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

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 (J. Chem. Phys. 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.