| 3 |
|
The combined system results in chapter \ref{chap:electrostatics} |
| 4 |
|
(sections \ref{sec:EnergyResults} through \ref{sec:FTDirResults}) show |
| 5 |
|
how the pairwise methods compare to the Ewald summation in the general |
| 6 |
< |
sense over all of the system types. It is also useful to consider |
| 7 |
< |
each of the studied systems in an individual fashion, so that we can |
| 8 |
< |
identify conditions that are particularly difficult for a selected |
| 9 |
< |
pairwise method to address. This allows us to further establish the |
| 10 |
< |
limitations of these pairwise techniques. In this appendix, the |
| 11 |
< |
energy difference, force vector, and torque vector analyses are |
| 12 |
< |
presented on an individual system basis. |
| 6 |
> |
sense over all of the system types investigated. It is also useful to |
| 7 |
> |
consider each of the studied systems in an individual fashion, so that |
| 8 |
> |
we can identify conditions that are particularly difficult for a |
| 9 |
> |
selected pairwise method to address. This allows us to further |
| 10 |
> |
establish the limitations of these pairwise techniques. In this |
| 11 |
> |
appendix, the energy difference, force vector, and torque vector |
| 12 |
> |
analyses are presented on an individual system basis. |
| 13 |
|
|
| 14 |
|
\section{SPC/E Water Results}\label{sec:WaterResults} |
| 15 |
|
|
| 174 |
|
\section{SPC/E Ice I$_\textrm{c}$ Results}\label{sec:IceResults} |
| 175 |
|
|
| 176 |
|
In addition to the disordered molecular system above, the ordered |
| 177 |
< |
molecular system of ice I$_\textrm{c}$ was also considered. Ice |
| 177 |
> |
molecular system of ice I$_\textrm{c}$ was also considered. Any ice |
| 178 |
|
polymorph could have been used to fit this role; however, ice |
| 179 |
|
I$_\textrm{c}$ was chosen because it can form an ideal periodic |
| 180 |
|
lattice with the same number of water molecules used in the disordered |
| 181 |
< |
liquid state case. The results for the energy gap comparisons and the |
| 182 |
< |
force and torque vector magnitude comparisons are shown in table |
| 181 |
> |
liquid state system. The results for the energy gap comparisons and |
| 182 |
> |
the force and torque vector magnitude comparisons are shown in table |
| 183 |
|
\ref{tab:ice}. The force and torque vector directionality results are |
| 184 |
|
displayed separately in table \ref{tab:iceAng}, where the effect of |
| 185 |
|
group-based cutoffs and switching functions on the {\sc sp} and {\sc |
| 392 |
|
|
| 393 |
|
Similar to the use of ice I$_\textrm{c}$ to investigate the role of |
| 394 |
|
order in molecular systems on the effectiveness of the pairwise |
| 395 |
< |
methods, the 1000~K NaCl crystal system was used to investigate the |
| 395 |
> |
methods, the 1000~K NaCl crystal system was sampled to investigate the |
| 396 |
|
accuracy of the pairwise summation methods in an ordered system of |
| 397 |
|
charged particles. The results for the energy gap comparisons and the |
| 398 |
|
force vector magnitude comparisons are shown in table \ref{tab:salt}. |
| 484 |
|
dynamics, this indicates that good long-time dynamics comes in part at |
| 485 |
|
the expense of short-time dynamics. |
| 486 |
|
|
| 487 |
< |
\section{0.11M NaCl Solution Results} |
| 487 |
> |
\section{0.11 M NaCl Solution Results} |
| 488 |
|
|
| 489 |
|
In an effort to bridge the charged atomic and neutral molecular |
| 490 |
< |
systems, Na$^+$ and Cl$^-$ ion charge defects were incorporated into |
| 491 |
< |
the liquid water system. This low ionic strength system consists of 4 |
| 492 |
< |
ions in the 1000 SPC/E water solvent ($\approx$0.11 M). The results |
| 493 |
< |
for the energy gap comparisons and the force and torque vector |
| 494 |
< |
magnitude comparisons are shown in table \ref{tab:solnWeak}. The |
| 495 |
< |
force and torque vector directionality results are displayed |
| 496 |
< |
separately in table \ref{tab:solnWeakAng}, where the effect of |
| 497 |
< |
group-based cutoffs and switching functions on the {\sc sp} and {\sc |
| 498 |
< |
sf} potentials are investigated. |
| 490 |
> |
systems, Na$^+$ and Cl$^-$ ions were incorporated into the liquid |
| 491 |
> |
water system. This low ionic strength system consists of 4 ions in the |
| 492 |
> |
1000 SPC/E water solvent ($\approx$0.11 M). The results for the energy |
| 493 |
> |
gap comparisons and the force and torque vector magnitude comparisons |
| 494 |
> |
are shown in table \ref{tab:solnWeak}. The force and torque vector |
| 495 |
> |
directionality results are displayed separately in table |
| 496 |
> |
\ref{tab:solnWeakAng}, where the effect of group-based cutoffs and |
| 497 |
> |
switching functions on the {\sc sp} and {\sc sf} potentials are |
| 498 |
> |
investigated. |
| 499 |
|
|
| 500 |
|
\begin{table}[htbp] |
| 501 |
|
\centering |
| 600 |
|
smooth incorporation of these ions; thus, all of the observations |
| 601 |
|
regarding these methods carry over from section |
| 602 |
|
\ref{sec:WaterResults}. The differences between these systems are more |
| 603 |
< |
visible for the {\sc rf} method. Though good force agreement is still |
| 604 |
< |
maintained, the energy gaps show a significant increase in the scatter |
| 605 |
< |
of the data. |
| 603 |
> |
visible for the {\sc rf} method. Good force agreement is still |
| 604 |
> |
maintained; however, the energy gaps show a significant increase in |
| 605 |
> |
the scatter of the data. |
| 606 |
|
|
| 607 |
< |
\section{1.1M NaCl Solution Results} |
| 607 |
> |
\section{1.1 M NaCl Solution Results} |
| 608 |
|
|
| 609 |
|
The bridging of the charged atomic and neutral molecular systems was |
| 610 |
|
further developed by considering a high ionic strength system |
| 611 |
< |
consisting of 40 ions in the 1000 SPC/E water solvent ($\approx$1.1 |
| 611 |
> |
consisting of 40 ions in the 1000 SPC/E water solvent ($\approx$1.1 |
| 612 |
|
M). The results for the energy gap comparisons and the force and |
| 613 |
|
torque vector magnitude comparisons are shown in table |
| 614 |
|
\ref{tab:solnStr}. The force and torque vector directionality |
| 726 |
|
|
| 727 |
|
\section{6~\AA\ Argon Sphere in SPC/E Water Results} |
| 728 |
|
|
| 729 |
< |
The final model system studied was a 6~\AA\ sphere of Argon solvated |
| 729 |
> |
The final model system studied was a 6~\AA\ sphere of argon solvated |
| 730 |
|
by SPC/E water. This serves as a test case of a specifically sized |
| 731 |
|
electrostatic defect in a disordered molecular system. The results for |
| 732 |
|
the energy gap comparisons and the force and torque vector magnitude |
