In modern electronic structure, sparsity is a common property of matrices that facilitates cost reduction. This is particularly relevant to methods whose frontier cost limitation touches or falls behind the chemical problems that motivate them. For example, Fock-space ansatz methods that aim to treat strongly correlated bonds in catalysis can be limited by the difficulty of manipulating the two-electron integral tensor. Here in Variational Monte Carlo, we explore importance sampling that exploits the sparsity of this tensor to further the reach of such Fock-space methods. Specifically, in each Monte Carlo configuration, we sample the most difficult part of the energy contribution with the aid of a Cauchy-Schwartz bound on the two-electron integrals that grow increasingly sparse with system size. We reduce the formal scaling of the Fock-space local energy calculation from O(n4) to O(n3), and the overall Fock-space VMC scaling for a Jastrow Geminal Power from O(n5) to O(n4). This enables us to attain the same scaling as real-space VMC while keeping the convenience of Fock-space occupation-based operators. We also present preliminary data on the computational cost compared with deterministic local energy evaluations.

Sparse energy sampling in Fock-space variational Monte Carlo

254th National Meeting (2017)

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