25 |
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Notre Dame, Notre Dame, IN 46556} |
26 |
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|
27 |
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\maketitle |
28 |
– |
\vfill |
29 |
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|
28 |
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Gold -- gold interactions were described by the quantum Sutton-Chen |
29 |
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(QSC) model.\cite{Qi:1999ph} The hexane solvent is described by the |
30 |
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TraPPE united atom model,\cite{TraPPE-UA.alkanes} where sites are |
32 |
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were used for intra-molecular sites closer than 3 bonds. Effective |
33 |
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Lennard-Jones potentials were used for non-bonded interactions. |
34 |
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|
35 |
+ |
\begin{table}[h] |
36 |
+ |
\centering |
37 |
+ |
\caption{Properties of the United atom sites. \label{tab:atypes}} |
38 |
+ |
\begin{tabular}{ c|cccc } |
39 |
+ |
\toprule |
40 |
+ |
atom type & mass (amu)& $\epsilon$ (kcal/mol) & $\sigma$ (\AA) & source \\ |
41 |
+ |
\colrule |
42 |
+ |
\ce{CH3} & 15.04 & 0.1947 & 3.75 & \\ |
43 |
+ |
\ce{CH2} & 14.03 & 0.09141 & 3.95 & \\ |
44 |
+ |
\ce{CH} & 13.02 & 0.01987 & 4.68 & \\ |
45 |
+ |
\ce{CHene} & 13.02 & 0.09340 & 3.73 & \\ |
46 |
+ |
\ce{CH2ene} & 14.03 & 0.16891 & 3.675 & \\ |
47 |
+ |
S & 32.0655 & 0.2504 & 4.45 & Refs. \protect\cite{landman:1998} ($\sigma$) and \protect\cite{vlugt:cpc2007154} ($\epsilon$) \\ |
48 |
+ |
\ce{CHar} & 13.02 & 0.1004 & 3.695 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
49 |
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\ce{CH2ar} & 14.03 & 0.1004 & 3.695 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
50 |
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\botrule |
51 |
+ |
\end{tabular} |
52 |
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\end{table} |
53 |
+ |
|
54 |
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The TraPPE-UA force field includes parameters for thiol |
55 |
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molecules\cite{TraPPE-UA.thiols} which were used for the |
56 |
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alkanethiolate molecules in our simulations. To derive suitable |
59 |
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modified the parameters for the CTS atom to maintain charge neutrality |
60 |
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in the molecule. |
61 |
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|
62 |
< |
To describe the interactions between metal (Au) and non-metal atoms, |
63 |
< |
potential energy terms were adapted from an adsorption study of alkyl |
47 |
< |
thiols on gold surfaces by Vlugt, \textit{et |
48 |
< |
al.}\cite{vlugt:cpc2007154} They fit an effective pair-wise |
49 |
< |
Lennard-Jones form of potential parameters for the interaction between |
50 |
< |
Au and pseudo-atoms CH$_x$ and S based on a well-established and |
51 |
< |
widely-used effective potential of Hautman and Klein for the Au(111) |
52 |
< |
surface.\cite{hautman:4994} |
62 |
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Bonds are typically rigid in TraPPE-UA, and for flexible bonds, we |
63 |
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utilized bond stretching spring constants from |
64 |
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|
65 |
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\begin{table}[h] |
66 |
|
\centering |
67 |
< |
\caption{Properties of the United atom sites. \label{tab:atypes}} |
68 |
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\begin{tabular}{ c|cccc } |
67 |
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\caption{Bond parameters. \label{tab:bond}} |
68 |
> |
\begin{tabular}{ cc|lll } |
69 |
|
\toprule |
70 |
< |
atom type & mass (amu)& $\epsilon$ (kcal/mol) & $\sigma$ (\AA) & source \\ |
70 |
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$i$&$j$ & $r_0$ (\AA) & $k (\mathrm{~kcal/mole/\AA}^2)$ & source\\ |
71 |
|
\colrule |
72 |
< |
CH3 & 15.04 & 0.1947 & 3.75 & \\ |
73 |
< |
CH2 & 14.03 & 0.09141 & 3.95 & \\ |
74 |
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CH & 13.02 & 0.01987 & 4.68 & \\ |
75 |
< |
CHene & 13.02 & 0.09340 & 3.73 & \\ |
76 |
< |
CH2ene & 14.03 & 0.16891 & 3.675 & \\ |
77 |
< |
S & 32.0655 & 0.2504 & 4.45 & Refs. \protect\cite{landman:1998} ($\sigma$) and \protect\cite{vlugt:cpc2007154} ($\epsilon$) \\ |
78 |
< |
CHar & 13.02 & 0.1004 & 3.695 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
79 |
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CH2ar & 14.03 & 0.1004 & 3.695 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
72 |
> |
\ce{CH3} & \ce{CH3} & 1.540 & 536 & \\ |
73 |
> |
\ce{CH3} & \ce{CH2} & 1.540 & 536 & \\ |
74 |
> |
\ce{CH3} & \ce{CH} & 1.540 & 536 & \\ |
75 |
> |
\ce{CH2} & \ce{CH2} & 1.540 & 536 & \\ |
76 |
> |
\ce{CH2} & \ce{CH} & 1.540 & 536 & \\ |
77 |
> |
\ce{CH} & \ce{CH} & 1.540 & 536 & \\ |
78 |
> |
\ce{CHene} & \ce{CHene} & 1.330 & 1098 & \\ |
79 |
> |
\ce{CH2ene} & \ce{CHene} & 1.330 & 1098 & \\ |
80 |
> |
\ce{CH3} & \ce{CHene} & 1.540 & 634 & \\ |
81 |
> |
\ce{CH2} & \ce{CHene} & 1.540 & 634 & \\ |
82 |
> |
S & \ce{CH2} & 1.820 & 444 & \\ |
83 |
> |
\ce{CHar} & \ce{CHar} & 1.40 & 938 & \\ |
84 |
> |
\ce{CHar} & \ce{CH2} & 1.540 & 536 & \\ |
85 |
> |
\ce{CHar} & \ce{CH3} & 1.540 & 536 & \\ |
86 |
> |
\ce{CH2ar} & \ce{CHar} & 1.40 & 938 & |
87 |
> |
\protect\cite{William-L.-Jorgensen:1996uq} \\ |
88 |
> |
S & \ce{CHar} & 1.80384 & 527.951 & fit \\ |
89 |
|
\botrule |
90 |
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\end{tabular} |
91 |
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\end{table} |
92 |
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|
93 |
+ |
|
94 |
+ |
To describe the interactions between metal (Au) and non-metal atoms, |
95 |
+ |
potential energy terms were adapted from an adsorption study of alkyl |
96 |
+ |
thiols on gold surfaces by Vlugt, \textit{et |
97 |
+ |
al.}\cite{vlugt:cpc2007154} They fit an effective pair-wise |
98 |
+ |
Lennard-Jones form of potential parameters for the interaction between |
99 |
+ |
Au and pseudo-atoms CH$_x$ and S based on a well-established and |
100 |
+ |
widely-used effective potential of Hautman and Klein for the Au(111) |
101 |
+ |
surface.\cite{hautman:4994} |
102 |
+ |
|
103 |
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Parameters not found in the TraPPE-UA force field for the |
104 |
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intramolecular interactions of the conjugated and the penultimate |
105 |
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alkenethiolate ligands were calculated using constrained geometry |
122 |
|
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). |
123 |
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\end{equation} |
124 |
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|
125 |
< |
Say something here about which molecules were used for which scans.... I did the butadiene. I am not sure what molecule was used for the penultimate calculations, that was done when I first came to ND. |
126 |
< |
Butadienethiolate was used for the shortest conjugated thiolate ligand. The molecule was made in Avogardo and a geometry optimization was performed before the scans of the bond, bend, and torsion were calculated. |
125 |
> |
For the penultimate thiolate ligands, the model molecule used was |
126 |
> |
2-Butene-1-thiol, for which one bend angle (\ce{S-CH2-CHene}) was |
127 |
> |
scanned to fit an equilibrium angle and force constant, as well as one |
128 |
> |
torsion (\ce{S-CH2-CHene-CHene}). The parameters for these two |
129 |
> |
potentials also served as model for the longer conjugated thiolate |
130 |
> |
ligands which require bend angle parameters for (\ce{S-CH2-CHar}) and |
131 |
> |
torsion parameters for (\ce{S-CH2-CHar-CHar}). |
132 |
|
|
133 |
< |
The fit values for the bond, bend, and torsional parameters were in |
134 |
< |
relatively good agreement with similar parameters already present in |
135 |
< |
TraPPE. |
133 |
> |
For the $C_4$ conjugated thiolate ligands, the model molecule for the |
134 |
> |
quantum mechanical calculations was 1,3-Butadiene-1-thiol. This |
135 |
> |
ligand required fitting one bond (\ce{S-CHar}), and one bend angle |
136 |
> |
(\ce{S-CHar-CHar}). |
137 |
|
|
138 |
+ |
The geometries of the model molecules were optimized prior to |
139 |
+ |
performing the constrained angle scans, and the fit values for the |
140 |
+ |
bond, bend, and torsional parameters were in relatively good agreement |
141 |
+ |
with similar parameters already present in TraPPE. |
142 |
|
|
103 |
– |
to find an equilibrium bend angles $\theta_0$ and spring constants, |
104 |
– |
$k$. Torsional parameters were fit to the same part of the |
105 |
– |
penultimate ligand (\(S - CH_{2}- CH-CH)\) |
106 |
– |
for the rotation around the \( CH_{2}- CH\) |
107 |
– |
bond. This potential energy surface was then fit to |
143 |
|
|
144 |
|
\begin{table}[h] |
145 |
|
\centering |
111 |
– |
\caption{Bond parameters. \label{tab:bond}} |
112 |
– |
\begin{tabular}{ cc|lll } |
113 |
– |
\toprule |
114 |
– |
$i$&$j$ & $r_0$ (\AA) & $k (\mathrm{~kcal/mole/\AA}^2)$ & source\\ |
115 |
– |
\colrule |
116 |
– |
CH3 & CH3 & 1.540 & 536 & \\ |
117 |
– |
CH3 & CH2 & 1.540 & 536 & \\ |
118 |
– |
CH3 & CH & 1.540 & 536 & \\ |
119 |
– |
CH2 & CH2 & 1.540 & 536 & \\ |
120 |
– |
CH2 & CH & 1.540 & 536 & \\ |
121 |
– |
CH & CH & 1.540 & 536 & \\ |
122 |
– |
Chene & CHene & 1.330 & 1098 & \\ |
123 |
– |
CH2ene & CHene & 1.330 & 1098 & \\ |
124 |
– |
CH3 & CHene & 1.540 & 634 & \\ |
125 |
– |
CH2 & CHene & 1.540 & 634 & \\ |
126 |
– |
S & CH2 & 1.820 & 444 & \\ |
127 |
– |
CHar & CHar & 1.40 & 938 & \\ |
128 |
– |
CHar & CH2 & 1.540 & 536 & \\ |
129 |
– |
CHar & CH3 & 1.540 & 536 & \\ |
130 |
– |
CH2ar & CHar & 1.40 & 938 & \\ |
131 |
– |
S & CHar & 1.80384 & 527.951 & fit \\ |
132 |
– |
\botrule |
133 |
– |
\end{tabular} |
134 |
– |
\end{table} |
135 |
– |
|
136 |
– |
\begin{table}[h] |
137 |
– |
\centering |
146 |
|
\caption{Bend angle parameters. The central atom in the bend is atom $j$.\label{tab:bend}} |
147 |
|
\begin{tabular}{ ccc|lll } |
148 |
|
\toprule |
149 |
|
$i$&$j$&$k$ & $\theta_0 (\degree)$ & $k (\mathrm{kcal/mole/rad}^2)$ & source\\ |
150 |
|
\colrule |
151 |
< |
CH2 & CH2 & S & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
152 |
< |
CH3 & CH2 & S & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
153 |
< |
CH3 & CH2 & CH3 & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
154 |
< |
CH3 & CH2 & CH2 & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
155 |
< |
CH2 & CH2 & CH2 & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
156 |
< |
CH3 & CH2 & CH & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
157 |
< |
CHene & CHene & CH3 & 119.7 & 139.94& Ref. \protect\cite{Maerzke:2009qy}\\ |
158 |
< |
CHene & CHene & CHene & 119.7 & 139.94& Ref. \protect\cite{Maerzke:2009qy}\\ |
159 |
< |
CH2ene & CHene & CH3 & 119.7 & 139.94& Ref. \protect\cite{Maerzke:2009qy}\\ |
160 |
< |
CHene & CHene & CH2 & 119.7 & 139.94& Ref. \protect\cite{Maerzke:2009qy}\\ |
161 |
< |
CH2 & CH2 & CHene & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
162 |
< |
CHar & CHar & CHar & 120.0 & 126.0 & Refs. \protect\cite{Maerzke:2009qy} and \\ |
163 |
< |
CHar & CHar & CH2 & 120.0 & 140.0 & Refs. \protect\cite{Maerzke:2009qy} and \\ |
164 |
< |
CHar & CHar & CH3 & 120.0 & 140.0 & Refs. \protect\cite{Maerzke:2009qy} and \\ |
165 |
< |
CHar & CHar & CH2ar & 120.0 & 126.0 & Refs. \protect\cite{Maerzke:2009qy} and \\ |
166 |
< |
S & CH2 & CHene & 109.97 & 127.37 & fit \\ |
167 |
< |
S & CH2 & CHar & 109.97 & 127.37 & fit \\ |
168 |
< |
S & CHar & CHar & 123.911 & 138.093 & fit \\ |
151 |
> |
\ce{CH2} & \ce{CH2} & S & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
152 |
> |
\ce{CH3} & \ce{CH2} & S & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
153 |
> |
\ce{CH3} & \ce{CH2} & \ce{CH3} & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
154 |
> |
\ce{CH3} & \ce{CH2} & \ce{CH2} & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
155 |
> |
\ce{CH2} & \ce{CH2} & \ce{CH2} & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
156 |
> |
\ce{CH3} & \ce{CH2} & \ce{CH} & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
157 |
> |
\ce{CHene} & \ce{CHene} & \ce{CH3} & 119.7 & 139.94& Ref. \protect\cite{Maerzke:2009qy}\\ |
158 |
> |
\ce{CHene} & \ce{CHene} & \ce{CHene} & 119.7 & 139.94& Ref. \protect\cite{Maerzke:2009qy}\\ |
159 |
> |
\ce{CH2ene} & \ce{CHene} & \ce{CH3} & 119.7 & 139.94& Ref. \protect\cite{Maerzke:2009qy}\\ |
160 |
> |
\ce{CHene} & \ce{CHene} & \ce{CH2} & 119.7 & 139.94& Ref. \protect\cite{Maerzke:2009qy}\\ |
161 |
> |
\ce{CH2} & \ce{CH2} & \ce{CHene} & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
162 |
> |
\ce{CHar} & \ce{CHar} & \ce{CHar} & 120.0 & 126.0 & Refs. \protect\cite{Maerzke:2009qy} and \\ |
163 |
> |
\ce{CHar} & \ce{CHar} & \ce{CH2} & 120.0 & 140.0 & Refs. \protect\cite{Maerzke:2009qy} and \\ |
164 |
> |
\ce{CHar} & \ce{CHar} & \ce{CH3} & 120.0 & 140.0 & Refs. \protect\cite{Maerzke:2009qy} and \\ |
165 |
> |
\ce{CHar} & \ce{CHar} & \ce{CH2ar} & 120.0 & 126.0 & Refs. \protect\cite{Maerzke:2009qy} and \\ |
166 |
> |
S & \ce{CH2} & \ce{CHene} & 109.97 & 127.37 & fit \\ |
167 |
> |
S & \ce{CH2} & \ce{CHar} & 109.97 & 127.37 & fit \\ |
168 |
> |
S & \ce{CHar} & \ce{CHar} & 123.911 & 138.093 & fit \\ |
169 |
|
\botrule |
170 |
|
\end{tabular} |
171 |
|
\end{table} |
172 |
|
|
165 |
– |
The conjugated system was fit to a bond, bend, and torsion. The |
166 |
– |
terminal bond for the shortest conjugated ligand \(CH-CH_2\) |
167 |
– |
was fit to a potential energy surface to find an equilibrium bond |
168 |
– |
length of 1.4 \AA and a spring constant of 938 kcal/mol using the |
169 |
– |
Harmonic Model: \(V_{bond} = \frac{k}{2} (b - b_0)^2\). |
170 |
– |
A bend parameter for the beginning the longer conjugated ligands |
171 |
– |
(\(S - CH_2- CH)\), |
172 |
– |
was approximated to be equal to the shortest penultimate ligand |
173 |
– |
parameters found. For the shortest conjugated ligand the first bend |
174 |
– |
(\(S - CH- CH)\) |
175 |
– |
was fit a potential energy surface in the same manor as the |
176 |
– |
penultimate bend. The torsion for the first four atoms of the two |
177 |
– |
longer conjugated systems is equal to the torsion calculated for the |
178 |
– |
penultimate system. |
179 |
– |
|
173 |
|
\begin{table}[h] |
174 |
|
\centering |
175 |
< |
\caption{Torsion parameters. The central atoms are atoms $j$ and $k$, and wildcard atom types are denoted by ``X''. All $c_n$ parameters have units of kcal/mol. \label{tab:torsion}} |
175 |
> |
\caption{Torsion parameters. The central atoms for each torsion are atoms $j$ and $k$, |
176 |
> |
and wildcard atom types are denoted by ``X''. All $c_n$ parameters |
177 |
> |
have units of kcal/mol. The torsions around doubly-bonded carbons |
178 |
> |
are harmonic and assume a trans (180$\degree$) geometry. The force |
179 |
> |
constant for this torsion is given in $\mathrm{kcal~mol~}^{-1}\mathrm{degrees}^{-2}$. \label{tab:torsion}} |
180 |
|
\begin{tabular}{ cccc|lllll } |
181 |
|
\toprule |
182 |
|
$i$&$j$&$k$&$l$& $c_0$&$c_1$& $c_2$ & $c_3$ & source\\ |
183 |
|
\colrule |
184 |
< |
CH3 & CH2 & CH2 & CH3 & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
185 |
< |
CH3 & CH2 & CH2 & CH2 & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
186 |
< |
CH3 & CH2 & CH2 & CH & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
187 |
< |
CH2 & CH2 & CH2 & CH2 & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
188 |
< |
CH2 & CH2 & CH2 & S & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
189 |
< |
CH3 & CH2 & CH2 & S & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ \colrule |
190 |
< |
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}} \\ |
191 |
< |
X & CHar & CHar & X & & & & & \\ \colrule |
192 |
< |
CH2 & CH2 & CHene & CHene & 1.368 & 0.1716 & -0.2181 & -0.56081 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
193 |
< |
CH2 & CH2 & CH2 & CHene & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
194 |
< |
CHene & CHene & CH2 & S & 3.20753 & 0.207417& -0.912929& -0.958538 & fit \\ |
195 |
< |
CHar & CHar & CH2 & S & 3.20753 & 0.207417& -0.912929& -0.958538 & fit \\ |
184 |
> |
\ce{CH3} & \ce{CH2} & \ce{CH2} & \ce{CH3} & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
185 |
> |
\ce{CH3} & \ce{CH2} & \ce{CH2} & \ce{CH2} & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
186 |
> |
\ce{CH3} & \ce{CH2} & \ce{CH2} & \ce{CH} & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
187 |
> |
\ce{CH2} & \ce{CH2} & \ce{CH2} & \ce{CH2} & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
188 |
> |
\ce{CH2} & \ce{CH2} & \ce{CH2} & S & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
189 |
> |
\ce{CH3} & \ce{CH2} & \ce{CH2} & S & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ \colrule |
190 |
> |
X & \ce{CHene} & \ce{CHene} & X & \multicolumn{4}{c}{\multirow{2}{*}{$V = \frac{0.008112}{2} (\phi - 180.0)^2$}} & \multirow{2}{*}{Ref. \protect\cite{TraPPE-UA.alkylbenzenes}} \\ |
191 |
> |
X & \ce{CHar} & \ce{CHar} & X & & & & & \\ \colrule |
192 |
> |
\ce{CH2} & \ce{CH2} & \ce{CHene} & \ce{CHene} & 1.368 & 0.1716 & -0.2181 & -0.56081 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
193 |
> |
\ce{CH2} & \ce{CH2} & \ce{CH2} & \ce{CHene} & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
194 |
> |
\ce{CHene} & \ce{CHene} & \ce{CH2} & S & 3.20753 & 0.207417& -0.912929& -0.958538 & fit \\ |
195 |
> |
\ce{CHar} & \ce{CHar} & \ce{CH2} & S & 3.20753 & 0.207417& -0.912929& -0.958538 & fit \\ |
196 |
|
\botrule |
197 |
|
\end{tabular} |
198 |
|
\end{table} |
199 |
|
|
203 |
– |
The conjugated system was fit to a bond, bend, and torsion. The |
204 |
– |
terminal bond for the shortest conjugated ligand \(CH-CH_2\) |
205 |
– |
was fit to a potential energy surface to find an equilibrium bond |
206 |
– |
length of 1.4 \AA and a spring constant of 938 kcal/mol using the |
207 |
– |
Harmonic Model: \(V_{bond} = \frac{k}{2} (b - b_0)^2\). |
208 |
– |
A bend parameter for the beginning the longer conjugated ligands |
209 |
– |
(\(S - CH_2- CH)\), |
210 |
– |
was approximated to be equal to the shortest penultimate ligand |
211 |
– |
parameters found. For the shortest conjugated ligand the first bend |
212 |
– |
(\(S - CH- CH)\) |
213 |
– |
was fit a potential energy surface in the same manor as the |
214 |
– |
penultimate bend. The torsion for the first four atoms of the two |
215 |
– |
longer conjugated systems is equal to the torsion calculated for the |
216 |
– |
penultimate system. |
217 |
– |
|
200 |
|
\begin{table}[h] |
201 |
|
\centering |
202 |
|
\caption{Non-bonded cross interaction parameters between gold atoms and the united atom sites\label{tab:nb}} |
204 |
|
\toprule |
205 |
|
$i$&$j$ & $\sigma$ (\AA)& $\epsilon$ $(kcal/mol)$ & source \\ |
206 |
|
\colrule |
207 |
< |
Au &CH3 &3.54 &0.2146& Ref. \protect\cite{vlugt:cpc2007154}\\ |
208 |
< |
Au &CH2 &3.54 &0.1749& Ref. \protect\cite{vlugt:cpc2007154}\\ |
209 |
< |
Au &CHene &3.4625 &0.1680& Ref. \protect\cite{vlugt:cpc2007154}\\ |
210 |
< |
Au &CHar &3.4625 &0.1680& Ref. \protect\cite{vlugt:cpc2007154}\\ |
211 |
< |
Au &CH2ar &3.4625 &0.1680& Ref. \protect\cite{vlugt:cpc2007154}\\ |
207 |
> |
Au &\ce{CH3} &3.54 &0.2146& Ref. \protect\cite{vlugt:cpc2007154}\\ |
208 |
> |
Au &\ce{CH2} &3.54 &0.1749& Ref. \protect\cite{vlugt:cpc2007154}\\ |
209 |
> |
Au &\ce{CHene} &3.4625 &0.1680& Ref. \protect\cite{vlugt:cpc2007154}\\ |
210 |
> |
Au &\ce{CHar} &3.4625 &0.1680& Ref. \protect\cite{vlugt:cpc2007154}\\ |
211 |
> |
Au &\ce{CH2ar} &3.4625 &0.1680& Ref. \protect\cite{vlugt:cpc2007154}\\ |
212 |
|
Au &S &2.40 &8.465& Ref. \protect\cite{vlugt:cpc2007154}\\ |
213 |
|
\botrule |
214 |
|
\end {tabular} |