Range-Separated Stochastic Resolution of Identity: Formulation and Application to Second Order Green's Function Theory

TL;DR

This paper introduces a range-separated stochastic resolution of identity method for electron repulsion integrals, significantly improving computational efficiency and accuracy in second-order Green's function calculations.

Contribution

It presents a novel range-separated stochastic resolution of identity approach that enhances efficiency and reduces statistical error in Green's function theory.

Findings

Achieves nearly two orders of magnitude speedup in computations.

Reduces statistical error compared to full stochastic methods.

Demonstrates effectiveness on hydrogen dimer chains.

Abstract

We develop a range-separated stochastic resolution of identity approach for the $4$-index electron repulsion integrals, where the larger terms (above a predefined threshold) are treated using a deterministic resolution of identity and the remaining terms are treated using a stochastic resolution of identity. The approach is implemented within a second-order Greens function formalism with an improved $O(N^3)$ scaling with the size of the basis set, $N$. Moreover, the range-separated approach greatly reduces the statistical error compared to the full stochastic version ({\it J. Chem. Phys.} {\bf 151}, 044144 (2019)), resulting in computational speedups of ground and excited state energies of nearly two orders of magnitude, as demonstrated for hydrogen dimer chains.