Diagrammatic Coupled Cluster Monte Carlo

Abstract

We propose a modified coupled cluster Monte Carlo algorithm that stochastically samples connected terms within the truncated Baker-Campbell-Hausdorff expansion of the similarity transformed Hamiltonian by construction of coupled cluster diagrams on the fly. Our new approach -diagCCMC -allows propagation to be performed using only the connected components of the similarity-transformed Hamiltonian, greatly reducing the memory cost associated with the stochastic solution of the coupled cluster equations. We show that for perfectly local, noninteracting systems, diagCCMC is able to represent the coupled cluster wavefunction with a memory cost that scales linearly with system size. The favorable memory cost is observed with the only assumption of fixed stochastic granularity and is valid for arbitrary levels of coupled cluster theory.Significant reduction in memory cost is also shown to smoothly appear with dissociation of a finite chain of helium atoms. This approach is also shown not to break down in the presence of strong correlation through the example of a stretched nitrogen molecule. Our novel methodology moves the theoretical basis of coupled cluster Monte Carlo closer to deterministic approaches. Graphical TOC EntryOver the last half-century the coupled cluster (CC) wavefunction Ansatz has proved remarkably effective at representing the solution of the Schrödinger equation in a polynomial scaling number of parameters while providing size-extensive and -consistent results. Despite reducing the full configuration interaction (FCI) N ! factorial scaling to polynomial, the computational cost of CC methods, measured in terms of both required CPU floating-point operations and memory, is still an issue. The coupled cluster with single and double substitutions (CCSD) and CCSD with perturbative triples correction (CCSD(T)) approximations provide a balance between computational cost and accuracy that has led to relatively wide adoption, but are eventually precluded for many large systems.Recent work has made great progress on this issue through application of various approximations, which enable calculations to be performed with reduced memory and computational costs. In particular, various approximations exploiting the locality of electron correlation allow calculations with costs asymptotically proportional to measures of system size.These include approaches based on orbital localisation, 1-39 molecular fragmentation, [40][41][42][43][44][45][46][47][48][49][50][51][52] and decompositions, such as resolution-of-the-identity, Cholesky or singular-value, of the two-electron integrals tensors. 19,20,[53][54][55][56][57][58] However, while providing large efficiencies in CCSD calculations, higher truncation levels will generally exceed available memory resources before such approximations are a reasonable proposition.In this letter we propose and demonstrate a coupled cluster-based projector Monte Carlo (MC) algorithm that enables automatic exploitation of the wavefunction sparsity for arbitrary excitation orders. Our met...

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“…We interpret the propagation in Equation for the similarity‐transformed Hamiltonian as the sampling of the algebraic expansion of the connected coupled‐cluster equations . This is equivalent to performing sampling in the space of diagrams , rather than in the space of determinants We have dubbed this approach diagrammatic coupled cluster Monte Carlo and we believe this approach will be useful in developing a practical route to CCMC response theory.…”