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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 Møller-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.

Stochastic Formulation of the Resolution of Identity: Application to Second Order Møller–Plesset Perturbation Theory