Cubic-scaling algorithm and self-consistent mean field for the random-phase approximation with second-order screened exchange

The random-phase approximation including second-order screened exchange (RPA+SOSEX) is an accurate model of electron correlation energy with two caveats. Its accuracy depends on an arbitrary mean field choice and its scaling of $\mathcal{O}$($n^5$) operations and $\mathcal{O}$($n^3$) memory for $n$ electrons cannot compete with the $\mathcal{O}$($n^3$) operations and $\mathcal{O}$($n^2$) memory scaling of density functional theory (DFT). We rederive RPA+SOSEX as an approximation of the Brueckner doubles coupled-cluster (BCCD) equations, which produces a self-consistent mean field and other model corrections. In addition, we present a new algorithm for RPA+SOSEX that matches the scaling of DFT. We verify the accuracy of the new model on H$_2$ dissociation and the uniform electron gas and verify the reduced scaling of the new algorithm on H$_n$ rings. \\ \\ This work was supported by the Laboratory Directed Research and Development program at Sandia National Laboratories. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.