| 806 |
|
EXPERIMENTAL DATA AT AMBIENT CONDITIONS} |
| 807 |
|
\footnotesize |
| 808 |
|
\centering |
| 809 |
< |
\begin{tabular}{ lccccc } |
| 809 |
> |
\begin{tabular}{ llccccc } |
| 810 |
|
\toprule |
| 811 |
|
\toprule |
| 812 |
< |
& SSD1 & SSD/E & SSD1 (RF) & SSD/RF & Expt. \\ |
| 812 |
> |
& & SSD1 & SSD/E & SSD1 (RF) & SSD/RF & Experiment [Ref.] \\ |
| 813 |
|
\midrule |
| 814 |
< |
$\rho$ (g/cm$^3$) & 0.999(1) & 0.996(1) & 0.972(2) & 0.997(1) & 0.997 \\ |
| 815 |
< |
$C_p$ (cal/mol K) & 28.80(11) & 25.45(9) & 28.28(6) & 23.83(16) & 17.98 \\ |
| 816 |
< |
$D$ ($10^{-5}$ cm$^2$/s) & 1.78(7) & 2.51(18) & 2.00(17) & 2.32(6) & 2.299\\ |
| 817 |
< |
Coordination Number ($n_C$) & 3.9 & 4.3 & 3.8 & 4.4 & 4.7 \\ |
| 818 |
< |
H-bonds per particle ($n_H$) & 3.7 & 3.6 & 3.7 & 3.7 & 3.5 \\ |
| 819 |
< |
$\tau_1$ (ps) & 10.9(6) & 7.3(4) & 7.5(7) & 7.2(4) & 5.7 \\ |
| 820 |
< |
$\tau_2$ (ps) & 4.7(4) & 3.1(2) & 3.5(3) & 3.2(2) & 2.3 \\ |
| 814 |
> |
$\rho$ & (g cm$^{-3}$) & 0.999(1) & 0.996(1) & 0.972(2) & 0.997(1) & 0.997 \cite{CRC80}\\ |
| 815 |
> |
$C_p$ & (cal mol$^{-1}$ K$^{-1}$) & 28.80(11) & 25.45(9) & 28.28(6) & 23.83(16) & 18.005 \cite{Wagner02}\\ |
| 816 |
> |
$D$ & ($10^{-5}$ cm$^2$ s$^{-1}$) & 1.78(7) & 2.51(18) & 2.00(17) & 2.32(6) & 2.299 \cite{Mills73}\\ |
| 817 |
> |
$n_C$ & & 3.9 & 4.3 & 3.8 & 4.4 & 4.7 \cite{Hura00}\\ |
| 818 |
> |
$n_H$ & & 3.7 & 3.6 & 3.7 & 3.7 & 3.5 \cite{Soper86}\\ |
| 819 |
> |
$\tau_1$ & (ps) & 10.9(6) & 7.3(4) & 7.5(7) & 7.2(4) & 5.7 \cite{Eisenberg69}\\ |
| 820 |
> |
$\tau_2$ & (ps) & 4.7(4) & 3.1(2) & 3.5(3) & 3.2(2) & 2.3 \cite{Krynicki66}\\ |
| 821 |
|
\bottomrule |
| 822 |
|
\end{tabular} |
| 823 |
|
\label{tab:liquidProperties} |
| 862 |
|
(\ref{eq:OrientCorr}) were $\alpha$ is equal to $z$. From these |
| 863 |
|
correlation functions, the orientational relaxation time of the dipole |
| 864 |
|
vector can be calculated from an exponential fit in the long-time |
| 865 |
< |
regime ($t > |
| 866 |
< |
\tau_l$).\cite{Rothschild84} Calculation of these time constants were |
| 867 |
< |
averaged over five detailed {\it NVE} simulations performed at the ambient |
| 868 |
< |
conditions for each of the respective models. It should be noted that |
| 869 |
< |
the commonly cited value of 1.9 ps for $\tau_2$ was determined from |
| 870 |
< |
the NMR data in Ref. \cite{Krynicki66} at a temperature near |
| 871 |
< |
34$^\circ$C.\cite{Rahman71} Because of the strong temperature |
| 872 |
< |
dependence of $\tau_2$, it is necessary to recalculate it at 298K to |
| 873 |
< |
make proper comparisons. The value shown in Table |
| 865 |
> |
regime ($t > \tau_l$).\cite{Rothschild84} Calculation of these time |
| 866 |
> |
constants were averaged over five detailed {\it NVE} simulations |
| 867 |
> |
performed at the ambient conditions for each of the respective |
| 868 |
> |
models. It should be noted that the commonly cited value of 1.9 ps for |
| 869 |
> |
$\tau_2$ was determined from the NMR data in Ref. \cite{Krynicki66} at |
| 870 |
> |
a temperature near 34$^\circ$C.\cite{Rahman71} Because of the strong |
| 871 |
> |
temperature dependence of $\tau_2$, it is necessary to recalculate it |
| 872 |
> |
at 298K to make proper comparisons. The value shown in Table |
| 873 |
|
\ref{tab:liquidProperties} was calculated from the same NMR data in the |
| 874 |
|
fashion described in Ref. \cite{Krynicki66}. Similarly, $\tau_1$ was |
| 875 |
|
recomputed for 298K from the data in Ref. \cite{Eisenberg69}. |
| 882 |
|
can be attributed to the use of the Ewald sum.\cite{Chandra99} |
| 883 |
|
|
| 884 |
|
\subsection{SSD/RF and Damped Electrostatics} |
| 885 |
+ |
|
| 886 |
+ |
In section \ref{sec:dampingMultipoles}, a method was described for |
| 887 |
+ |
applying the damped {\sc sf} or {\sc sp} techniques to for systems |
| 888 |
+ |
containing point multipoles. The SSD family of water models is the |
| 889 |
+ |
perfect test case because of the dipole-dipole (and |
| 890 |
+ |
charge-dipole/quadrupole) interactions that are present. The {\sc sf} |
| 891 |
+ |
and {\sc sp} techniques were presented as a pairwise replacement for |
| 892 |
+ |
the Ewald summation. It has been suggested that models parametrized |
| 893 |
+ |
for the Ewald summation (like TIP5P-E) would be appropriate for use |
| 894 |
+ |
with a reaction field and vice versa.\cite{Rick04} Therefore, we |
| 895 |
+ |
decided to test the SSD/RF water model with this damped electrostatic |
| 896 |
+ |
technique in place of the reaction field to see how the calculated |
| 897 |
+ |
properties change. |
| 898 |
|
|
| 899 |
|
\begin{table} |
| 900 |
< |
\caption{PROPERTIES OF SSD/RF WHEN USING VARIOUS ELECTROSTATIC CORRECTION METHODS} |
| 900 |
> |
\caption{PROPERTIES OF SSD/RF WHEN USING DIFFERENT ELECTROSTATIC CORRECTION METHODS} |
| 901 |
|
\footnotesize |
| 902 |
|
\centering |
| 903 |
< |
\begin{tabular}{ lccc } |
| 903 |
> |
\begin{tabular}{ llccc } |
| 904 |
|
\toprule |
| 905 |
|
\toprule |
| 906 |
< |
& Reaction Field & Damped Electrostatics & Expt. \\ |
| 907 |
< |
& $\epsilon = 80$ & $\alpha = 0.2125\AA$ & \\ |
| 906 |
> |
& & Reaction Field & Damped Electrostatics & Experiment [Ref.] \\ |
| 907 |
> |
& & $\epsilon = 80$ & $\alpha = 0.2125$\AA$^{-1}$ & \\ |
| 908 |
|
\midrule |
| 909 |
< |
$\rho$ (g/cm$^3$) & 0.997(1) & 1.004(4) & 0.997 \\ |
| 910 |
< |
$C_p$ (cal/mol K) & 23.8(2) & 27(1) & 17.98 \\ |
| 911 |
< |
$D$ ($10^{-5}$ cm$^2$/s) & 2.32(6) & 2.33(2) & 2.299\\ |
| 912 |
< |
Coordination Number ($n_C$) & 4.4 & 4.3 & 4.7 \\ |
| 913 |
< |
H-bonds per particle ($n_H$) & 3.7 & 3.7 & 3.5 \\ |
| 914 |
< |
$\tau_1$ (ps) & 7.2(4) & 5.82(1) & 5.7 \\ |
| 915 |
< |
$\tau_2$ (ps) & 3.2(2) & 2.42(1) & 2.3 \\ |
| 909 |
> |
$\rho$ & (g cm$^{-3}$) & 0.997(1) & 1.004(4) & 0.997 \cite{CRC80}\\ |
| 910 |
> |
$C_p$ & (cal mol$^{-1}$ K$^{-1}$) & 23.8(2) & 27(1) & 18.005 \cite{Wagner02} \\ |
| 911 |
> |
$D$ & ($10^{-5}$ cm$^2$ s$^{-1}$) & 2.32(6) & 2.33(2) & 2.299 \cite{Mills73}\\ |
| 912 |
> |
$n_C$ & & 4.4 & 4.4 & 4.7 \cite{Hura00}\\ |
| 913 |
> |
$n_H$ & & 3.7 & 3.7 & 3.5 \cite{Soper86}\\ |
| 914 |
> |
$\tau_1$ & (ps) & 7.2(4) & 5.86(8) & 5.7 \cite{Eisenberg69}\\ |
| 915 |
> |
$\tau_2$ & (ps) & 3.2(2) & 2.45(7) & 2.3 \cite{Krynicki66}\\ |
| 916 |
|
\bottomrule |
| 917 |
|
\end{tabular} |
| 918 |
|
\label{tab:dampedSSDRF} |
| 930 |
|
|
| 931 |
|
\section{Tetrahedrally Restructured Elongated Dipole (TRED) Water Model} |
| 932 |
|
|
| 933 |
+ |
\begin{table} |
| 934 |
+ |
\caption{PROPERTIES OF TRED COMPARED WITH SSD/RF AND EXPERIMENT} |
| 935 |
+ |
\footnotesize |
| 936 |
+ |
\centering |
| 937 |
+ |
\begin{tabular}{ llccc } |
| 938 |
+ |
\toprule |
| 939 |
+ |
\toprule |
| 940 |
+ |
& & SSD/RF & TRED & Experiment [Ref.]\\ |
| 941 |
+ |
& & $\alpha = 0.2125$\AA$^{-1}$ & $\alpha = 0.2125$\AA$^{-1}$ & \\ |
| 942 |
+ |
\midrule |
| 943 |
+ |
$\rho$ & (g cm$^{-3}$) & 1.004(4) & 0.996(4) & 0.997 \cite{CRC80}\\ |
| 944 |
+ |
$C_p$ & (cal mol$^{-1}$ K$^{-1}$) & 27(1) & & 18.005 \cite{Wagner02} \\ |
| 945 |
+ |
$D$ & ($10^{-5}$ cm$^2$ s$^{-1}$) & 2.33(2) & 2.30(5) & 2.299 \cite{Mills73}\\ |
| 946 |
+ |
$n_C$ & & 4.4 & 5.3 & 4.7 \cite{Hura00}\\ |
| 947 |
+ |
$n_H$ & & 3.7 & 4.1 & 3.5 \cite{Soper86}\\ |
| 948 |
+ |
$\tau_1$ & (ps) & 5.86(8) & 6.0(1) & 5.7 \cite{Eisenberg69}\\ |
| 949 |
+ |
$\tau_2$ & (ps) & 2.45(7) & 2.49(5) & 2.3 \cite{Krynicki66}\\ |
| 950 |
+ |
$\epsilon_0$ & & 82.6(6) & & 78.3 \cite{Malmberg56}\\ |
| 951 |
+ |
$\tau_D$ & (ps) & & & 8.2(4) \cite{Kindt96}\\ |
| 952 |
+ |
\bottomrule |
| 953 |
+ |
\end{tabular} |
| 954 |
+ |
\label{tab:tredProps} |
| 955 |
+ |
\end{table} |
| 956 |
+ |
|
| 957 |
|
\section{Conclusions} |
| 958 |
|
|
| 959 |
|
In the above sections, the density maximum and temperature dependence |
