| 83 |
|
energy conservation properties that make it an excellent choice for |
| 84 |
|
efficient computation of electrostatic interactions in molecular |
| 85 |
|
dynamics simulations. Both SP and GSF are able to reproduce |
| 86 |
< |
structural and dyanamical properties in the liquid models with |
| 86 |
> |
structural and dynamical properties in the liquid models with |
| 87 |
|
excellent fidelity. |
| 88 |
|
\end{abstract} |
| 89 |
|
|
| 171 |
|
problem.\cite{Zahn:2002hc,Fennell:2006lq} Related real-space methods |
| 172 |
|
were also proposed by Chen \textit{et |
| 173 |
|
al.}\cite{Chen:2004du,Chen:2006ii,Denesyuk:2008ez,Rodgers:2006nw} |
| 174 |
< |
and by Wu and Brooks.\cite{Wu:044107} Recently, Fukuda has successfuly |
| 174 |
> |
and by Wu and Brooks.\cite{Wu:044107} Recently, Fukuda has successfully |
| 175 |
|
used additional neutralization of higher order moments for systems of |
| 176 |
|
point charges.\cite{Fukuda:2013sf} |
| 177 |
|
|
| 238 |
|
dynamics in molecular simulations, and the damped shifted force (DSF) |
| 239 |
|
energy kernel provides consistent energies and forces on charged atoms |
| 240 |
|
within the cutoff sphere. Both the energy and the force go smoothly to |
| 241 |
< |
zero as an atom aproaches the cutoff radius. The comparisons of the |
| 241 |
> |
zero as an atom approaches the cutoff radius. The comparisons of the |
| 242 |
|
accuracy these quantities between the DSF kernel and SPME was |
| 243 |
|
surprisingly good.\cite{Fennell:2006lq} As a result, the DSF method |
| 244 |
|
has seen increasing use in molecular systems with relatively uniform |
| 485 |
|
\caption{The parameters used in the systems used to evaluate the new |
| 486 |
|
real-space methods. The most comprehensive test was a liquid |
| 487 |
|
composed of 2000 SSDQ molecules with 48 dissolved ions (24 \ce{Na+} and 24 \ce{Cl-} |
| 488 |
< |
ions). This test excercises all orders of the multipolar |
| 488 |
> |
ions). This test exercises all orders of the multipolar |
| 489 |
|
interactions developed in the first paper.\label{tab:pars}} |
| 490 |
|
\begin{tabularx}{\textwidth}{r|cc|YYccc|Yccc} \hline |
| 491 |
|
& \multicolumn{2}{c|}{LJ parameters} & |
| 641 |
|
simulations. Because the real space methods reweight the different |
| 642 |
|
orientational contributions to the energies, it is also important to |
| 643 |
|
understand how the methods impact the \textit{directionality} of the |
| 644 |
< |
force and torque vectors. Fisher developed a probablity density |
| 644 |
> |
force and torque vectors. Fisher developed a probability density |
| 645 |
|
function to analyse directional data sets, |
| 646 |
|
\begin{equation} |
| 647 |
|
p_f(\theta) = \frac{\kappa}{2 \sinh\kappa}\sin\theta e^{\kappa \cos\theta} |
| 931 |
|
treatment.\label{fig:gofr}} |
| 932 |
|
\end{figure} |
| 933 |
|
|
| 934 |
< |
There is a minor overstructuring of the first solvation shell when |
| 934 |
> |
There is a minor over-structuring of the first solvation shell when |
| 935 |
|
using TSF or when overdamping with any of the real-space methods. |
| 936 |
|
With moderate damping, GSF and SP produce pair distributions that are |
| 937 |
|
identical (within numerical noise) to their Ewald counterparts. The |
| 938 |
< |
degree of overstructuring can be measured most easily using the |
| 938 |
> |
degree of over-structuring can be measured most easily using the |
| 939 |
|
coordination number, |
| 940 |
|
\begin{equation} |
| 941 |
|
n_C = 4\pi\rho \int_{0}^{a}r^2\text{g}(r)dr, |
| 1074 |
|
significantly more gentle approach. |
| 1075 |
|
|
| 1076 |
|
The GSF method produces quantitative agreement with Ewald energies, |
| 1077 |
< |
forcse, and torques. It also performs well in conserving energy in MD |
| 1077 |
> |
forces, and torques. It also performs well in conserving energy in MD |
| 1078 |
|
simulations. The Taylor-shifted (TSF) model provides smooth dynamics, |
| 1079 |
|
but these take place on a potential energy surface that is |
| 1080 |
|
significantly perturbed from Ewald-based electrostatics. Because it |
| 1112 |
|
Based on the results of this work, we can conclude that the GSF method |
| 1113 |
|
is a suitable and efficient replacement for the Ewald sum for |
| 1114 |
|
evaluating electrostatic interactions in modern MD simulations, and |
| 1115 |
< |
the SP meethod would be an excellent choice for Monte Carlo |
| 1115 |
> |
the SP method would be an excellent choice for Monte Carlo |
| 1116 |
|
simulations where smooth forces and energy conservation are not |
| 1117 |
|
important. Both the SP and GSF methods retain excellent fidelity to |
| 1118 |
|
the Ewald energies, forces and torques. Additionally, the energy |
