--- trunk/electrostaticMethodsPaper/SupportingInfo.tex 2006/03/22 21:00:07 2658 +++ trunk/electrostaticMethodsPaper/SupportingInfo.tex 2006/03/23 05:59:41 2660 @@ -29,7 +29,7 @@ vector magnitude, and force and torque vector directio tabular listing of the results for the $\Delta E$, force and torque vector magnitude, and force and torque vector direction comparisons. -\section{\label{app-water}Liquid Water} +\section{\label{app:water}Liquid Water} 500 liquid state configurations were generated as described in the Methods section using the SPC/E model of water.\cite{Berendsen87} The @@ -66,10 +66,8 @@ GSC & & 0.918 & 0.862 & 0.852 & 0.756 & 0.801 & 0. & 0.2 & 0.992 & 0.989 & 1.001 & 0.995 & 0.994 & 0.996 \\ & 0.3 & 0.984 & 0.980 & 0.996 & 0.985 & 0.982 & 0.987 \\ GSC & & 0.918 & 0.862 & 0.852 & 0.756 & 0.801 & 0.700 \\ -RF & & 0.971 & 0.958 & 0.975 & 0.987 & 0.959 & 0.983 \\ - +RF & & 0.971 & 0.958 & 0.975 & 0.987 & 0.959 & 0.983 \\ \midrule - PC & & -1.647 & 0.000 & -0.127 & 0.000 & -0.979 & 0.000 \\ SP & 0.0 & 0.735 & 0.368 & 0.813 & 0.537 & 0.865 & 0.659 \\ & 0.1 & 0.850 & 0.612 & 0.956 & 0.887 & 0.992 & 0.979 \\ @@ -81,9 +79,7 @@ RF & & 0.999 & 0.995 & 1.000 & 0.999 & 1.000 & 1. & 0.3 & 0.996 & 0.998 & 0.997 & 0.998 & 0.996 & 0.998 \\ GSC & & 0.998 & 0.995 & 1.000 & 0.999 & 1.000 & 1.000 \\ RF & & 0.999 & 0.995 & 1.000 & 0.999 & 1.000 & 1.000 \\ - \midrule - PC & & 2.387 & 0.000 & 0.183 & 0.000 & 1.282 & 0.000 \\ SP & 0.0 & 0.847 & 0.543 & 0.904 & 0.694 & 0.935 & 0.786 \\ & 0.1 & 0.922 & 0.749 & 0.980 & 0.934 & 0.996 & 0.988 \\ @@ -183,7 +179,7 @@ potentials. nothing for cases were error is introduced by overdamping the potentials. -\section{\label{app-ice}Solid Water: Ice I$_\textrm{c}$} +\section{\label{app:ice}Solid Water: Ice I$_\textrm{c}$} In addition to the disordered molecular system above, the ordered molecular system of ice I$_\textrm{c}$ was also considered. The @@ -306,7 +302,7 @@ sphere. by actively enforcing a zeroed dipole moment within each cutoff sphere. -\section{\label{app-melt}NaCl Melt} +\section{\label{app:melt}NaCl Melt} A high temperature NaCl melt was tested to gauge the accuracy of the pairwise summation methods in a highly charge disordered system. The @@ -378,9 +374,18 @@ SF & 0.0 & 1.693 & 0.603 & 0.256 \\ \label{tab:meltAng} \end{table} -The molten NaCl system shows the a +The molten NaCl system shows more sensitivity to the electrostatic +damping than the water systems. The most noticeable point is that the +undamped {\sc sf} method does very well at replicating the {\sc spme} +configurational energy differences and forces. Light damping appears +to minimally improve the dynamics, but this comes with a deterioration +of the energy gap results. In contrast, this light damping improves +the {\sc sp} energy gaps and forces. Moderate and heavy electrostatic +damping reduce the agreement with {\sc spme} for both methods. From +these observations, the undamped {\sc sf} method is the best choice +for disordered systems of charges. -\section{\label{app-salt}NaCl Crystal} +\section{\label{app:salt}NaCl Crystal} A 1000K NaCl crystal was used to investigate the accuracy of the pairwise summation methods in an ordered system of charged @@ -459,8 +464,27 @@ SF & 0.0 & 10.025 & 3.555 & 1.648 \\ \label{tab:saltAng} \end{table} -\section{\label{app-sol1}Weak NaCl Solution} +The crystalline NaCl system is the most challenging test case for the +pairwise summation methods, as evidenced by the results in tables +\ref{tab:salt} and \ref{tab:saltAng}. The undamped and weakly damped +{\sc sf} methods with a 12 \AA\ cutoff radius seem to be the best +choices. These methods match well with {\sc spme} across the energy +gap, force magnitude, and force directionality tests. The {\sc sp} +method struggles in all cases with the exception of good dynamics +reproduction when using weak electrostatic damping with a large cutoff +radius. +The moderate electrostatic damping case is not as good as we would +expect given the good long-time dynamics results observed for this +system. Since these results are a test of instantaneous dynamics, this +indicates that good long-time dynamics comes in part at the expense of +short-time dynamics. Further indication of this comes from the full +power spectra shown in the main text. It appears as though a +distortion is introduced between 200 to 300 cm$^{-1}$ with increased +$\alpha$. + +\section{\label{app:solnWeak}Weak NaCl Solution} + In an effort to bridge the charged atomic and neutral molecular systems, Na$^+$ and Cl$^-$ ion charge defects were incorporated into the liquid water system. This low ionic strength system consists of 4 @@ -571,17 +595,28 @@ GSSF & 0.0 & 1.541 & 0.301 & 0.096 & 6.407 & 1.316 & \label{tab:solnWeakAng} \end{table} -\section{\label{app-sol10}Strong NaCl Solution} +This weak ionic strength system can be considered as a perturbation of +the pure liquid water system. The {\sc sp} and {\sc sf} methods are +not significantly affected by the inclusion of a few ions. The aspect +of cutoff sphere neutralization aids in the smooth incorporation of +these ions; thus, all of the observations regarding these methods +carry over from section \ref{app:water}. The differences between these +systems are visible for the {\sc rf} method. Though good force +reproduction is still maintained, the energy gaps show a significant +increase in the data scatter. This foreshadows the breakdown of the +method as we introduce system inhomogeneities. +\section{\label{app:solnStr}Strong NaCl Solution} + The bridging of the charged atomic and neutral molecular systems was -furthered by considering a high ionic strength system consisting of 40 -ions in the 1000 SPC/E water solvent ($\approx$1.1 M). The results for -the energy gap comparisons and the force and torque vector magnitude -comparisons are shown in table \ref{tab:solnWeak}. The force and -torque vector directionality results are displayed separately in table -\ref{tab:solnWeakAng}, where the effect of group-based cutoffs and -switching functions on the {\sc sp} and {\sc sf} potentials are -investigated. +further developed by considering a high ionic strength system +consisting of 40 ions in the 1000 SPC/E water solvent ($\approx$1.1 +M). The results for the energy gap comparisons and the force and +torque vector magnitude comparisons are shown in table +\ref{tab:solnWeak}. The force and torque vector directionality +results are displayed separately in table\ref{tab:solnWeakAng}, where +the effect of group-based cutoffs and switching functions on the {\sc +sp} and {\sc sf} potentials are investigated. \begin{table}[htbp] \centering @@ -676,8 +711,20 @@ GSSF & 0.0 & 2.494 & 0.546 & 0.217 & 16.391 & 3.230 & \label{tab:solnStrAng} \end{table} -\section{\label{app-argon}Argon Sphere in Water} +The {\sc rf} method struggles with the jump in ionic strength. The +configuration energy difference degrade to unuseable levels while the +forces and torques degrade in a more modest fashion. The {\sc rf} +method was designed for homogeneous systems, and this restriction is +apparent in these results. +The {\sc sp} and {\sc sf} methods require larger cutoffs to maintain +their agreement with {\sc spme}. With these results, we still +recommend no to moderate damping for the {\sc sf} method and moderate +damping for the {\sc sp} method, both with cutoffs greater than 12 +\AA. + +\section{\label{app:argon}Argon Sphere in Water} + The final model system studied was 6 \AA\ sphere of Argon solvated by SPC/E water. The results for the energy gap comparisons and the force and torque vector magnitude comparisons are shown in table @@ -784,6 +831,8 @@ GSSF & 0.0 & 1.173 & 0.292 & 0.113 & 3.452 & 1.347 & \label{tab:argonAng} \end{table} +This system appears not to show in any significant deviation in the previously observed results. The {\sc sp} and {\sc sf} methods give result qualities similar to those observed in section \ref{app:water}. The only significant difference is the improvement for the configuration energy differences for the {\sc rf} method. This is surprising in that we are introducing an inhomogeneity to the system; however, this inhomogeneity is charge-neutral and does not result in charged cutoff spheres. The charge-neutrality, which the {\sc sp} and {\sc sf} methods explicity enforce, seems to play a greater role in the stability of the {\sc rf} method than the necessity of a homogeneous environment. + \newpage \bibliographystyle{jcp2}