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

• Published in: Journal of chemical theory and computation Vol. 13; no. 10; pp. 4605 - 4610
• Main Authors: Takeshita, Tyler Y, de Jong, Wibe A, Neuhauser, Daniel, Baer, Roi, Rabani, Eran
• Format: Journal Article
• Language: English
• Published: United States American Chemical Society 10.10.2017
• Subjects: Basis functions; Chemistry; Clusters; Eris (dwarf planet); INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Molecular chains; Perturbation theory; Physics; Water chemistry
• ISSN: 1549-9618; 1549-9626
• DOI: 10.1021/acs.jctc.7b00343

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.