Title: A Stochastic Formulation of the Resolution of Identity: Application to Second Order Møller-Plesset Perturbation Theory,
Abstract: A stochastic orbital approach to the resolution of identity (RI)
approximation for 4-index 2-electron electron repulsion integrals (ERIs) is
presented. The stochastic RI-ERIs are then applied to M\o ller-Plesset
perturbation theory (MP2) utilizing a \textit{multiple stochastic orbital
approach}. The introduction of multiple stochastic orbitals results in an $N^3$
scaling for both the stochastic RI-ERIs and stochastic RI-MP2. We demonstrate
that this method exhibits a small prefactor and an observed scaling of
$N^{2.4}$ for a range of water clusters, already outperforming MP2 for clusters
with as few as 21 water molecules.