Accelerated density matrix expansions for Born-Oppenheimer molecular dynamics

TL;DR

This paper introduces an accelerated polynomial expansion method for constructing the density matrix in quantum molecular dynamics, significantly reducing computational costs by improving the conditioning phase of the recursive expansion.

Contribution

It presents a novel acceleration scheme that extracts interior eigenvalue estimates from the recursive expansion with minimal additional cost, enhancing efficiency in density matrix calculations.

Findings

Significant reduction in computational effort during density matrix construction.

Effective extraction of eigenvalue estimates from recursive expansions.

Improved conditioning phase leads to faster quantum molecular dynamics simulations.

Abstract

An accelerated polynomial expansion scheme to construct the density matrix in quantum mechanical molecular dynamics simulations is proposed. The scheme is based on recursive density matrix expansions, e.g. [Phys. Rev. B. 66 (2002), p. 155115], which are accelerated by a scale-and-fold technique [J. Chem. Theory Comput. 7 (2011), p. 1233]. The acceleration scheme requires interior eigenvalue estimates, which may be expensive and cumbersome to come by. Here we show how such eigenvalue estimates can be extracted from the recursive expansion by a simple and robust procedure at a negligible computational cost. Our method is illustrated with density functional tight-binding Born-Oppenheimer molecular dynamics simulations, where the computational effort is dominated by the density matrix construction. In our analysis we identify two different phases of the recursive polynomial expansion, the conditioning and purification phases, and we show that the acceleration represents an improvement of the conditioning phase, which typically gives a significant reduction of the computational cost.