| 856 |
|
by: |
| 857 |
|
\begin{equation} |
| 858 |
|
C_{l}(t) = \langle P_l[\hat{\mathbf{u}}_j(0)\cdot\hat{\mathbf{u}}_j(t)]\rangle, |
| 859 |
+ |
\label{eq:reorientCorr} |
| 860 |
|
\end{equation} |
| 861 |
|
where $P_l$ are Legendre polynomials of order $l$ and |
| 862 |
|
$\hat{\mathbf{u}}_j$ is the unit vector pointing along the molecular |
| 951 |
|
the visual contours in the figure. This highlights the qualitative |
| 952 |
|
nature of contour plotting. |
| 953 |
|
|
| 954 |
< |
\section{Tetrahedrally Restructured Elongated Dipole (TRED) Water Model} |
| 954 |
> |
\section{Tetrahedrally Restructured Elongated Dipole (TRED) Water Model}\label{sec:tredWater} |
| 955 |
|
|
| 956 |
|
The SSD/RF model works well with damped electrostatics, but because of |
| 957 |
|
its point multipole character, there is no charge neutralization |
| 1017 |
|
to the tenths place. We also unified the sticky parameters for the |
| 1018 |
|
switching functions on the repulsive and attractive interactions in |
| 1019 |
|
the interest of simplicity, and we left the quadrupole moment elements |
| 1020 |
< |
and $\omega^\circ$ unaltered. Finally, the strength of the sticky |
| 1020 |
> |
and $\omega^\circ$ unaltered. It should be noted that additional logic |
| 1021 |
> |
needs to be included into the electrostatic code when using TRED to |
| 1022 |
> |
insure that the charges of each water do not interact with the other |
| 1023 |
> |
water's quadrupole moment. Finally, the strength of the sticky |
| 1024 |
|
interaction ($v_0$) was modified to improve the shape of the first |
| 1025 |
|
peaks in $g_\textrm{OO}(r)$ and $g_\textrm{OH}(r)$, while the $\sigma$ |
| 1026 |
|
and $\epsilon$ values were varied to adjust the location of the first |
| 1083 |
|
\ref{fig:tredGofR}), $n_C$ and $n_H$ counts increase because of the |
| 1084 |
|
further first minimum distance locations. This results in the |
| 1085 |
|
integration extending over a larger water volume. If we integrate to |
| 1086 |
< |
the first minimum value of the experimental $g_\textrm{OO}(r)$ (3.42 |
| 1087 |
< |
\AA ) in both the SSD/RF and TRED plots, the $n_C$ values for both are |
| 1088 |
< |
much closer to experiment (4.7 for SSD/RF and 4.9 for TRED). |
| 1086 |
> |
the first minimum value of the experimental $g_\textrm{OO}(r)$ |
| 1087 |
> |
(3.42~\AA ) in both the SSD/RF and TRED plots, the $n_C$ values for |
| 1088 |
> |
both are much closer to experiment (4.7 for SSD/RF and 4.9 for TRED). |
| 1089 |
|
|
| 1090 |
|
\begin{figure} |
| 1091 |
|
\centering |
| 1101 |
|
bottom of table \ref{tab:tredProperties}. The static dielectric |
| 1102 |
|
constant results for SSD/RF and TRED are identical within error. This |
| 1103 |
|
is not surprising given the similar dipole moment, similar sticky |
| 1104 |
< |
interaction strength, and identical applied damping constant. Comparing the static dielectric constant contour map (figure \ref{fig:tredDielectric}) with the dielectric map for SSD/RF |
| 1104 |
> |
interaction strength, and identical applied damping |
| 1105 |
> |
constant. Comparing the static dielectric constant contour map (figure |
| 1106 |
> |
\ref{fig:tredDielectric}) with the dielectric map for SSD/RF (figure |
| 1107 |
> |
\ref{fig:dielectricMap}D) highlights the similarities in how these |
| 1108 |
> |
models respond to dielectric damping and how the dipolar and monopolar |
| 1109 |
> |
electrostatic damping act in an equivalent fashion. Both these |
| 1110 |
> |
dielectric maps span a larger range than the 3, 4, and 5 point-charge |
| 1111 |
> |
water models; however, the SSD/RF range is greater than TRED, |
| 1112 |
> |
indicating that multipoles are a little more sensitive to damping than |
| 1113 |
> |
monopoles. |
| 1114 |
|
|
| 1115 |
+ |
The final dielectric comparison comes through the Debye relaxation |
| 1116 |
+ |
time ($\tau_D$) or the collective dipolar relaxation time when |
| 1117 |
+ |
assuming a Debye treatment for the dielectric |
| 1118 |
+ |
relaxation.\cite{Chandra99,Kindt96} This value is calculated through |
| 1119 |
+ |
equation (\ref{eq:reorientCorr}) applied to the total system dipole |
| 1120 |
+ |
moment. The values for both of the models are a slower than the |
| 1121 |
+ |
experimental relaxation; however, they compare compare very well to |
| 1122 |
+ |
experiment considering the Debye relaxation times calculated for the |
| 1123 |
+ |
original SSD (11.95~ps) and the SPC/E (6.95~ps) and TIP3P (6.1~ps) |
| 1124 |
+ |
values. The $\tau_D$ for TRED is about 1.5~ps slower than the $\tau_D$ |
| 1125 |
+ |
for SSD/RF, most likely due to the slower decay of the charge-charge |
| 1126 |
+ |
interaction, even when screened by the same damping constant. |
| 1127 |
+ |
|
| 1128 |
|
\section{Conclusions} |
| 1129 |
|
|
| 1130 |
|
In the above sections, the density maximum and temperature dependence |
| 1146 |
|
when changing the method of calculating long-range electrostatic |
| 1147 |
|
interactions. |
| 1148 |
|
|
| 1149 |
+ |
We also showed that SSD/RF performs well under the alternative damped |
| 1150 |
+ |
electrostatic conditions, validating the multipolar damping work in |
| 1151 |
+ |
the previous chapter. To improve the modeling of water when {\sc sf}, |
| 1152 |
+ |
the TRED water model was developed. This model maintains improves upon |
| 1153 |
+ |
the thermodynamic properties of SSD/RF using damped electrostatics |
| 1154 |
+ |
while maintaining the exceptional depiction of water dynamics. |
| 1155 |
+ |
|
| 1156 |
|
The simple water models investigated here are excellent choices for |
| 1157 |
|
representing explicit water in large scale simulations of biochemical |
| 1158 |
|
systems. They are more computationally efficient than the common |
| 1159 |
|
charge based water models, and, in many cases, exhibit more realistic |
| 1160 |
|
bulk phase fluid properties. These models are one of the few cases in |
| 1161 |
|
which maximizing efficiency does not result in a loss in realistic |
| 1162 |
< |
representation. |
| 1162 |
> |
liquid water representation. |
