/NPthiols/Sup_Info.tex

\documentclass[aps,jcp,preprint,showpacs,superscriptaddress,groupedaddress]{revtex4}  % for double-spaced preprint
\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{tablefootnote}
\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}

\maketitle
\vfill
\par Parameters not found in the TraPPE-UA force field for the intramolecular interactions of the conjugated and the penultimate alkenethiolate ligands were calculated using a potential energy surface scan at the B3LYP, 6-31G(d,p) level. Then all potential energy surfaces were fit to a Harmonic potential. A bend parameter for the beginning of the shortest penultimate thiolate ligand (\(S - CH_{2}- CH)\)was calculated by fitting \(V_{bend} = \frac{k}{2} (\theta - \theta_0)^2\) to the potential energy surface. To find an equilibrium bend angle at 109.97\degree and a spring constant of 127.37 \(kcal/mol/rad^2\). A torsional parameter was fit to the same part of the penultimate ligand (\(S - CH_{2}- CH-CH)\) for the rotation around the \( CH_{2}- CH\) bond. This potential energy surface was then fit to \(V_{tor} = c0 + c1 * [1 + \cos(\phi)] + c2 * [1 - \cos(2\phi)] + c3 * [1 + \cos(3\phi)]\).

\begin{tabular}{ |cc|cc|l| }
 \hline
 \multicolumn{5}{|c|}{Bond Parameters} \\
 \hline
 $i$&$j$ & $\theta_0 (\degree)$ & $k (\mathrm{kcal/mole/rad}^2)$ & source\\
 \hline
CH3     &    CH3  &             1.540   &       536             &  \\
CH3     &    CH2  &             1.540   &       536             &  \\
CH3      &    CH  &             1.540    &      536      &         \\
CH2     &    CH2  &             1.540   &       536             &  \\
CH2      &    CH  &             1.540    &      536      &         \\
CH       &    CH  &             1.540    &      536      &         \\
Chene    &  CHene &             1.330    &       1098    &         \\
CH2ene   &  CHene &             1.330    &       1098    &         \\
CH3      &  CHene &             1.540    &        634    &         \\
CH2      &  CHene &             1.540    &        634    &         \\
S        &    CH2 &             1.820    &        444    &         \\
CHar     &   CHar &             1.40     &        938    & \\
CHar     &   CH2  &             1.540    &        536    & \\
CHar     &   CH3  &             1.540    &        536    & \\
CH2ar    &   CHar &             1.40     &        938    & \\
S       &   CHar  &             1.80384  &      527.951         & fit \\
 \hline
\end{tabular}

 Most
    parameters are taken from references \bibpunct{}{}{,}{n}{}{,}
    \protect\cite{TraPPE-UA.alkanes} and
    \protect\cite{TraPPE-UA.thiols}. Cross-interactions with the Au
    atoms were adapted from references
    \protect\cite{landman:1998},~\protect\cite{vlugt:cpc2007154},~and
    \protect\cite{hautman:4994}.


\begin{tabular}{ |ccc|cc|l| }
 \hline
 \multicolumn{6}{|c|}{Bend Parameters (central atom is atom $j$)} \\
 \hline
 $i$&$j$&$k$ & $\theta_0 (\degree)$ & $k (\mathrm{kcal/mole/rad}^2)$ & source\\
 \hline
CH2    &  CH2    &  S      &         114.0  &   124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ 
CH3    &  CH2    &  S      &         114.0  &   124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ 
CH3    &  CH2    &  CH3    &         114.0  &   124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ 
CH3    &  CH2    &  CH2    &         114.0  &   124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ 
CH2    &  CH2    &  CH2    &         114.0  &   124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ 
CH3    &  CH2    &  CH     &         114.0  &   124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ 
CHene  &  CHene  &  CH3    &         119.7  &   139.94& Ref. \protect\cite{Maerzke:2009qy}\\ 
CHene  &  CHene  &  CHene  &         119.7  &   139.94& Ref. \protect\cite{Maerzke:2009qy}\\ 
CH2ene &  CHene  &  CH3    &         119.7  &   139.94& Ref. \protect\cite{Maerzke:2009qy}\\ 
CHene  &  CHene  &  CH2    &         119.7  &   139.94& Ref. \protect\cite{Maerzke:2009qy}\\ 
CH2    &  CH2    &  CHene  &         114.0  &   124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ 
CHar   &  CHar   &  CHar   &         120.0  &   126.0 & Refs. \protect\cite{Maerzke:2009qy} and \\ 
CHar   &  CHar   &  CH2    &         120.0  &   140.0 & Refs. \protect\cite{Maerzke:2009qy} and \\
CHar   &  CHar   &  CH3    &         120.0  &   140.0 & Refs. \protect\cite{Maerzke:2009qy} and \\
CHar   &  CHar   &  CH2ar  &         120.0  &   126.0 & Refs. \protect\cite{Maerzke:2009qy} and \\
S      &  CH2    &  CHene  &         109.97  &  127.37 & fit  \\
S      &  CH2    &  CHar   &         109.97  &  127.37 & fit  \\
S      &  CHar   &  CHar   &         123.911 & 138.093 & fit  \\
 \hline
\end{tabular}
\par The conjugated system was fit to a bond, bend, and torsion. The terminal bond for the shortest conjugated ligand \(CH-CH_2\) was fit to a potential energy surface to find an equilibrium bond length of 1.4 \AA and a spring constant of 938 kcal/mol using the Harmonic Model: \(V_{bond} = \frac{k}{2} (b - b_0)^2\). A bend parameter for the beginning the longer conjugated ligands (\(S - CH_2- CH)\), was approximated to be equal to the shortest penultimate ligand parameters found. For the shortest conjugated ligand the first bend (\(S - CH- CH)\) was fit a potential energy surface in the same manor as the penultimate bend. The torsion for the first four atoms of the two longer conjugated systems is equal to the torsion calculated for the penultimate system. 
\begin{tabular}{ |cccc|cccc|l| }
 \hline
 \multicolumn{9}{|c|}{Torsion Parameters (central atoms are atoms $j$ and $k$)} \\
 \hline
 $i$&$j$&$k$&$l$& c0&c1& c2 & c3 & source\\
 \hline
CH3   &   CH2   &  CH2    &  CH3     &     0.0     &     0.7055   & -0.13551  &  1.5725    & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\
CH3   &   CH2   &  CH2    &  CH2     &     0.0     &     0.7055   & -0.13551  &  1.5725    & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\
CH3   &   CH2   &  CH2    &  CH      &     0.0     &     0.7055   & -0.13551  &  1.5725    & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\
CH2   &   CH2   &  CH2    &  CH2     &     0.0     &     0.7055   & -0.13551  &  1.5725    & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\
CH2   &   CH2   &  CH2    &  S       &     0.0     &     0.7055   & -0.13551  &  1.5725    & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\
CH3   &   CH2   &  CH2    &  S       &     0.0     &     0.7055   & -0.13551  &  1.5725    & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ \hline
X     &   CHene &   CHene &  X       &     \multicolumn{4}{|c|}{\multirow{2}{*}{$V = 0.008112 (\phi - 180.0)^2$}} & \multirow{2}{*}{Ref. \protect\cite{TraPPE-UA.alkylbenzenes}} \\
X     &   CHar  &   CHar  &  X       &   & & & & \\ \hline
CH2   &   CH2   &   CHene &  CHene   &     1.368   &      0.1716  &  -0.2181  &  -0.56081  & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\
CH2   &   CH2   &   CH2   &  CHene   &     0.0     &      0.7055  &  -0.13551 &   1.5725   & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\
CHene &   CHene &   CH2   &   S      &     3.20753 &      0.207417&  -0.912929&  -0.958538 & fit \\
CHar  &   CHar  &   CH2   &   S      &     3.20753 &      0.207417&  -0.912929&  -0.958538 & fit \\
 \hline
\end{tabular}
\par The conjugated system was fit to a bond, bend, and torsion. The terminal bond for the shortest conjugated ligand \(CH-CH_2\) was fit to a potential energy surface to find an equilibrium bond length of 1.4 \AA and a spring constant of 938 kcal/mol using the Harmonic Model: \(V_{bond} = \frac{k}{2} (b - b_0)^2\). A bend parameter for the beginning the longer conjugated ligands (\(S - CH_2- CH)\), was approximated to be equal to the shortest penultimate ligand parameters found. For the shortest conjugated ligand the first bend (\(S - CH- CH)\) was fit a potential energy surface in the same manor as the penultimate bend. The torsion for the first four atoms of the two longer conjugated systems is equal to the torsion calculated for the penultimate system.  
\newpage
\bibliographystyle{aip}
\bibliography{NPthiols}

\end{document}
Revision:	4376
Committed:	Mon Oct 26 19:00:52 2015 UTC (8 years, 8 months ago) by gezelter
Content type:	application/x-tex
File size:	8422 byte(s)
Log Message:	Supporting infoZ
#	User	Rev	Content
1	skucera	4375	\documentclass[aps,jcp,preprint,showpacs,superscriptaddress,groupedaddress]{revtex4} % for double-spaced preprint
2			\usepackage{graphicx} % needed for figures
3			\usepackage{dcolumn} % needed for some tables
4			\usepackage{bm} % for math
5			\usepackage{amssymb} % for math
6			%\usepackage{booktabs}
7			\usepackage[english]{babel}
8			\usepackage{multirow}
9			\usepackage{tablefootnote}
10			\usepackage{times}
11			\usepackage[version=3]{mhchem}
12			\usepackage{lineno}
13			\usepackage{gensymb}
14	gezelter	4376	\usepackage{multirow}
15	skucera	4375
16			\begin{document}
17
18			\title{Supporting Information for: Interfacial Thermal Conductance of Thiolate-Protected
19			Gold Nanospheres}
20			\author{Kelsey M. Stocker}
21			\author{Suzanne M. Neidhart}
22			\author{J. Daniel Gezelter}
23			\email{gezelter@nd.edu}
24			\affiliation{Department of Chemistry and Biochemistry, University of
25			Notre Dame, Notre Dame, IN 46556}
26
27			\maketitle
28			\vfill
29			\par Parameters not found in the TraPPE-UA force field for the intramolecular interactions of the conjugated and the penultimate alkenethiolate ligands were calculated using a potential energy surface scan at the B3LYP, 6-31G(d,p) level. Then all potential energy surfaces were fit to a Harmonic potential. A bend parameter for the beginning of the shortest penultimate thiolate ligand (\(S - CH_{2}- CH)\)was calculated by fitting \(V_{bend} = \frac{k}{2} (\theta - \theta_0)^2\) to the potential energy surface. To find an equilibrium bend angle at 109.97\degree and a spring constant of 127.37 \(kcal/mol/rad^2\). A torsional parameter was fit to the same part of the penultimate ligand (\(S - CH_{2}- CH-CH)\) for the rotation around the \( CH_{2}- CH\) bond. This potential energy surface was then fit to \(V_{tor} = c0 + c1 * [1 + \cos(\phi)] + c2 * [1 - \cos(2\phi)] + c3 * [1 + \cos(3\phi)]\).
30
31	gezelter	4376	\begin{tabular}{ \|cc\|cc\|l\| }
32	skucera	4375	\hline
33	gezelter	4376	\multicolumn{5}{\|c\|}{Bond Parameters} \\
34	skucera	4375	\hline
35	gezelter	4376	$i$&$j$ & $\theta_0 (\degree)$ & $k (\mathrm{kcal/mole/rad}^2)$ & source\\
36	skucera	4375	\hline
37	gezelter	4376	CH3 & CH3 & 1.540 & 536 & \\
38			CH3 & CH2 & 1.540 & 536 & \\
39			CH3 & CH & 1.540 & 536 & \\
40			CH2 & CH2 & 1.540 & 536 & \\
41			CH2 & CH & 1.540 & 536 & \\
42			CH & CH & 1.540 & 536 & \\
43			Chene & CHene & 1.330 & 1098 & \\
44			CH2ene & CHene & 1.330 & 1098 & \\
45			CH3 & CHene & 1.540 & 634 & \\
46			CH2 & CHene & 1.540 & 634 & \\
47			S & CH2 & 1.820 & 444 & \\
48			CHar & CHar & 1.40 & 938 & \\
49			CHar & CH2 & 1.540 & 536 & \\
50			CHar & CH3 & 1.540 & 536 & \\
51			CH2ar & CHar & 1.40 & 938 & \\
52			S & CHar & 1.80384 & 527.951 & fit \\
53	skucera	4375	\hline
54			\end{tabular}
55
56	gezelter	4376	Most
57			parameters are taken from references \bibpunct{}{}{,}{n}{}{,}
58			\protect\cite{TraPPE-UA.alkanes} and
59			\protect\cite{TraPPE-UA.thiols}. Cross-interactions with the Au
60			atoms were adapted from references
61			\protect\cite{landman:1998},~\protect\cite{vlugt:cpc2007154},~and
62			\protect\cite{hautman:4994}.
63
64
65			\begin{tabular}{ \|ccc\|cc\|l\| }
66	skucera	4375	\hline
67	gezelter	4376	\multicolumn{6}{\|c\|}{Bend Parameters (central atom is atom $j$)} \\
68	skucera	4375	\hline
69	gezelter	4376	$i$&$j$&$k$ & $\theta_0 (\degree)$ & $k (\mathrm{kcal/mole/rad}^2)$ & source\\
70	skucera	4375	\hline
71	gezelter	4376	CH2 & CH2 & S & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\
72			CH3 & CH2 & S & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\
73			CH3 & CH2 & CH3 & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\
74			CH3 & CH2 & CH2 & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\
75			CH2 & CH2 & CH2 & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\
76			CH3 & CH2 & CH & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\
77			CHene & CHene & CH3 & 119.7 & 139.94& Ref. \protect\cite{Maerzke:2009qy}\\
78			CHene & CHene & CHene & 119.7 & 139.94& Ref. \protect\cite{Maerzke:2009qy}\\
79			CH2ene & CHene & CH3 & 119.7 & 139.94& Ref. \protect\cite{Maerzke:2009qy}\\
80			CHene & CHene & CH2 & 119.7 & 139.94& Ref. \protect\cite{Maerzke:2009qy}\\
81			CH2 & CH2 & CHene & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\
82			CHar & CHar & CHar & 120.0 & 126.0 & Refs. \protect\cite{Maerzke:2009qy} and \\
83			CHar & CHar & CH2 & 120.0 & 140.0 & Refs. \protect\cite{Maerzke:2009qy} and \\
84			CHar & CHar & CH3 & 120.0 & 140.0 & Refs. \protect\cite{Maerzke:2009qy} and \\
85			CHar & CHar & CH2ar & 120.0 & 126.0 & Refs. \protect\cite{Maerzke:2009qy} and \\
86			S & CH2 & CHene & 109.97 & 127.37 & fit \\
87			S & CH2 & CHar & 109.97 & 127.37 & fit \\
88			S & CHar & CHar & 123.911 & 138.093 & fit \\
89	skucera	4375	\hline
90			\end{tabular}
91			\par The conjugated system was fit to a bond, bend, and torsion. The terminal bond for the shortest conjugated ligand \(CH-CH_2\) was fit to a potential energy surface to find an equilibrium bond length of 1.4 \AA and a spring constant of 938 kcal/mol using the Harmonic Model: \(V_{bond} = \frac{k}{2} (b - b_0)^2\). A bend parameter for the beginning the longer conjugated ligands (\(S - CH_2- CH)\), was approximated to be equal to the shortest penultimate ligand parameters found. For the shortest conjugated ligand the first bend (\(S - CH- CH)\) was fit a potential energy surface in the same manor as the penultimate bend. The torsion for the first four atoms of the two longer conjugated systems is equal to the torsion calculated for the penultimate system.
92	gezelter	4376	\begin{tabular}{ \|cccc\|cccc\|l\| }
93	skucera	4375	\hline
94	gezelter	4376	\multicolumn{9}{\|c\|}{Torsion Parameters (central atoms are atoms $j$ and $k$)} \\
95	skucera	4375	\hline
96	gezelter	4376	$i$&$j$&$k$&$l$& c0&c1& c2 & c3 & source\\
97	skucera	4375	\hline
98	gezelter	4376	CH3 & CH2 & CH2 & CH3 & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\
99			CH3 & CH2 & CH2 & CH2 & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\
100			CH3 & CH2 & CH2 & CH & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\
101			CH2 & CH2 & CH2 & CH2 & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\
102			CH2 & CH2 & CH2 & S & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\
103			CH3 & CH2 & CH2 & S & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ \hline
104			X & CHene & CHene & X & \multicolumn{4}{\|c\|}{\multirow{2}{}{$V = 0.008112 (\phi - 180.0)^2$}} & \multirow{2}{}{Ref. \protect\cite{TraPPE-UA.alkylbenzenes}} \\
105			X & CHar & CHar & X & & & & & \\ \hline
106			CH2 & CH2 & CHene & CHene & 1.368 & 0.1716 & -0.2181 & -0.56081 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\
107			CH2 & CH2 & CH2 & CHene & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\
108			CHene & CHene & CH2 & S & 3.20753 & 0.207417& -0.912929& -0.958538 & fit \\
109			CHar & CHar & CH2 & S & 3.20753 & 0.207417& -0.912929& -0.958538 & fit \\
110	skucera	4375	\hline
111			\end{tabular}
112			\par The conjugated system was fit to a bond, bend, and torsion. The terminal bond for the shortest conjugated ligand \(CH-CH_2\) was fit to a potential energy surface to find an equilibrium bond length of 1.4 \AA and a spring constant of 938 kcal/mol using the Harmonic Model: \(V_{bond} = \frac{k}{2} (b - b_0)^2\). A bend parameter for the beginning the longer conjugated ligands (\(S - CH_2- CH)\), was approximated to be equal to the shortest penultimate ligand parameters found. For the shortest conjugated ligand the first bend (\(S - CH- CH)\) was fit a potential energy surface in the same manor as the penultimate bend. The torsion for the first four atoms of the two longer conjugated systems is equal to the torsion calculated for the penultimate system.
113	gezelter	4376	\newpage
114			\bibliographystyle{aip}
115			\bibliography{NPthiols}
116
117	skucera	4375	\end{document}