Grassmann extrapolation of density matrices for Born-Oppenheimer molecular dynamics

TL;DR

This paper introduces a novel Grassmann extrapolation method for density matrices in Born-Oppenheimer molecular dynamics, enabling more efficient density guesses while preserving physical constraints.

Contribution

It proposes a new bijective map on the density matrix manifold that allows linear extrapolation in tangent space, maintaining physical properties.

Findings

Improved extrapolation accuracy in BOMD simulations

Reduced computational cost for density matrix predictions

Effective application to multiscale QM/MM systems

Abstract

Born-Oppenheimer Molecular Dynamics (BOMD) is a powerful but expensive technique. The main bottleneck in a density functional theory bomd calculation is the solution to the Kohn-Sham (KS) equations, that requires an iterative procedure that starts from a guess for the density matrix. Converged densities from previous points in the trajectory can be used to extrapolate a new guess, however, the non-linear constraint that an idempotent density needs to satisfy make the direct use of standard linear extrapolation techniques not possible. In this contribution, we introduce a locally bijective map between the manifold where the density is defined and its tangent space, so that linear extrapolation can be performed in a vector space while, at the same time, retaining the correct physical properties of the extrapolated density using molecular descriptors. We apply the method to real-life, multiscale polarizable QM/MM.