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

Abstract

The random-phase approximation with second-order screened exchange (RPA+SOSEX) is a model of electron correlation energy with two caveats: its accuracy 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 a new self-consistent field that approximates Brueckner coupled-cluster doubles (BCCD) theory with RPA+SOSEX, referred to as Brueckner RPA (BRPA) theory. The algorithm comparably reduces the scaling of second-order M$\mathrm{ø}$ller-Plesset (MP2) perturbation theory with smaller cost prefactors than RPA+SOSEX. Within a semiempirical model, we study H${}_2$ dissociation to test accuracy and H${}_n$ rings to verify scaling.

15 pages, 2 figures, 2 tables, 6 algorithms

References in corpus (4)

• Jastrow correlation factor for atoms, molecules, and solids
• The Ground State Correlation Energy of the Random Phase Approximation from a Ring Coupled Cluster Doubles Approach
• Bond Breaking and Bond Formation: How Electron Correlation is Captured in Many-Body Perturbation Theory and Density-Functional Theory
• Cubic-scaling algorithm and self-consistent field for the random-phase approximation with second-order screened exchange

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• Lowering of the complexity of quantum chemistry methods by choice of representation
• Minimax rational approximation of the Fermi-Dirac distribution
• Staggered mesh method for correlation energy calculations of solids: Random phase approximation in direct ring coupled cluster doubles and adiabatic connection formalisms
• The Enduring Relevance of Semiempirical Quantum Mechanics
• Block Tensor Decomposition: A dual grid scheme with formal O(N3) for THC decomposition of molecular systems
• Minimax separation of the Cauchy kernel