Multireference Brillouin-Wigner Coupled-Cluster Theory. Single-root approach.

Mášik, Jozef; Hubač, Ivan

doi:10.1016/s0065-3276(08)60184-7

Cited by 153 publications

(57 citation statements)

References 89 publications

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“…We can also think of using the CISDt or CISDtq [7,120,122,123] approaches, in which triply and quadruply excited configurations of the single-reference CI method are selected via active orbitals, to construct wave functions |Ψ µ in Eq. (33). In either case, we should be able to significantly improve the quality of the SUMRCCSD results and reinforce a fully symmetric treatment of the manifolds of excitations corresponding to different reference configurations, which is broken by the SUMRCCSD and other SUMRCC approximations.…”

Section: (P)mentioning

confidence: 95%

“…(33) and considering the truncated MM-SUCC(m A , m B ) schemes will cause the resulting energies to be no longer strictly size extensive (in a sense of introducing the unlinked terms into the MM-SUMRCC energies). However, our experience with the CI-based singlereference MMCC methods [7,120,122,123] and the MBPT-based renormalized CC approaches, such as CR-CCSD(T) [7, 26, 117-119, 121, 132, 133], demonstrates that the presence of unlinked terms in the MMCC approximations does not have an effect on the excellent performance of the approximate MMCC schemes.…”

Section: ⊥(P)mentioning

confidence: 99%

“…The direct use of the final energy expressions in CC calculations, as is done in our MMCC theory [7,[118][119][120][121][122][123] and its multi-reference extension discussed here and in Ref. 117, which may result in the introduction of unlinked terms, is also exploited in the Brillouin-Wigner MRCC method [32][33][34][35][36][37]. As in the approximate MMCC case, the Brillouin-Wigner MRCC approach is not size extensive.…”

Section: ⊥(P)mentioning

confidence: 99%

“…In this paper, we focus on the genuine multi-reference CC (MRCC) theories, which are based on the concept of effective Hamiltonian acting in a multi-dimensional reference or model space [4,6,[8][9][10][11][12] and which use the exponential CC ansatz to parametrize the solutions of the generalized Bloch equation [8]. The state-specific (SS) MRCC methods [4,6], including the active-space CC approaches of Adamowicz, Piecuch, Bartlett, and their collaborators [13][14][15][16][17][18][19][20][21][22][23][24][25][26] and their more recent excited-state extensions [27][28][29], the SSMRCC approach of Mahapatra et al [30,31], and the highly promising Brillouin-Wigner MRCC approach [32][33][34][35][36][37], will not be discussed in this work, although the similarity of the wave function ansatz used in the genuine state-universal MRCC theory [4,6,, considered in this paper, and the form of the wave function exploited by the SSMRCC and Brillouin-Wigner MRCC approaches of Refs. 30, 31 and 32-37, respectively, should be noted.…”

Section: Introductionmentioning

confidence: 99%

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The State-Universal Multi-Reference Coupled-Cluster Theory: An Overview of Some Recent Advances

Piecuch

Kowalski

2002

IJMS

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Some recent advances in the area of multi-reference coupled-cluster theory of the state-universal type are overviewed. An emphasis is placed on the following new developments: (i) the idea of combining the state-universal multi-reference coupled-cluster singles and doubles method (SUMRCCSD) with the multi-reference many-body perturbation theory (MRMBPT), in which cluster amplitudes of the SUM-RCCSD formalism that carry only core and virtual orbital indices are replaced by their first-order MRMBPT estimates; and (ii) the idea of combining the recently proposed method of moments of coupled-cluster equations with the SUMRCC formalism. It is demonstrated that the new SUMRCCSD(1) method, obtained by approximating the SUMRCCSD cluster amplitudes carrying only core and virtual orbital indices by their first-order MRMBPT values, provides the results that are comparable to those obtained with the complete SUMRCCSD approach.

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Section: (P)mentioning

confidence: 95%

Section: ⊥(P)mentioning

confidence: 99%

Section: ⊥(P)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The State-Universal Multi-Reference Coupled-Cluster Theory: An Overview of Some Recent Advances

Piecuch

Kowalski

2002

IJMS

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“…a MRCEPA or MR(SC) 2 CI) formalism is not an easy task 29,30 . If one lets aside the MRCC methods that attribute a specific role to a single reference 31 , a few state-specific strictly multi-reference CC methods have been proposed, one by one of the authors and collaborators 1 , another one by Mukherjee and coworkers 32 , a third one in a Brillouin Wigner context 33,34 . We return here on the first proposal which had only be tested on a single problem.…”

Section: Introductionmentioning

confidence: 99%

A simple approach to the state-specific MR-CC using the intermediate Hamiltonian formalism

Giner

David

Scemama

et al. 2016

The Journal of Chemical Physics

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The multi-reference Coupled Cluster method first proposed by Meller et al (J. Chem. Phys. 1996) 1 has been implemented and tested. Guess values of the amplitudes of the single and double excitations (thê T operator) on the top of the references are extracted from the knowledge of the coefficients of the Multi Reference Singles and Doubles Configuration Interaction (MRSDCI) matrix. The multiple parentage problem is solved by scaling these amplitudes on the interaction between the references and the Singles and Doubles. Then one proceeds to a dressing of the MRSDCI matrix under the effect of the Triples and Quadruples, the coefficients of which are estimated from the action ofT 2 . This dressing follows the logics of the intermediate effective Hamiltonian formalism. The dressed MRSDCI matrix is diagonalized and the process is iterated to convergence. The method is tested on a series of benchmark systems from Complete Active Spaces (CAS) involving 2 or 4 active electrons up to bond breakings. The comparison with Full Configuration Interaction (FCI) results shows that the errors are of the order of a few milli-hartree, five times smaller than those of the CASSDCI. The method is totally uncontracted, parallelizable, and extremely flexible since it may be applied to selected MR and/or selected SDCI. Some potential generalizations are briefly discussed.

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Brillouin–Wigner Expansions for Molecular Electronic Structure

Hubač

Wilson

1998

Encyclopedia of Computational Chemistry

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The use of Brillouin–Wigner expansions in describing electron correlation effects in systems requiring the use of a multireference formalism is described. Brillouin–Wigner‐based methods avoid the intruder state problem which plagues Rayleigh–Schrödinger‐based methods. Such methods can be applied to many‐body systems either (i) by applying the Brillouin–Wigner expansion to solve the equations of an explicitly many‐body method; or (ii) by developing a posteriori corrections. The Brillouin–Wigner coupled cluster theory is presented in both its single reference and multireference forms. Single and multireference configuration interaction expansions are described together with the accompanying a posteriori correction procedures.

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Multireference Brillouin-Wigner Coupled-Cluster Theory. Single-root approach.

Cited by 153 publications

References 89 publications

The State-Universal Multi-Reference Coupled-Cluster Theory: An Overview of Some Recent Advances

The State-Universal Multi-Reference Coupled-Cluster Theory: An Overview of Some Recent Advances

A simple approach to the state-specific MR-CC using the intermediate Hamiltonian formalism

Brillouin–Wigner Expansions for Molecular Electronic Structure

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