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

The recently developed Doubles Connected Moments (DCM) expansion offers a tractable approach for computing the correlation energy, exhibiting a noniterative O(N6) scaling with system size N. Benchmark calculations on a set of molecules demonstrate that 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(N6) step, while all other steps do not exceed O(N4) at each recursion and reliably reproduce the results of conventional DCM. Our sRI-DCM achieves an overall experimental scaling of O(N4.1) for series hydrogen dimer chains, demonstrating that it is attractive and practical for large systems containing hundreds of electrons.