| 720 |
|
in all {\sc spme} calculations, resulting in Ewald coefficients of 0.4200, |
| 721 |
|
0.3119, and 0.2476\AA$^{-1}$ for cutoff radii of 9, 12, and 15\AA\ |
| 722 |
|
respectively. |
| 723 |
– |
|
| 724 |
– |
|
| 725 |
– |
\section{Discussion on the Pairwise Technique Evaluation} |
| 723 |
|
|
| 724 |
< |
\subsection{Configuration Energy Differences}\label{sec:EnergyResults} |
| 724 |
> |
\section{Combined Configuration Energy Difference Results}\label{sec:EnergyResults} |
| 725 |
|
In order to evaluate the performance of the pairwise electrostatic |
| 726 |
< |
summation methods for Monte Carlo simulations, the energy differences |
| 727 |
< |
between configurations were compared to the values obtained when using |
| 728 |
< |
{\sc spme}. The results for the combined regression analysis of all |
| 729 |
< |
of the systems are shown in figure \ref{fig:delE}. |
| 726 |
> |
summation methods for Monte Carlo (MC) simulations, the energy |
| 727 |
> |
differences between configurations were compared to the values |
| 728 |
> |
obtained when using {\sc spme}. The results for the combined |
| 729 |
> |
regression analysis of all of the systems are shown in figure |
| 730 |
> |
\ref{fig:delE}. |
| 731 |
|
|
| 732 |
|
\begin{figure} |
| 733 |
|
\centering |
| 780 |
|
systems; although it does provide results that are an improvement over |
| 781 |
|
those from an unmodified cutoff. |
| 782 |
|
|
| 783 |
< |
\sub |
| 783 |
> |
\section{Magnitude of the Force and Torque Vector Results} |
| 784 |
|
|
| 787 |
– |
\subsection{Magnitudes of the Force and Torque Vectors} |
| 788 |
– |
|
| 785 |
|
Evaluation of pairwise methods for use in Molecular Dynamics |
| 786 |
|
simulations requires consideration of effects on the forces and |
| 787 |
|
torques. Figures \ref{fig:frcMag} and \ref{fig:trqMag} show the |
| 856 |
|
molecular bodies. Therefore it is not surprising that reaction field |
| 857 |
|
performs best of all of the methods on molecular torques. |
| 858 |
|
|
| 859 |
< |
\subsection{Directionality of the Force and Torque Vectors} |
| 859 |
> |
\section{Directionality of the Force and Torque Vector Results} |
| 860 |
|
|
| 861 |
|
It is clearly important that a new electrostatic method can reproduce |
| 862 |
|
the magnitudes of the force and torque vectors obtained via the Ewald |
| 984 |
|
observations, empirical damping up to 0.2\AA$^{-1}$ is beneficial, |
| 985 |
|
but damping may be unnecessary when using the {\sc sf} method. |
| 986 |
|
|
| 987 |
< |
\subsection{Short-Time Dynamics: Velocity Autocorrelation Functions of NaCl Crystals} |
| 987 |
> |
\section{Individual System Analysis Results} |
| 988 |
> |
|
| 989 |
> |
The combined results of the previous sections show how the pairwise |
| 990 |
> |
methods compare to the Ewald summation in the general sense over all |
| 991 |
> |
of the system types. It is also useful to consider each of the |
| 992 |
> |
studied systems in an individual fashion, so that we can identify |
| 993 |
> |
conditions that are particularly difficult for a selected pairwise |
| 994 |
> |
method to address. This allows us to further establish the limitations |
| 995 |
> |
of these pairwise techniques. Below, the energy difference, force |
| 996 |
> |
vector, and torque vector analyses are presented on an individual |
| 997 |
> |
system basis. |
| 998 |
|
|
| 999 |
+ |
\subsection{SPC/E Water Results} |
| 1000 |
+ |
|
| 1001 |
+ |
\subsection{SPC/E Ice I$_\textrm{c}$ Results} |
| 1002 |
+ |
|
| 1003 |
+ |
\subsection{NaCl Melt Results} |
| 1004 |
+ |
|
| 1005 |
+ |
\subsection{NaCl Crystal Results} |
| 1006 |
+ |
|
| 1007 |
+ |
\subsection{0.1M NaCl Solution Results} |
| 1008 |
+ |
|
| 1009 |
+ |
\subsection{1M NaCl Solution Results} |
| 1010 |
+ |
|
| 1011 |
+ |
\subsection{6\AA\ Argon Sphere in SPC/E Water Results} |
| 1012 |
+ |
|
| 1013 |
+ |
\section{Short-Time Dynamics: Velocity Autocorrelation Functions of NaCl Crystals} |
| 1014 |
+ |
|
| 1015 |
|
Zahn {\it et al.} investigated the structure and dynamics of water |
| 1016 |
|
using eqs. (\ref{eq:ZahnPot}) and |
| 1017 |
|
(\ref{eq:WolfForces}).\cite{Zahn02,Kast03} Their results indicated |
| 1062 |
|
constructed out of the damped electrostatic interaction are less |
| 1063 |
|
important. |
| 1064 |
|
|
| 1065 |
< |
\subsection{Collective Motion: Power Spectra of NaCl Crystals} |
| 1065 |
> |
\section{Collective Motion: Power Spectra of NaCl Crystals} |
| 1066 |
|
|
| 1067 |
|
To evaluate how the differences between the methods affect the |
| 1068 |
|
collective long-time motion, we computed power spectra from long-time |
