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The random-phase approximation with second-order screened exchange(RPA+SOSEX) is a model of electron correlation energy with two caveats: itsaccuracy depends on an arbitrary choice of mean field, and it scales as$\mathcal{O}(n^5)$ operations and $\mathcal{O}(n^3)$ memory for $n$ electrons.We derive a new algorithm that reduces its scaling to $\mathcal{O}(n^3)$operations and $\mathcal{O}(n^2)$ memory using controlled approximations and anew self-consistent field that approximates Brueckner coupled-cluster doubles(BCCD) theory with RPA+SOSEX, referred to as Brueckner RPA (BRPA) theory. Thealgorithm comparably reduces the scaling of second-orderM$\mathrm{{\o}}$ller-Plesset (MP2) perturbation theory with smaller costprefactors than RPA+SOSEX. Within a semiempirical model, we study H$_2$dissociation to test accuracy and H$_n$ rings to verify scaling.

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