Random Green's function method for large-scale electronic structure calculation

TL;DR

This paper introduces a linear-scaling random Green's function method for large-scale electronic structure calculations, enabling efficient and accurate simulations of extensive systems like water clusters with thousands of molecules.

Contribution

The paper presents a novel stochastic Green's function approach that reduces computational cost and improves applicability in large-scale electronic structure calculations.

Findings

Achieved ~1meV per H2O accuracy in total energy calculations.

Successfully applied to water clusters up to 9984 molecules.

Circumvents large Chebyshev expansions for density matrices.

Abstract

We report a linear-scaling random Green's function (rGF) method for large-scale electronic structure calculation. In this method, the rGF is defined on a set of random states to stochastically express the density matrix, and rGF is calculated with the linear-scaling computational cost. We show the rGF method is generally applicable to the nonorthogonal localized basis, and circumvent the large Chebyshev expansion for the density matrix. As a demonstration, we implement rGF with density-functional Tight-Binding method and apply it to self-consistently calculate water clusters up 9984 H2Os. We find the rGF method combining with a simple fragment correction can reach an error of ~1meV per H2O in total energy, compared to the deterministic calculations, due to the self-average. The development of rGF method advances the stochastic electronic structure theory to a new stage of the efficiency and applicability.