A fast and accurate computational method for the linear-combination-based isotropic periodic sum

Kazuaki Z Takahashi,Kenji Yasuoka,Takuma Nozawa

doi:10.1038/s41598-018-30364-2

Abstract

An isotropic periodic sum (IPS) is a powerful technique to reasonably calculate intermolecular interactions for wide range of molecular systems under periodic boundary conditions. A linear-combination-based IPS (LIPS) has been developed to attain computational accuracy close to an exact lattice sum, such as the Ewald sum. The algorithm of the original LIPS method has a high computational cost because it needs long-range interaction calculations in real space. This becomes a performance bottleneck for long-time molecular simulations. In this work, the combination of an LIPS and fast Fourier transform (FFT) was developed, and evaluated on homogeneous and heterogeneous molecular systems. This combinational approach of LIPS/FFT attained computational efficiency close to that of a smooth particle mesh Ewald while maintaining the same high accuracy as the original LIPS. We concluded that LIPS/FFT has great potential to extend the capability of IPS techniques for the fast and accurate computation of many types of molecular systems.

Highlights

Molecular dynamics (MD) simulations continue to evolve
To directly evaluate the accuracy of the electrostatic forces calculated by linear-combination-based IPS (LIPS)/fast Fourier transform (FFT), the following two steps were performed: (i) The instantaneous value of the electrostatic forces was calculated for each method using exactly the same coordinates of molecular systems that had been equilibrated using the smooth PME (SPME)
The results show that LIPS/FFT was in better agreement with the SPME than isotropic periodic sum (IPS)/DFFT

Summary

Introduction

Molecular dynamics (MD) simulations continue to evolve. Recent advances in computer power and algorithmic developments have made it possible to simulate a wide range of molecular systems with reasonable time and length scales for scientific and industrial applications[1,2,3,4,5]. The Barnes-Hut tree-code[54] and the fast multipole method[55] are lattice sum methods that use hierarchical tree structures These tree-based method can attain stronger scaling than FFT because it does not contain reciprocal space calculations that require all-to-all communications on massively parallel machines[53]. The LIPS provides periodic reaction fields that can design pseudo pair potentials in the range of extended IPS theory This pseudo pair potential has the high accuracy that achieves computational results close to an exact lattice sum. The algorithm of the original LIPS has a high computational cost because it requires long-range interaction calculations in real space This becomes a performance bottleneck for long-time molecular simulations using the LIPS. We conclude that LIPS/FFT has great potential to extend the capability of IPS techniques for the fast and accurate computation of many types of molecular systems

Methods

Results

Conclusion