Stochastic Formulation of the Resolution of Identity: Application to Second Order Moller-Plesset Perturbation Theory

A stochastic orbital approach to the resolution of identity (RI) approximation for 4-index electron repulsion integrals (ERIs) is presented. The stochastic RI-ERIs are then applied to second order Moller-Plesset perturbation theory (MP2) utilizing a multiple stochastic orbital approach. The introduction of multiple stochastic orbitals results in an O(N-AO(3)) scaling for both the stochastic RI-ERIs and stochastic RI-MP2, N-AO being the number of basis functions. For a range of water clusters we demonstrate that this method exhibits a small prefactor and observed scalings of O(N-e(2.4)) for total energies and O(N-e(3.1)) for forces (N-e being the number of correlated electrons), outperforming MP2 for clusters with as few as 21 water molecules.