Multireference Brillouin—Wigner Coupled-Cluster Theory: Hilbert Space Approach

Mášik, Jozef; Hubač, Ivan

doi:10.1007/978-94-011-4894-8_16

Cited by 38 publications

(29 citation statements)

References 38 publications

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“…Such a cluster expansion Ansatz was first used by Jeziorski and Monkhorst in the context of the effective hamiltonian based stateuniversal multi-reference coupled-cluster (SU-MRCC) theory [2] and has later been exploited in the state-specific formulations too [9,10,36]. Since each φ µ has different sets of active orbitals, any specific core-to-particle excitation would lead to a different virtual determinant from each φ µ .…”

Section: Preliminariesmentioning

confidence: 99%

“…There are both non-perturbative and perturbative developments. There have been three formalisms [9,10,30,36], based on this idea. One of them is our SS-MRCC formalism [9,10] on which the present SS-MRPT [12,13] are based.…”

Section: Introductionmentioning

confidence: 99%

“…One of them is our SS-MRCC formalism [9,10] on which the present SS-MRPT [12,13] are based. There are two other SS formalisms [30,36] which bear kinship with our SS-MRCC formulation. A common aspect of all these formalisms is the use of the same virtual determinant (or, the CSFs) to generate equations for excitation amplitudes for operators exciting from each model functions.…”

Section: Introductionmentioning

confidence: 99%

“…Our SS-MRCC theory, however, is invariant with respect to rotations with the active and virtual orbitals separately, and thus is size-consistent in either localized or delocalised orbitals. A SS Brillouin-Wigner type of MRCC approach, proposed by Hubač and co-workers [36], has a simpler structure compared to the more elaborate expression of our SS-MRCC theory. It is however not rigorously size-extensive or size-consistent.…”

Section: Introductionmentioning

confidence: 99%

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State-specific Multi-reference Perturbation Theories with Relaxed Coefficients: Molecular Applications

Ghosh

Chattopadhyay

Jana

et al. 2002

IJMS

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We present in this paper two new versions of Rayleigh-Schrödinger (RS) and the Brillouin-Wigner (BW) state-specific multi-reference perturbative theories (SS-MRPT) which stem from our state-specific multi-reference coupled-cluster formalism (SS-MRCC), developed with a complete active space (CAS). They are manifestly sizeextensive and are designed to avoid intruders. The combining coefficients c µ for the model functions φ µ are completely relaxed and are obtained by diagonalizing an effective operator in the model space, one root of which is the target eigenvalue of interest. By invoking suitable partitioning of the hamiltonian, very convenient perturbative versions of the formalism in both the RS and the BW forms are developed for the second order energy. The unperturbed hamiltonians for these theories can be chosen to be of both Mφller-Plesset (MP) and Epstein-Nesbet (EN) type. However, we choose the corresponding Fock operator f µ for each model function φ µ , whose diagonal elements are used to define the unperturbed hamiltonian in the MP partition. In the EN partition, we additionally include all the diagonal direct and exchange ladders. Our SS-MRPT thus utilizes a multi-partitioning strategy. Illustrative numerical applications are presented for potential energy surfaces (PES) of the ground ( 1 Σ + ) and the first delta ( 1 ∆) states of CH + which possess pronounced multi-reference character. Comparison of the results with the corresponding full CI values indicates the efficacy of our formalisms.

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Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

State-specific Multi-reference Perturbation Theories with Relaxed Coefficients: Molecular Applications

Ghosh

Chattopadhyay

Jana

et al. 2002

IJMS

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“…Section 17.5.4). Historically, the derivation of the MR Brillouin -Wigner coupled-clusters method (BWCC), as originally proposed by Hubač,Čársky, and Mášik [97,98,139,140], was based on the state-specific Lippmann -Schwinger-like equation…”

Section: Brillouin -Wigner Mr CC Methodsmentioning

confidence: 99%

Multireference Coupled-Cluster Methods: Recent Developments

Paldus

Pittner

Čárský

2010

Challenges and Advances in Computational Chemistry and Physics

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Abstract:The objective of this paper is to provide an overview of various multi-reference (MR) coupled-cluster (CC) approaches, particularly those relating to our own research. Although MR CC methods have been around for almost three decades and much work has been expended on their development and implementation, no general purpose codes are presently available. In view of the complexity, inherent difficulties, and computational demands of both genuine valence and state universal (VU and SU) MR CC methods, attention has been directed towards the state selective or state specific (SS) approaches that focus on one state at a time. These methods are based on either the genuine MR CC formalism or on a singlereference (SR) CC Ansatz, in which higher-than-pair clusters are accounted for by relying on basic ideas of general MR approaches. This is achieved either internally by relying on CC or MBPT formalism or by exploiting some external source providing approximate values of these clusters and accomplished by either correcting equations yielding the cluster amplitudes or directly by evaluating the corrections to the CCSD energy. Nowadays there exists a whole plethora of such various approaches for handling of quasi-degenerate states with a various degree of MR character and our goal is to outline their basic features and comment on their pro's and con's, their usefulness and weaknesses, as well as point out their mutual relationship.

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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: Hilbert Space Approach

Cited by 38 publications

References 38 publications

State-specific Multi-reference Perturbation Theories with Relaxed Coefficients: Molecular Applications

State-specific Multi-reference Perturbation Theories with Relaxed Coefficients: Molecular Applications

Multireference Coupled-Cluster Methods: Recent Developments

Brillouin–Wigner Expansions for Molecular Electronic Structure

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