Describing Strong Correlation with Block-Correlated Coupled Cluster Theory

Wang, Qingchun; Duan, Mingzhou; Xu, Enhua; Zou, Jingxiang; Li, Shuhua

doi:10.1021/acs.jpclett.0c02117

Cited by 18 publications

(32 citation statements)

References 34 publications

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“…28 While formal considerations of the present work apply to a general MR starting point, applications resort to a GVB reference. From this point of view, the present work contributes to the computational arsenal of GVB correction schemes, falling in line with previous studies based on, for example, perturbation theory, 42,43 linearized CC, 44 Block Correlated CC, 45 or the Extended Random Phase Approximation. 46,47 The forerunner of the present study applied the ring approximation in the same MR-CC context, based on a GVB reference.…”

Section: Introductionsupporting

confidence: 83%

Dressing of Vertices by Cumulants in Multi-Reference Coupled Cluster

Margócsy

Szabados

2021

J. Chem. Theory Comput.

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A new scheme is introduced in Multi-Reference (MR) Coupled Cluster (CC) based on the MR Generalized Normal Ordering (MRGNO) and the corresponding MR Generalized Wick Theorem (MRGWT) of Kutzelnigg and Mukherjee. The key element is the identification of a structure in MRGWT generated terms, facilitated by Goldstone diagram techniques. This allows for bundling the many terms of the MRGWT expansion and introduces a hierarchy in the equations that can be harnessed in devising approximations. One-and two-particle interaction vertices are found to be uniformly substituted for their counterpart dressed by density cumulants. This allows for a straightforward rewriting of the ordinary energy expression of CC with interaction dressed (id) one-and two-particle terms and reveals the presence of threeand higher-rank dressed interaction vertices too. Cumulants appearing out of dressed interaction vertices contribute to the amplitude equations and can be interpreted to have an amplitude dressing role. Dressing of one-and two-particle interaction vertices is the most straightforward to implement and does not hinder computational feasibility, provided that the reference function involves strictly limited active space sizes. The Generalized Valence Bond wave function, underlying pilot numerical tests, fulfills this criterion. Results on multiple bond breaking scenarios point to the need of stepping beyond one-and two-particle id. An extremely simple version of incorporating amplitude dressing in addition to one-and two-particle id is seen to cure the potential energy curves remarkably, stimulating further investigations along this line.

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Section: Introductionsupporting

confidence: 83%

Dressing of Vertices by Cumulants in Multi-Reference Coupled Cluster

Margócsy

Szabados

2021

J. Chem. Theory Comput.

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“…The coupled-cluster with single, double and perturbative triple excitations retained in the ansatz (known as CCSD(T)) is often referred to as the 'gold standard' of quantum chemistry where the correlations are not too strong [179], while other approximate coupled-cluster forms suitable for stronger correlation effects have also been developed (for recent examples, see Ref. [180,181]). The coupled cluster is also the motivation of the use of the unitary coupled cluster ansatz of VQE [130], where a similar structure of exponentiated excitations based around a reference configuration is constructed (see Sec.6.2.2), with modifications to ensure efficient use on a unitary set of quantum circuits.…”

Section: Efficient Approximate Wavefunction Parameterizations For Con...mentioning

confidence: 99%

The Variational Quantum Eigensolver: a review of methods and best practices

Tilly¹,

Chen²,

Cao³

et al. 2021

Preprint

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“…Jiménez-Hoyos and co-workers used a simple perturbation theory to capture this correlation. 50 Block correlated coupled cluster (BCCC) 52,59 , excitonic coupled cluster (XCC) 53,54 and the recently proposed cluster-CCSD (cCCSD) 55 use the coupled cluster ansatz in a TPS framework. The BCCC uses a generalized valence bond (GVB) reference while the XCC approach uses an approximate basis formed using a local Hamiltonian as the reference.…”

Section: Theorymentioning

confidence: 99%

“…The BCCC uses a generalized valence bond (GVB) reference while the XCC approach uses an approximate basis formed using a local Hamiltonian as the reference. 59 The cCCSD method uses the cMF reference but has not yet been extended to molecules. Similar to determinants, these coupled cluster based approaches in the TPS framework would also be much harder to extend to a multi-reference framework.…”

Section: Theorymentioning

confidence: 99%

Coupled electron pair-type approximations for tensor product state wavefunctions

Abraham,

Mayhall

2022

Preprint

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Size extensivity, defined as the correct scaling of energy with system size, is a desirable property for any many-body method. Traditional CI methods are not size extensive hence the error increases as the system gets larger. Coupled electron pair approximation (CEPA) methods can be constructed as simple extensions of truncated configuration interaction (CI) that ensures size extensivity. One of the major issues with the CEPA and its variants is that singularities arise in the amplitude equations when the system starts to be strongly correlated. In this work, we extend the traditional Slater determinant-based coupled electron pair approaches like CEPA-0, averaged coupled-pair functional (ACPF) and average quadratic coupled-cluster (AQCC) to a new formulation based on tensor product states (TPS). We show that a TPS basis can often be chosen such that it removes the singularities that commonly destroy the accuracy of CEPA-based methods. A suitable TPS representation can be formed by partitioning the system into separate disjoint clusters and forming the final wavefunction as the tensor product of the many body states of these clusters. We demonstrate the application of these methods on simple bond breaking systems such as CH4 and F2 where determinant based CEPA methods fail. We further apply the TPS-CEPA approach to stillbene isomerization and few planar π-conjugated systems. Overall the results show that the TPS-CEPA method can remove the singularities and provide improved numerical results compared to common electronic structure methods.

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Describing Strong Correlation with Block-Correlated Coupled Cluster Theory

Cited by 18 publications

References 34 publications

Dressing of Vertices by Cumulants in Multi-Reference Coupled Cluster

Dressing of Vertices by Cumulants in Multi-Reference Coupled Cluster

The Variational Quantum Eigensolver: a review of methods and best practices

Coupled electron pair-type approximations for tensor product state wavefunctions

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