Stochastic Coupled Cluster Theory

Thom, Alex J. W.

doi:10.1103/physrevlett.105.263004

Cited by 101 publications

(147 citation statements)

References 13 publications

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“…This means population control bias is likely to be more of a problem for calculations which require smaller timesteps, such as strongly correlated systems, or calculations using coupled cluster Monte Carlo. 11 We also note that converging FCIQMC calculations to µE h accuracy has previously been attempted. 32 In this regime, the population control bias could potentially become similar in magnitude to the stochastic error.…”

Section: Discussionmentioning

confidence: 99%

Minimising biases in full configuration interaction quantum Monte Carlo

Vigor

Spencer

Bearpark

et al. 2015

The Journal of Chemical Physics

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Articles you may be interested in A deterministic alternative to the full configuration interaction quantum Monte Carlo method J. Chem. Phys. 145, 044112 (2016); 10.1063/1.4955109 Semi-stochastic full configuration interaction quantum Monte Carlo: Developments and application Approaching exact hyperpolarizabilities via sum-overstates Monte Carlo configuration interaction Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models Unbiased stochastic sampling of the one-and two-body reduced density matrices is achieved in full configuration interaction quantum Monte Carlo with the introduction of a second, "replica" ensemble of walkers, whose population evolves in imaginary time independently from the first and which entails only modest additional computational overheads. The matrices obtained from this approach are shown to be representative of full configuration-interaction quality and hence provide a realistic opportunity to achieve high-quality results for a range of properties whose operators do not necessarily commute with the Hamiltonian. A density-matrix formulated quasi-variational energy estimator having been already proposed and investigated, the present work extends the scope of the theory to take in studies of analytic nuclear forces, molecular dipole moments, and polarisabilities, with extensive comparison to exact results where possible. These new results confirm the suitability of the sampling technique and, where sufficiently large basis sets are available, achieve close agreement with experimental values, expanding the scope of the method to new areas of investigation. C 2015 AIP Publishing LLC. [http://dx.

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Section: Discussionmentioning

confidence: 99%

Minimising biases in full configuration interaction quantum Monte Carlo

Vigor

Spencer

Bearpark

et al. 2015

The Journal of Chemical Physics

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“…It is observed that CCMC calculations have a higher plateau than configuration interaction quantum Monte Carlo (CIQMC) calculations at the same truncation level. 39 It is likely that this is because the excips have to explore a larger effective Hilbert space than the psips in the equivalent CIQMC simulation, so more excips are required to make the annihilation rate high enough to suppress the in-phase signal.…”

Section: Discussionmentioning

confidence: 99%

The sign problem and population dynamics in the full configuration interaction quantum Monte Carlo method

Spencer

Blunt

Foulkes

2012

The Journal of Chemical Physics

109

187

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The recently proposed full configuration interaction quantum Monte Carlo method allows access to essentially exact ground-state energies of systems of interacting fermions substantially larger than previously tractable without knowledge of the nodal structure of the ground-state wave function. We investigate the nature of the sign problem in this method and how its severity depends on the system studied. We explain how cancellation of the positive and negative particles sampling the wave function ensures convergence to a stochastic representation of the many-fermion ground state and accounts for the characteristic population dynamics observed in simulations.

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“…In the CCMC and full configuration interaction quantum Monte Carlo (FCIQMC) approaches, a population of particles in Fock space represents the wavefunction and evolves according to simple rules of spawning, death, and annihilation. 83,87 For a CC Ansatz, unit particles may represent nonunit contributions to CC amplitudes by letting the intermediate normalisation condition vary with the population on the reference determi-…”

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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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Stochastic Coupled Cluster Theory

Cited by 101 publications

References 13 publications

Minimising biases in full configuration interaction quantum Monte Carlo

Minimising biases in full configuration interaction quantum Monte Carlo

The sign problem and population dynamics in the full configuration interaction quantum Monte Carlo method

Diagrammatic Coupled Cluster Monte Carlo

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