Stochastic coupled cluster theory: Efficient sampling of the coupled cluster expansion

Scott, Charles; Thom, Alex J. W.

doi:10.1063/1.4991795

Cited by 35 publications

(76 citation statements)

References 71 publications

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“…In this letter, we propose a new way of obtaining accurate energetics equivalent to high-level CC calculations, even when electronic quasi-degeneracies and higher-than-two-body clusters become significant, at the small fraction of the computational cost, while preserving the black-box character (minimum input information) of conventional single-reference computations. The key idea is a merger of the deterministic methodology, abbreviated as CC(P ;Q) [21][22][23][24], with the stochastic FCI Quantum Monte Carlo (FCIQMC) [25,26] and CC Monte Carlo (CCMC) [27][28][29][30] approaches. As shown in Figs.…”

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confidence: 99%

Converging High-Level Coupled-Cluster Energetics by Monte Carlo Sampling and Moment Expansions

2017

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We propose a new approach to the determination of accurate electronic energies that are equivalent to the results of high-level coupled-cluster (CC) calculations. The approach is based on merging the CC(P;Q) formalism, which corrects energies obtained with an arbitrary truncation in the cluster operator, with the stochastic configuration interaction and CC ideas. The advantages of the proposed methodology are illustrated by molecular examples, where the goal is to recover the energetics obtained in the CC calculations with a full treatment of singly, doubly, and triply excited clusters.

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Converging High-Level Coupled-Cluster Energetics by Monte Carlo Sampling and Moment Expansions

2017

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“…wherever possible we aspire to have p diagram ∝ |w diagram |. 86 We will now demonstrate the ability of diagCCMC to recover energies at high levels of CC theory on the nitrogen molecule in a stretched geometry (r NN = 3.6 a 0 ). It has previously been shown that connected contributions up to hextuples are vital to obtaining high accuracy for this system.…”

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confidence: 86%

Diagrammatic Coupled Cluster Monte Carlo

Scott

Remigio

Crawford

et al. 2019

J. Phys. Chem. Lett.

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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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“…methods, resulting in the CCMC approaches, 66 where instead of sampling determinants by walkers, one samples amplitudes of "excitors" by "excips." [79][80][81] One can further speed-up the convergence of i-FCIQMC computations by the perturbative corrections built from the information discarded when applying initiator criteria. 82 The CIQMC and CCMC methodologies have several appealing features that are useful in the context of the ground-state considerations 67,77 and, as shown in this communication, in designing the stochastically driven excited-state EOMCC framework.…”

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Accurate excited-state energetics by a combination of Monte Carlo sampling and equation-of-motion coupled-cluster computations

Deustua

Yuwono

Piecuch

2019

The Journal of Chemical Physics

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The recently proposed idea of identifying the most important higher-than-doubly excited determinants in the ground-state coupled-cluster (CC) calculations through stochastic configuration interaction Quantum Monte Carlo propagations [J. E. Deustua et al., Phys. Rev. Lett. 119, 223003 (2017)] is extended to excited electronic states via the equation-of-motion (EOM) CC methodology. The advantages of the new approach are illustrated by calculations aimed at recovering the ground-and excited-state energies of the CH + molecule at the equilibrium and stretched geometries resulting from the EOMCC calculations with a full treatment of singles, doubles, and triples.

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Stochastic coupled cluster theory: Efficient sampling of the coupled cluster expansion

Cited by 35 publications

References 71 publications

Converging High-Level Coupled-Cluster Energetics by Monte Carlo Sampling and Moment Expansions

Converging High-Level Coupled-Cluster Energetics by Monte Carlo Sampling and Moment Expansions

Diagrammatic Coupled Cluster Monte Carlo

Accurate excited-state energetics by a combination of Monte Carlo sampling and equation-of-motion coupled-cluster computations

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