Consistent generalization of the Møller-Plesset partitioning to open-shell and multiconfigurational SCF reference states in many-body perturbation theory

Woliński, Krzysztof; Sellers, Harrell; Pulay, Péter

doi:10.1016/0009-2614(87)80448-7

Cited by 167 publications

(86 citation statements)

References 35 publications

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“…The effect of intruder states on perturbation theories has been discussed extensively in the literature. [21][22][23][24][25][26][27][28][29][30] In the case of CH 2 , the CASPT2 potential energy curve is artificially depressed as the angle approaches 180 deg. This produces an incorrect maximum in the potential energy curve around 155 deg.…”

Section: B Ch 2 Bend Potentialmentioning

confidence: 99%

A natural orbital diagnostic for multiconfigurational character in correlated wave functions

Gordon

Schmidt

Chaban

et al. 1999

The Journal of Chemical Physics

100

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The natural orbitals and their corresponding occupation numbers are constructed for several interesting problems to demonstrate that the existence of negative natural orbital occupation numbers for single reference correlation methods provides a simple diagnostic for the need for a multiconfigurational description of the wave function. Keywords Wave functions, Correlation functions, Physics demonstrations Disciplines Chemistry CommentsThe following article appeared in Journal of Chemical Physics 110 (1999): 4199, and may be found at doi:10.1063/1.478301. RightsWorks produced by employees of the U.S. Government as part of their official duties are not copyrighted within the U.S. The content of this document is not copyrighted. The natural orbitals and their corresponding occupation numbers are constructed for several interesting problems to demonstrate that the existence of negative natural orbital occupation numbers for single reference correlation methods provides a simple diagnostic for the need for a multiconfigurational description of the wave function. Authors

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Section: B Ch 2 Bend Potentialmentioning

confidence: 99%

A natural orbital diagnostic for multiconfigurational character in correlated wave functions

Gordon

Schmidt

Chaban

et al. 1999

The Journal of Chemical Physics

100

View full text Add to dashboard Cite

show abstract

“…[21][22][23] Analogues of these methods for multireference problems, such as multireference perturbation theory, [24][25][26][27][28][29] multireference configuration interaction, [30][31][32][33] and multireference coupled cluster and canonical transformation [34][35][36][37][38][39][40][41][42][43][44] theories have also been formulated. However, all of these multireference formulations are algebraically more opaque and computationally much more expensive than their singlereference counterparts.…”

Section: Introductionmentioning

confidence: 99%

A transformed framework for dynamic correlation in multireference problems

Sokolov

Chan

2015

The Journal of Chemical Physics

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We describe how multireference dynamic correlation theories can be naturally obtained as singlereference correlation theories in a canonically transformed frame. Such canonically transformed correlation theories are very simple and involve identical expressions to their single-reference counterparts. The corresponding excitations involve quasiparticles rather than the bare particles of the system. High-order density matrices (or their approximations) and the numerical metric instabilities common to multireference correlation theories do not appear. As an example, we formulate the Bogoliubov canonically transformed version of second-order Møller-Plesset perturbation theory and demonstrate its performance in H 2 , H 2 O, N 2 , and BeH 2 bond dissociation. C 2015 AIP Publishing LLC. [http://dx

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“…For the perturbation of wave functions consisting of several Slaterdeterminants various MRPT approaches have been proposed [21][22][23][24][25][26][27][28][29][30][31][32][33]. We discuss here the one developed in our laboratory [147] which was termed multi-configurational perturbation theory (MCPT).…”

Section: Multi-configurational Perturbation Theorymentioning

confidence: 99%

“…To name a few, we do not know the necessary and sufficient conditions for the convergence of the PT series, we do not have a general and robust method to deal with the case of quasidegenerate zero order, and there is no established method to fix the best partitioning. In addition, in many-body PT (MBPT), the handling of multi-reference zero order state(s) is an open issue [21][22][23][24][25][26][27][28][29][30][31][32][33], just like a clear and general theory to correct coupled-cluster type wave functions perturbatively [34][35][36][37][38][39][40][41][42][43][44][45]. The handling of symmetry in PT can also be a difficult task, especially when the zero order problem has lower symmetry than the perturbed problem, a situation one meets e.g.…”

Section: Introductionmentioning

confidence: 99%

Appendix to “Studies in Perturbation Theory”: The Problem of Partitioning

Śurján

Szabados

2004

Fundamental World of Quantum Chemistry

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The problem of partitioning in perturbation theory is reviewed starting from the classical works by Epstein and Nesbet or by Møller and Plesset, up to optimized partitionings introduced recently. Equations for optimal sets of level shift parameters are presented. Attention is paid to the specific problems appearing if the zero order solution is not a single Slater determinant. A special formalism for multi-configurational perturbation theories is outlined. It is shown that divergent perturbation series, like that of an anharmonic oscillator, can be converted to a convergent series by an appropriate redefinition of the zero order Hamiltonian via level shifts. The possible use of effective one-particle energies in many-body perturbation theory is also discussed. Partitioning optimization in a constant denominator perturbation theory leads to second order correction familiar from connected moment expansion techniques. Ionization potentials, computed perturbatively, are found sensitive to the choice of partitioning, and ordinary approximations are improved upon level shift optimization.

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Consistent generalization of the Møller-Plesset partitioning to open-shell and multiconfigurational SCF reference states in many-body perturbation theory

Cited by 167 publications

References 35 publications

A natural orbital diagnostic for multiconfigurational character in correlated wave functions

A natural orbital diagnostic for multiconfigurational character in correlated wave functions

A transformed framework for dynamic correlation in multireference problems

Appendix to “Studies in Perturbation Theory”: The Problem of Partitioning

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