How to Convert SPME to P3M: Influence Functions and Error Estimates

被引:20
作者
Ballenegger, V. [1 ]
Cerda, J. J. [2 ]
Holm, C. [3 ]
机构
[1] Univ Franche Comte, Inst UTINAM, UMR 6213, F-25030 Besancon, France
[2] Univ Illes Balears, Inst Fis Interdisciplinar & Sistemas Complejos, IFISC CSIC UIB, E-07122 Palma De Mallorca, Spain
[3] Univ Stuttgart, Inst Comp Phys, D-70569 Stuttgart, Germany
关键词
PARTICLE MESH EWALD; MOLECULAR-DYNAMICS; SIMULATION; SUMS; PACKAGE; MATTER;
D O I
10.1021/ct2001792
中图分类号
O64 [物理化学(理论化学)、化学物理学];
学科分类号
070304 ; 081704 ;
摘要
We demonstrate explicitly how the two seemingly different particle mesh Ewald methods, the smooth particle mesh Ewald (SPME) and the particle particle particle mesh (P3M), can be mathematically transformed into each other. This allows us in particular to convert the error estimate of the P3M method in the energy-conserving scheme (also known as "P3M with analytic differentiation") into an error estimate for the SPME method, via a simple change of the lattice Green function. Our error estimate is valid for any values of the SPME parameters (mesh size, spline interpolation order, Ewald splitting parameter, real-space cutoff distance), including odd orders of splines. The problem with the self-forces is avoided thanks to an analytical formula that allows to subtract them directly within the particle mesh calculation. Plots of the accuracy of the SPME forces are provided for a wide range of parameter values. The main use of the error estimate is to allow simulation program to scan quickly the multidimensional parameter space to find the best set of parameters to achieve a target accuracy at the smallest computational cost. As a byproduct, we show how a SPME code can be transformed into a P3M version by changing a few lines of code. We demonstrate also that the P3M lattice Green function can be approximated by a closed farm expression, computable on-the-fly, that provides essentially the same accuracy as the full function.
引用
收藏
页码:936 / 947
页数:12
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