An Efficient Approach to Ab Initio Monte Carlo Simulation

TL;DR

This paper introduces an optimized Nested Markov chain Monte Carlo method that efficiently computes equilibrium averages using accurate potentials like density functional theory, significantly reducing computational cost.

Contribution

The paper develops an on-the-fly optimization of the reference system in NMC, improving efficiency and robustness for ab initio simulations compared to previous methods.

Findings

Acceptance probabilities increased by up to 28 times with optimization.

Speedups were greater when using lower-quality reference potentials.

Efficiency comparable to standard ab initio molecular dynamics.

Abstract

We present a Nested Markov chain Monte Carlo (NMC) scheme for building equilibrium averages based on accurate potentials such as density functional theory. Metropolis sampling of a reference system, defined by an inexpensive but approximate potential, was used to substantially decorrelate configurations at which the potential of interest was evaluated, thereby dramatically reducing the number needed to build ensemble averages at a given level of precision. The efficiency of this procedure was maximized on-the-fly through variation of the reference system thermodynamic state (characterized here by its inverse temperature $\beta^0$), which was otherwise unconstrained. Local density approximation (LDA) results are presented for shocked states of argon at pressures from 4 to 60 GPa, where - depending on the quality of the reference system potential - acceptance probabilities were enhanced by factors of 1.2-28 relative to unoptimized NMC. The optimization procedure compensated strongly for reference potential shortcomings, as evidenced by significantly higher speedups when using a reference potential of lower quality. The efficiency of optimized NMC is shown to be competitive with that of standard ab initio molecular dynamics in the canonical ensemble.