Stress tensor and constant pressure simulation for polarizable Gaussian multipole model

Abstract

Our previous article has established the theory of molecular dynamics (MD) simulations for systems modeled with the polarizable Gaussian multipole (pGM) electrostatics [Wei et al., J. Chem. Phys. 153(11), 114116 (2020)]. Specifically, we proposed the covalent basis vector framework to define the permanent multipoles and derived closed-form energy and force expressions to facilitate an efficient implementation of pGM electrostatics. In this study, we move forward to derive the pGM internal stress tensor for constant pressure MD simulations with the pGM electrostatics. Three different formulations are presented for the flexible, rigid, and short-range screened systems, respectively. The analytical formulations were implemented in the SANDER program in the Amber package and were first validated with the finite-difference method for two different boxes of pGM water molecules. This is followed by a constant temperature and constant pressure MD simulation for a box of 512 pGM water molecules. Our results show that the simulation system stabilized at a physically reasonable state and maintained the balance with the externally applied pressure. In addition, several fundamental differences were observed between the pGM and classic point charge models in terms of the simulation behaviors, indicating more extensive parameterization is necessary to utilize the pGM electrostatics.

FIG. 1.

The finite-difference validation of the analytical virial expressions in the xx direction. (a) is for the flexible case and (b) is for the rigid body case. x axis refers to the proportional changes of simulation box dimension in the x direction. The star on the y axis is the analytical virial value given by Eqs. (19) and (22), respectively. The finite-difference values were obtained using Eq. (4). Testing along the yy and zz directions are available in the supplementary material. An additional set of testing was also conducted for a 4096-water box, available in the supplementary material.

FIG. 2.

Time evolutions of density and pressure of the NPT simulation for the 512-water box. The red lines are the running averages of every 10 ps. The time evolutions of total energy and temperature are available in the supplementary material. The time evolutions of density, total energy, and temperature of the Monte Carlo pressure-regulated simulation are also available in the supplementary material.