Abstract
Ewald summation method, based on Non-Uniform FFTs (ENUF) to compute the electrostatic interactions and forces, is implemented in two different particle simulation schemes to model molecular and soft matter, in classical all-atom Molecular Dynamics and in Dissipative Particle Dynamics for coarse-grained particles. The method combines the traditional Ewald method with a non-uniform fast Fourier transform library (NFFT), making it highly efficient. It scales linearly with the number of particles as , while being both robust and accurate. It conserves both energy and the momentum to float point accuracy. As demonstrated here, it is straight- forward to implement the method in existing computer simulation codes to treat the electrostatic interactions either between point-charges or charge distributions. It should be an attractive alternative to mesh-based Ewald methods.
Highlights
Computer modeling and simulation of molecular systems is an established discipline rapidly expanding and widely used from Materials Science to Biological systems
ENUF: A Fast Method for Calculating Electrostatic Interactions In Section 2 we summarized known results and prepared the ground for the development of a fast method for Ewald summation using the discrete nonuniform fast Fourier transform (NDFT)
The customization of the window function used in the non-uniform fast Fourier transform library (NFFT) algorithm---Gaussian functions, dilated cardinal B-splines, Sinc functions, or Kaiser-Bessel functions---is currently achieved by recompiling the NFFT library and relinking the application
Summary
Computer modeling and simulation of molecular systems is an established discipline rapidly expanding and widely used from Materials Science to Biological systems. Collecting and dividing the diffuse and fluctuating electron densities inside and around molecules on single atomic sites are a crude but conceptually simple and effective approximation, since Coulomb’s law can be invoked This simplification comes at a price since the interactions between point charges stretch over very long distances. Our method combines the traditional Ewald summation technique with the NFFT to calculate electrostatic energies and forces in molecular computer simulations. By a suitable choice of parameters, ENUF can be made to behave as traditional Ewald summation but at the same time gives a computational complexity of (N log N ) , where N is the number of electrostatic interaction sites in the system.
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