Acceleration Schemes for Ab-Initio Molecular Dynamics and Electronic Structure Calculations

TL;DR

This paper introduces a damped second-order dynamics method that accelerates convergence in electronic structure calculations, analyzes stability factors affecting time step size, and proposes preconditioning techniques to eliminate instabilities, validated on silicon and carbon systems.

Contribution

It presents a novel damped second-order dynamics approach with improved convergence, and introduces preconditioning schemes to address charge sloshing in ab-initio molecular dynamics.

Findings

Faster convergence than steepest descent algorithms.

Preconditioning effectively eliminates large wavevector instabilities.

Numerical tests confirm efficiency on silicon and carbon systems.

Abstract

We study the convergence and the stability of fictitious dynamical methods for electrons. First, we show that a particular damped second-order dynamics has a much faster rate of convergence to the ground-state than first-order steepest descent algorithms while retaining their numerical cost per time step. Our damped dynamics has efficiency comparable to that of conjugate gradient methods in typical electronic minimization problems. Then, we analyse the factors that limit the size of the integration time step in approaches based on plane-wave expansions. The maximum allowed time step is dictated by the highest frequency components of the fictitious electronic dynamics. These can result either from the large wavevector components of the kinetic energy or from the small wavevector components of the Coulomb potential giving rise to the so called {\it charge sloshing} problem. We show how to eliminate large wavevector instabilities by adopting a preconditioning scheme that is implemented here for the first-time in the context of Car-Parrinello ab-initio molecular dynamics simulations of the ionic motion. We also show how to solve the charge-sloshing problem when this is present. We substantiate our theoretical analysis with numerical tests on a number of different silicon and carbon systems having both insulating and metallic character.