Stochastic Resolution of Identity for Correlation Energy Prediction via Doubles Connected Moments Expansion

TL;DR

This paper introduces a stochastic resolution-of-identity variant of the Doubles Connected Moments (DCM) method, significantly improving efficiency for large-scale correlation energy calculations while maintaining accuracy.

Contribution

The authors develop a stochastic DCM method that reduces computational scaling and enables practical large-system correlation energy predictions.

Findings

sRI-DCM reproduces conventional DCM results reliably.

sRI-DCM achieves an overall scaling of approximately O(N^{4.46}) for hydrogen chains.

The method is practical for systems with hundreds of electrons.

Abstract

The recently developed Doubles Connected Moments (DCM) expansion offers a tractable approach for computing correlation energy, exhibiting an noniterative O(N^6) scaling with system size N. Benchmark calculations on a set of molecules demonstrate that the DCM can outperform CCSD in terms of accuracy. To further enhance its efficiency, we present a stochastic variant of DCM by introducing a stochastic resolution-of-identity (sRI) technique, which decomposes the essential four-index intermediates. The resulting sRI-DCM scheme only involves one O(N^6) step, while all other steps do not exceed O(N^4) at each recursion, and reliably reproduces the results of conventional DCM. Our sRI-DCM achieves an overall experimental scaling of O(N^{4.46}) for series hydrogen dimer chains, demonstrating that it is attractive and practical for large systems containing hundreds of electrons.