| 2588 |
|
cutoff radius for several different water models. To calculate the |
| 2589 |
|
static dielectric constant, we performed 5ns $NPT$ calculations at 9, |
| 2590 |
|
10, 11, and 12\AA cutoff radii, each with damping parameter values |
| 2591 |
< |
ranging from 0 to 0.35\AA$^{-1}$ using the SPC/E, TIP4P-Ew, TIP5P-E, |
| 2591 |
> |
ranging from 0 to 0.35\AA$^{-1}$ using the TIP5P-E, TIP4P-Ew, SPC/E, |
| 2592 |
|
and SSD/RF water models. TIP4P-Ew is a reparametrized version of the |
| 2593 |
|
four-point transferable intermolecular potential (TIP4P) for water |
| 2594 |
|
targeted for use with the Ewald summation.\cite{Horn04} SSD/RF is the |
| 2596 |
|
for water, and this model is discussed in more detail in the next |
| 2597 |
|
chapter. One thing to note about it, electrostatic interactions are |
| 2598 |
|
handled via dipole-dipole interactions rather than charge-charge |
| 2599 |
< |
interactions like the other three models. |
| 2600 |
< |
|
| 2599 |
> |
interactions like the other three models. Damping of the dipole-dipole |
| 2600 |
> |
interaction was handled as described in section |
| 2601 |
> |
\ref{sec:dampingMultipoles}. |
| 2602 |
|
\begin{figure} |
| 2603 |
|
\centering |
| 2604 |
< |
\includegraphics[width=3.5in]{./figures/ssdrfDielectric.pdf} |
| 2605 |
< |
\caption{The dielectric constant for the SSD/RF water model as a |
| 2606 |
< |
function of cutoff radius ($R_\textrm{c}$) and damping coefficient |
| 2607 |
< |
($\alpha$).} |
| 2608 |
< |
\label{fig:ssdrfDielectric} |
| 2604 |
> |
\includegraphics[width=3.5in]{./figures/dielectricMap.pdf} |
| 2605 |
> |
\caption{The static dielectric constant for the A: TIP5P-E, B: TIP4P-Ew, |
| 2606 |
> |
C: SPC/E, and D: SSD/RF water models as a function of cutoff radius |
| 2607 |
> |
($R_\textrm{c}$) and damping coefficient ($\alpha$).} |
| 2608 |
> |
\label{fig:dielectricMap} |
| 2609 |
|
\end{figure} |
| 2610 |
|
|
| 2611 |
+ |
The results of these calculations are displayed in figure |
| 2612 |
+ |
\ref{fig:dielectricMap} in the form of shaded contour plots. An |
| 2613 |
+ |
interesting aspect of all four contour plots is that the dielectric |
| 2614 |
+ |
constant is effectively linear with respect to $\alpha$ and |
| 2615 |
+ |
$R_\textrm{c}$ in the low to moderate damping regions. Another point |
| 2616 |
+ |
to note is that choosing $\alpha$ and $R_\textrm{c}$ identical to |
| 2617 |
+ |
those used in studies with the Ewald summation results in the same |
| 2618 |
+ |
calculated dielectric constant. As an example, in the paper outlining |
| 2619 |
+ |
the development of TIP5P-E, the real-space cutoff and Ewald |
| 2620 |
+ |
coefficient were tethered to the system size, and for a 512 molecule |
| 2621 |
+ |
system are approximately 12\AA and 0.25\AA$^{-1}$ |
| 2622 |
+ |
respectively.\cite{Rick04} These parameters resulted in a dielectric |
| 2623 |
+ |
constant of 92$\pm$14, while with {\sc sf} these parameters give a |
| 2624 |
+ |
dielectric constant of 90.8$\pm$0.9. Another example comes from the |
| 2625 |
+ |
TIP4P-Ew paper where $\alpha$ and $R_\textrm{c}$ were chosen to be |
| 2626 |
+ |
9.5\AA and 0.35\AA$^{-1}$, and these parameters resulted in a |
| 2627 |
+ |
$\epsilon_0$ equal to 63$\pm$1.\cite{Horn04} We did not perform |
| 2628 |
+ |
calculations with these exact parameters, but interpolating between |
| 2629 |
+ |
surrounding values gives a $\epsilon_0$ of 61$\pm$1. Seeing a |
| 2630 |
+ |
dependence of the dielectric constant on $\alpha$ and $R_\textrm{c}$ |
| 2631 |
+ |
with the {\sc sf} technique, it might be interesting to investigate |
| 2632 |
+ |
the dielectric dependence when using the Ewald summation. |
| 2633 |
+ |
|
| 2634 |
+ |
|
| 2635 |
+ |
|
| 2636 |
+ |
|
| 2637 |
|
\section{Conclusions}\label{sec:PairwiseConclusions} |
| 2638 |
|
|
| 2639 |
|
The above investigation of pairwise electrostatic summation techniques |
