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\title{Is the Ewald summation still necessary? \\ |
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Pairwise alternatives to the accepted standard for \\ |
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long-range electrostatics} |
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long-range electrostatics in molecular simulations} |
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|
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\author{Christopher J. Fennell and J. Daniel Gezelter\footnote{Corresponding author. \ Electronic mail: |
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gezelter@nd.edu} \\ |
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to the direct pairwise sum. They also lack the added periodicity of |
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the Ewald sum, so they can be used for systems which are non-periodic |
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or which have one- or two-dimensional periodicity. Below, these |
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methods are evaluated using a variety of model systems to establish |
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their usability in molecular simulations. |
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> |
methods are evaluated using a variety of model systems to |
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establish their usability in molecular simulations. |
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|
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\subsection{The Ewald Sum} |
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The complete accumulation of the electrostatic interactions in a system with |
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interfaces and membranes, the intrinsic three-dimensional periodicity |
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can prove problematic. The Ewald sum has been reformulated to handle |
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2D systems,\cite{Parry75,Parry76,Heyes77,deLeeuw79,Rhee89}, but the |
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new methods are computationally expensive.\cite{Spohr97,Yeh99} |
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Inclusion of a correction term in the Ewald summation is a possible |
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direction for handling 2D systems while still enabling the use of the |
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modern optimizations.\cite{Yeh99} |
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new methods are computationally expensive.\cite{Spohr97,Yeh99} More |
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recently, there have been several successful efforts toward reducing |
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> |
the computational cost of 2D lattice summations, often enabling the |
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> |
use of the mentioned |
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optimizations.\cite{Yeh99,Kawata01,Arnold02,deJoannis02,Brodka04} |
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|
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Several studies have recognized that the inherent periodicity in the |
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Ewald sum can also have an effect on three-dimensional |
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\label{fig:linearFit} |
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\end{figure} |
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|
| 542 |
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Each system type (detailed in section \ref{sec:RepSims}) was |
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represented using 500 independent configurations. Additionally, we |
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used seven different system types, so each of the alternative |
| 545 |
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(non-Ewald) electrostatic summation methods was evaluated using |
| 546 |
< |
873,250 configurational energy differences. |
| 542 |
> |
Each of the seven system types (detailed in section \ref{sec:RepSims}) |
| 543 |
> |
were represented using 500 independent configurations. Thus, each of |
| 544 |
> |
the alternative (non-Ewald) electrostatic summation methods was |
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> |
evaluated using an accumulated 873,250 configurational energy |
| 546 |
> |
differences. |
| 547 |
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|
| 548 |
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Results and discussion for the individual analysis of each of the |
| 549 |
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system types appear in the supporting information, while the |
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NaCl crystal is composed of two different atom types, the average of |
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the two resulting power spectra was used for comparisons. Simulations |
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were performed under the microcanonical ensemble, and velocity |
| 625 |
< |
information was saved every 5 fs over 100 ps trajectories. |
| 625 |
> |
information was saved every 5~fs over 100~ps trajectories. |
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|
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\subsection{Representative Simulations}\label{sec:RepSims} |
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A variety of representative simulations were analyzed to determine the |
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relative effectiveness of the pairwise summation techniques in |
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reproducing the energetics and dynamics exhibited by {\sc spme}. We wanted |
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to span the space of modern simulations (i.e. from liquids of neutral |
| 632 |
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molecules to ionic crystals), so the systems studied were: |
| 628 |
> |
A variety of representative molecular simulations were analyzed to |
| 629 |
> |
determine the relative effectiveness of the pairwise summation |
| 630 |
> |
techniques in reproducing the energetics and dynamics exhibited by |
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> |
{\sc spme}. We wanted to span the space of typical molecular |
| 632 |
> |
simulations (i.e. from liquids of neutral molecules to ionic |
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> |
crystals), so the systems studied were: |
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\begin{enumerate} |
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\item liquid water (SPC/E),\cite{Berendsen87} |
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\item crystalline water (Ice I$_\textrm{c}$ crystals of SPC/E), |
