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\begin{document} |
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\title{Supporting Information for: Interfacial Thermal Conductance of Thiolate-Protected |
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Gold Nanospheres} |
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\author{Kelsey M. Stocker} |
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\author{Suzanne M. Neidhart} |
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\author{J. Daniel Gezelter} |
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\email{gezelter@nd.edu} |
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\affiliation{Department of Chemistry and Biochemistry, University of |
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Notre Dame, Notre Dame, IN 46556} |
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|
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\maketitle |
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\vfill |
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\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 \(V_{tor} = c0 + c1 * [1 + \cos(\phi)] + c2 * [1 - \cos(2\phi)] + c3 * [1 + \cos(3\phi)]\). |
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|
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\begin{tabular}{ |cc|cc|l| } |
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\hline |
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\multicolumn{5}{|c|}{Bond Parameters} \\ |
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\hline |
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$i$&$j$ & $\theta_0 (\degree)$ & $k (\mathrm{kcal/mole/rad}^2)$ & source\\ |
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\hline |
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CH3 & CH3 & 1.540 & 536 & \\ |
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CH3 & CH2 & 1.540 & 536 & \\ |
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CH3 & CH & 1.540 & 536 & \\ |
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CH2 & CH2 & 1.540 & 536 & \\ |
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CH2 & CH & 1.540 & 536 & \\ |
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CH & CH & 1.540 & 536 & \\ |
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Chene & CHene & 1.330 & 1098 & \\ |
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CH2ene & CHene & 1.330 & 1098 & \\ |
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CH3 & CHene & 1.540 & 634 & \\ |
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CH2 & CHene & 1.540 & 634 & \\ |
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S & CH2 & 1.820 & 444 & \\ |
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CHar & CHar & 1.40 & 938 & \\ |
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CHar & CH2 & 1.540 & 536 & \\ |
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CHar & CH3 & 1.540 & 536 & \\ |
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CH2ar & CHar & 1.40 & 938 & \\ |
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S & CHar & 1.80384 & 527.951 & fit \\ |
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\hline |
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\end{tabular} |
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|
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Most |
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parameters are taken from references \bibpunct{}{}{,}{n}{}{,} |
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\protect\cite{TraPPE-UA.alkanes} and |
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\protect\cite{TraPPE-UA.thiols}. Cross-interactions with the Au |
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atoms were adapted from references |
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\protect\cite{landman:1998},~\protect\cite{vlugt:cpc2007154},~and |
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\protect\cite{hautman:4994}. |
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|
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|
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\begin{tabular}{ |ccc|cc|l| } |
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\hline |
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\multicolumn{6}{|c|}{Bend Parameters (central atom is atom $j$)} \\ |
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\hline |
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$i$&$j$&$k$ & $\theta_0 (\degree)$ & $k (\mathrm{kcal/mole/rad}^2)$ & source\\ |
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\hline |
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CH2 & CH2 & S & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
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CH3 & CH2 & S & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
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CH3 & CH2 & CH3 & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
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CH3 & CH2 & CH2 & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
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CH2 & CH2 & CH2 & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
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CH3 & CH2 & CH & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
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CHene & CHene & CH3 & 119.7 & 139.94& Ref. \protect\cite{Maerzke:2009qy}\\ |
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CHene & CHene & CHene & 119.7 & 139.94& Ref. \protect\cite{Maerzke:2009qy}\\ |
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CH2ene & CHene & CH3 & 119.7 & 139.94& Ref. \protect\cite{Maerzke:2009qy}\\ |
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CHene & CHene & CH2 & 119.7 & 139.94& Ref. \protect\cite{Maerzke:2009qy}\\ |
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CH2 & CH2 & CHene & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
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CHar & CHar & CHar & 120.0 & 126.0 & Refs. \protect\cite{Maerzke:2009qy} and \\ |
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CHar & CHar & CH2 & 120.0 & 140.0 & Refs. \protect\cite{Maerzke:2009qy} and \\ |
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CHar & CHar & CH3 & 120.0 & 140.0 & Refs. \protect\cite{Maerzke:2009qy} and \\ |
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CHar & CHar & CH2ar & 120.0 & 126.0 & Refs. \protect\cite{Maerzke:2009qy} and \\ |
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S & CH2 & CHene & 109.97 & 127.37 & fit \\ |
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S & CH2 & CHar & 109.97 & 127.37 & fit \\ |
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S & CHar & CHar & 123.911 & 138.093 & fit \\ |
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\hline |
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\end{tabular} |
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\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. |
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\begin{tabular}{ |cccc|cccc|l| } |
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\hline |
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\multicolumn{9}{|c|}{Torsion Parameters (central atoms are atoms $j$ and $k$)} \\ |
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\hline |
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$i$&$j$&$k$&$l$& c0&c1& c2 & c3 & source\\ |
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\hline |
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CH3 & CH2 & CH2 & CH3 & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
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CH3 & CH2 & CH2 & CH2 & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
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CH3 & CH2 & CH2 & CH & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
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CH2 & CH2 & CH2 & CH2 & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
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CH2 & CH2 & CH2 & S & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
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CH3 & CH2 & CH2 & S & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ \hline |
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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}} \\ |
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X & CHar & CHar & X & & & & & \\ \hline |
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CH2 & CH2 & CHene & CHene & 1.368 & 0.1716 & -0.2181 & -0.56081 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
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CH2 & CH2 & CH2 & CHene & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
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CHene & CHene & CH2 & S & 3.20753 & 0.207417& -0.912929& -0.958538 & fit \\ |
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CHar & CHar & CH2 & S & 3.20753 & 0.207417& -0.912929& -0.958538 & fit \\ |
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\hline |
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\end{tabular} |
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\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. |
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\newpage |
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\bibliographystyle{aip} |
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\bibliography{NPthiols} |
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\end{document} |
