A combined on-the-fly/interpolation procedure for evaluating energy values needed in molecular simulations

TL;DR

This paper introduces an on-the-fly interpolation algorithm for efficiently estimating potential energy values in molecular simulations, improving computational performance for harmonic and anharmonic systems.

Contribution

It presents a novel combined interpolation method with adaptive mesh updates, enhancing energy evaluation accuracy and efficiency in molecular dynamics and Monte Carlo simulations.

Findings

Effective in harmonic systems due to exactness property.

Improves performance in anharmonic systems with anisotropic mesh.

Validated on quartic oscillators and isotope effect calculations.

Abstract

We propose an algorithm for molecular dynamics or Monte Carlo simulations that uses an interpolation procedure to estimate potential energy values from energies and gradients evaluated previously at points of a simplicial mesh. We chose an interpolation procedure which is exact for harmonic systems and considered two possible mesh types: Delaunay triangulation and an alternative anisotropic triangulation designed to improve performance in anharmonic systems. The mesh is generated and updated on the fly during the simulation. The procedure is tested on two-dimensional quartic oscillators and on the path integral Monte Carlo evaluation of HCN/DCN equilibrium isotope effect.