Expeditious Stochastic Calculation of Random-Phase Approximation Energies for Thousands of Electrons in 3 Dimensions

TL;DR

This paper introduces a rapid stochastic method for calculating RPA correlation energies in large electronic systems, achieving near-linear scaling and enabling analysis of nanocrystals with thousands of electrons.

Contribution

The paper presents a novel stochastic approach for efficiently computing RPA energies with quadratic to near-linear scaling, suitable for large-scale systems.

Findings

Method scales quadratically but effectively linearly with system size.

RPA correlation energies per electron are size-independent in nanocrystals.

Demonstrated on nanocrystals with over 1500 electrons.

Abstract

A fast method is developed for calculating the Random-Phase-Approximation (RPA) correlation energy for density functional theory. The correlation energy is given by a trace over a projected RPA response matrix and the trace is taken by a stochastic approach using random perturbation vectors. The method scales, at most, quadratically with the system size but in practice, due to self-averaging, requires less statistical sampling as the system grows and the performance is close to linear scaling. We demonstrate the method by calculating the RPA correlation energy for cadmium selenide and silicon nanocrystals with over 1500 electrons. In contrast to 2nd order M{\o}ller-Plesset correlation energies, we find that the RPA correlation energies per electron are largely independent on the nanocrystal size.