A random batch Ewald method for charged particles in the isothermal–isobaric ensemble

Abstract

We develop an accurate, highly efficient, and scalable random batch Ewald (RBE) method to conduct molecular dynamics simulations in the isothermal–isobaric ensemble (the NPT ensemble) for charged particles in a periodic box. After discretizing the Langevin equations of motion derived using suitable Lagrangians, the RBE method builds the mini-batch strategy into the Fourier space in the Ewald summation for the pressure and forces such that the computational cost is reduced to [Formula: see text] per time step. We implement the method in the Large-scale Atomic/Molecular Massively Parallel Simulator package and report accurate simulation results for both dynamical quantities and statistics for equilibrium for typical systems including all-atom bulk water and a semi-isotropic membrane system. Numerical simulations on massive supercomputing cluster are also performed to show promising central processing unit efficiency of the RBE.

A Screening Condition Imposed Stochastic Approximation for Long-Range Electrostatic Correlations

“…The obtained symmetry-preserving RBE (SRBE) algorithm now maintains the same O ( N ) complexity and the superscalability of the original RBE method but with an additional advantage of accounting for long-range electrostatic effects. The present finding highlights the superiority of the new version of the RBE-type method, making it promising to simulate a broader range of crucial problems as demonstrated before. , Consider a charged system of N particles located at r j for j = 1, ..., N in a cubic box of length L and volume V = L 3 . Under periodic boundary conditions, the electrostatic interaction among particles is usually evaluated by the Ewald summation, where the Coulomb kernel is split into the near and far parts for the convenience of computation 1 r = erfc ( α r ) r + erf ( α r ) r where α is a positive parameter with a dimension of inverse length, and erf(·) and erfc(·) are the error and complementary error functions, respectively.…”

“…13 These algorithms are communicationintensive because the involved Fast Fourier Transform (FFT) summation results in a scalability bottleneck for massively parallel computing of large-scale systems. 14 Recently, an essentially different approach for charged systems, the random batch Ewald (RBE) method, 15,16 has been proposed. The RBE is an Ewald-type algorithm that does not require the lattice summation and avoids the use of FFT.…”

“…The present finding highlights the superiority of the new version of the RBE-type method, making it promising to simulate a broader range of crucial problems as demonstrated before. 15,16 Consider a charged system of N particles located at r j for j = 1, ..., N in a cubic box of length L and volume V = L 3 . Under periodic boundary conditions, the electrostatic interaction among particles is usually evaluated by the Ewald summation, 50 where the Coulomb kernel is split into the near and far parts for the convenience of computation r r r r r…”

Pressure of Coulomb systems with volume-dependent long-range potentials

“…In particular, we analyze both the Ewald potential and the AAEP and show that the virial theorem and the differentiation of free energy lead to the same result for the pressure. We also show that the expression for the pressure in the recent paper [35] is incorrect. We derive the correct expression in which the pressure is completely defined by the potential energy.…”

“…Thus, f[U pair ] = (36) + (37) = −U pair . Now we show that criterion (35) for constant contributions in TCP and OCP is satisfied:…”