| 148 |
|
The pure cutoff ({\sc pc}) method performs poorly, again mirroring the |
| 149 |
|
observations in the main portion of this paper. In contrast to the |
| 150 |
|
combined values, however, the use of a switching function and group |
| 151 |
< |
based cutoffs really improves the results for these neutral water |
| 151 |
> |
based cutoffs greatly improves the results for these neutral water |
| 152 |
|
molecules. The group switched cutoff ({\sc gsc}) does not mimic the |
| 153 |
|
energetics of {\sc spme} as well as the {\sc sp} (with moderate |
| 154 |
|
damping) and {\sc sf} methods, but the dynamics are quite good. The |
| 155 |
< |
switching functions corrects discontinuities in the potential and |
| 155 |
> |
switching functions correct discontinuities in the potential and |
| 156 |
|
forces, leading to these improved results. Such improvements with the |
| 157 |
< |
use of a switching function has been recognized in previous |
| 157 |
> |
use of a switching function have been recognized in previous |
| 158 |
|
studies,\cite{Andrea83,Steinbach94} and this proves to be a useful |
| 159 |
|
tactic for stably incorporating local area electrostatic effects. |
| 160 |
|
|
| 168 |
|
show how incorporating some implicit properties of the surroundings |
| 169 |
|
(i.e. $\epsilon_\textrm{S}$) can improve the solvent depiction. |
| 170 |
|
|
| 171 |
< |
A final note for the liquid water system, use of group cutoffs and a |
| 171 |
> |
As a final note for the liquid water system, use of group cutoffs and a |
| 172 |
|
switching function leads to noticeable improvements in the {\sc sp} |
| 173 |
|
and {\sc sf} methods, primarily in directionality of the force and |
| 174 |
|
torque vectors (table \ref{tab:spceAng}). The {\sc sp} method shows |
| 286 |
|
|
| 287 |
|
Highly ordered systems are a difficult test for the pairwise methods |
| 288 |
|
in that they lack the periodicity term of the Ewald summation. As |
| 289 |
< |
expected, the energy gap agreement with {\sc spme} reduces for the |
| 289 |
> |
expected, the energy gap agreement with {\sc spme} is reduced for the |
| 290 |
|
{\sc sp} and {\sc sf} methods with parameters that were acceptable for |
| 291 |
|
the disordered liquid system. Moving to higher $R_\textrm{c}$ helps |
| 292 |
|
improve the agreement, though at an increase in computational cost. |
| 307 |
|
|
| 308 |
|
A high temperature NaCl melt was tested to gauge the accuracy of the |
| 309 |
|
pairwise summation methods in a charged disordered system. The results |
| 310 |
< |
for the energy gap comparisons and the force and torque vector |
| 311 |
< |
magnitude comparisons are shown in table \ref{tab:melt}. The force |
| 312 |
< |
and torque vector directionality results are displayed separately in |
| 313 |
< |
table \ref{tab:meltAng}, where the effect of group-based cutoffs and |
| 314 |
< |
switching functions on the {\sc sp} and {\sc sf} potentials are |
| 315 |
< |
investigated. |
| 310 |
> |
for the energy gap comparisons and the force vector magnitude |
| 311 |
> |
comparisons are shown in table \ref{tab:melt}. The force vector |
| 312 |
> |
directionality results are displayed separately in table |
| 313 |
> |
\ref{tab:meltAng}. |
| 314 |
|
|
| 315 |
|
\begin{table}[htbp] |
| 316 |
|
\centering |
| 389 |
|
A 1000K NaCl crystal was used to investigate the accuracy of the |
| 390 |
|
pairwise summation methods in an ordered system of charged |
| 391 |
|
particles. The results for the energy gap comparisons and the force |
| 392 |
< |
and torque vector magnitude comparisons are shown in table |
| 393 |
< |
\ref{tab:salt}. The force and torque vector directionality results |
| 394 |
< |
are displayed separately in table \ref{tab:saltAng}, where the effect |
| 397 |
< |
of group-based cutoffs and switching functions on the {\sc sp} and |
| 398 |
< |
{\sc sf} potentials are investigated. |
| 392 |
> |
vector magnitude comparisons are shown in table \ref{tab:salt}. The |
| 393 |
> |
force vector directionality results are displayed separately in table |
| 394 |
> |
\ref{tab:saltAng}. |
| 395 |
|
|
| 396 |
|
\begin{table}[htbp] |
| 397 |
|
\centering |
| 472 |
|
radius. |
| 473 |
|
|
| 474 |
|
The moderate electrostatic damping case is not as good as we would |
| 475 |
< |
expect given the good long-time dynamics results observed for this |
| 476 |
< |
system. Since the data tabulated in table \ref{tab:salt} and |
| 475 |
> |
expect given the long-time dynamics results observed for this |
| 476 |
> |
system. Since the data tabulated in tables \ref{tab:salt} and |
| 477 |
|
\ref{tab:saltAng} are a test of instantaneous dynamics, this indicates |
| 478 |
|
that good long-time dynamics comes in part at the expense of |
| 479 |
< |
short-time dynamics. Further indication of this comes from the full |
| 484 |
< |
power spectra shown in the main text. It appears as though a |
| 485 |
< |
distortion is introduced between 200 to 350 cm$^{-1}$ with increased |
| 486 |
< |
$\alpha$. |
| 479 |
> |
short-time dynamics. |
| 480 |
|
|
| 481 |
|
\section{\label{app:solnWeak}Weak NaCl Solution} |
| 482 |
|
|
| 497 |
|
system. Tabulated results include $\Delta E$ values (top set), force |
| 498 |
|
vector magnitudes (middle set) and torque vector magnitudes (bottom |
| 499 |
|
set). PC = Pure Cutoff, SP = Shifted Potential, SF = Shifted Force, |
| 500 |
< |
GSC = Group Switched Cutoff, RF = Reaction Field (where $\varepsilon |
| 501 |
< |
\approx \infty$), GSSP = Group Switched Shifted Potential, and GSSF = |
| 509 |
< |
Group Switched Shifted Force.} |
| 500 |
> |
GSC = Group Switched Cutoff, and RF = Reaction Field (where $\varepsilon |
| 501 |
> |
\approx \infty$).} |
| 502 |
|
\begin{tabular}{@{} ccrrrrrr @{}} |
| 503 |
|
\\ |
| 504 |
|
\toprule |
| 607 |
|
consisting of 40 ions in the 1000 SPC/E water solvent ($\approx$1.1 |
| 608 |
|
M). The results for the energy gap comparisons and the force and |
| 609 |
|
torque vector magnitude comparisons are shown in table |
| 610 |
< |
\ref{tab:solnWeak}. The force and torque vector directionality |
| 611 |
< |
results are displayed separately in table \ref{tab:solnWeakAng}, where |
| 610 |
> |
\ref{tab:solnStr}. The force and torque vector directionality |
| 611 |
> |
results are displayed separately in table \ref{tab:solnStrAng}, where |
| 612 |
|
the effect of group-based cutoffs and switching functions on the {\sc |
| 613 |
|
sp} and {\sc sf} potentials are investigated. |
| 614 |
|
|
| 706 |
|
\end{table} |
| 707 |
|
|
| 708 |
|
The {\sc rf} method struggles with the jump in ionic strength. The |
| 709 |
< |
configuration energy difference degrade to unusable levels while the |
| 709 |
> |
configuration energy differences degrade to unusable levels while the |
| 710 |
|
forces and torques show a more modest reduction in the agreement with |
| 711 |
|
{\sc spme}. The {\sc rf} method was designed for homogeneous systems, |
| 712 |
|
and this attribute is apparent in these results. |
| 719 |
|
|
| 720 |
|
\section{\label{app:argon}Argon Sphere in Water} |
| 721 |
|
|
| 722 |
< |
The final model system studied was 6 \AA\ sphere of Argon solvated by |
| 723 |
< |
SPC/E water. The results for the energy gap comparisons and the force |
| 724 |
< |
and torque vector magnitude comparisons are shown in table |
| 725 |
< |
\ref{tab:solnWeak}. The force and torque vector directionality |
| 726 |
< |
results are displayed separately in table \ref{tab:solnWeakAng}, where |
| 722 |
> |
The final model system studied was a 6 \AA\ sphere of Argon solvated |
| 723 |
> |
by SPC/E water. The results for the energy gap comparisons and the |
| 724 |
> |
force and torque vector magnitude comparisons are shown in table |
| 725 |
> |
\ref{tab:argon}. The force and torque vector directionality |
| 726 |
> |
results are displayed separately in table \ref{tab:argonAng}, where |
| 727 |
|
the effect of group-based cutoffs and switching functions on the {\sc |
| 728 |
|
sp} and {\sc sf} potentials are investigated. |
| 729 |
|
|
| 730 |
|
\begin{table}[htbp] |
| 731 |
|
\centering |
| 732 |
< |
\caption{Regression results for the 6 \AA\ argon sphere in liquid |
| 732 |
> |
\caption{Regression results for the 6 \AA\ Argon sphere in liquid |
| 733 |
|
water system. Tabulated results include $\Delta E$ values (top set), |
| 734 |
|
force vector magnitudes (middle set) and torque vector magnitudes |
| 735 |
|
(bottom set). PC = Pure Cutoff, SP = Shifted Potential, SF = Shifted |
| 788 |
|
\centering |
| 789 |
|
\caption{Variance results from Gaussian fits to angular |
| 790 |
|
distributions of the force and torque vectors in the 6 \AA\ sphere of |
| 791 |
< |
argon in liquid water system. PC = Pure Cutoff, SP = Shifted |
| 791 |
> |
Argon in liquid water system. PC = Pure Cutoff, SP = Shifted |
| 792 |
|
Potential, SF = Shifted Force, GSC = Group Switched Cutoff, RF = |
| 793 |
|
Reaction Field (where $\varepsilon \approx \infty$), GSSP = Group |
| 794 |
|
Switched Shifted Potential, and GSSF = Group Switched Shifted Force.} |
| 825 |
|
\label{tab:argonAng} |
| 826 |
|
\end{table} |
| 827 |
|
|
| 828 |
< |
This system appears not to show in any significant deviation in the |
| 829 |
< |
previously observed results. The {\sc sp} and {\sc sf} methods give |
| 830 |
< |
result qualities similar to those observed in section |
| 828 |
> |
This system does not appear to show any significant deviations from |
| 829 |
> |
the previously observed results. The {\sc sp} and {\sc sf} methods |
| 830 |
> |
have aggrements similar to those observed in section |
| 831 |
|
\ref{app:water}. The only significant difference is the improvement |
| 832 |
< |
for the configuration energy differences for the {\sc rf} method. This |
| 832 |
> |
in the configuration energy differences for the {\sc rf} method. This |
| 833 |
|
is surprising in that we are introducing an inhomogeneity to the |
| 834 |
|
system; however, this inhomogeneity is charge-neutral and does not |
| 835 |
|
result in charged cutoff spheres. The charge-neutrality of the cutoff |
