On convergence guarantees for the multi-configuration self-consistent field theory

Wood, Melvyn H.; Veillard, A.

doi:10.1080/00268977300101921

Cited by 42 publications

(4 citation statements)

References 25 publications

(39 reference statements)

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“…One cannot prove that the proposed sequential diagonalization technique will converge to the same solution as obtained in the other approaches. However, the same characterizes any of the computational techniques for the MCSCF theory currently in use [34]. The present technique is obviously very convenient from the point of view of the perturbation MC SCF calculations, but its detailed justification should be sought for in an extensive numerical study.…”

Section: Appendixmentioning

confidence: 93%

Analytic techniques for the coupled multiconfiguration SCF perturbation theory

Jaszuński

Sadlej

1977

Int J of Quantum Chemistry

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AbstractsThe perturbation theory based on the paired excitation multiconfiguration self-consistent field approach of Clementi and Veillard is considered. The coupled first-order perturbed orbital equations are analysed and an appropriate computational scheme for their solution is discussed. The proposed computational scheme is analogous to the technique employed for the solution of the coupled Hartree-Fock equations in the one-configuration approximation. However, because of the presence of nondiagonal Lagrangian multipliers and the use of different one-electron operators for different orbitals, the present scheme raises some new computational problems. In this context a new technique for the solution of the unperturbed multiconfiguration self-consistent field equations is proposed. A simple illustration of the superiority of the multiconfiguration perturbation approach with respect to the ordinary coupled Hartree-Fock scheme is given. Also the validity of the variation formulation of the presented scheme and its relation to the finite-field approach are discussed. La theorie des perturbations fondte sur le proctde MC-SCF avec des excitations appariees de Clementi et Veillard est discutee. Les equations coupltes du premier ordre pour les orbitales perturbtes sont analystes et un schtma de calcul convenable pour leur solution est discutt. Ce schtma est analogue au procCdC employe pour la solution des tquatidns de Hartree-Fock coupltes dans le cas d'une seule configuration. Cependant B cause des multiplicateurs de Lagrange nondiagonaux et de l'emploi d'op6rateurs a un Clectron difftrents pour des orbitales difftrentes, le schtma propost prtsente quelques probltmes de calcul nouveaux. Un p r o d d t nouveau pour la solution des tquations MC-SCF non perturbees est propose. On donne une illustration simple de la superiorit6 d e la mtthode MC perturbative en comparaison avec le schema Hartree-Fock couplt ordinaire. La validitt de la formulation variationnelle du schtma proposC ici et sa relation avec le p r o d d t avec un champ fini son discuttes. Die auf das Mc-ScF-Verfahren mit Paaranregungen basierende Storungstheorie von Clementi und Veillard wird diskutiert. Die gekoppelten Gleichungen erster Ordnung fur die gestorten Orbitale werden analysiert und ein angemessenes Rechnungsverfahren fur ihre Liisung wird diskutiert. Dasvorgeschlagene Verfahren ist zu dem analog, das fur die Liisung der gekoppelten Hartree-Fock-Gleichungen im Einkonfigurationenfall angewandt wird. Wegen der nicht-diagonalen Lagrange-Multiplikatoren und der Venvendung von verschiedenen Einelektronoperatoren fur verschiedene Orbitale weist aber das hier vorgeschlagene Verfahren gewisse neue Berechnungsprobleme auf. Ein neues Verfahren fur die Liisung der ungestorten Mc-scF-Gleichungen wird vorgeschlagen. Eine einfache Illustration der Uberlegenheit des multikonfigurationellen Storungsverfahrens mit Riicksicht auf die iiblichen gekoppelten Hartree-Fock-Gleichungen wird gegeben. Die Gultigkeit der Variationsformulierung des prasentierten Schemas und ...

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Section: Appendixmentioning

confidence: 93%

Analytic techniques for the coupled multiconfiguration SCF perturbation theory

Jaszuński

Sadlej

1977

Int J of Quantum Chemistry

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“…In the levelshifting method proposed [1] the off-diagonal elements in the first term of equation (5) always vanish and Brillouin condition holds. We can set up a similar MHF operator as equation (7) for Wood and Veillard's extension to the multi-configuration SCF equation [4].…”

Section: Modified Hartree-fock Equationsmentioning

confidence: 99%

“…Pongor [3] applauded their method. Wood and Veillard [4] extended their method to the multi-configuration SCF equation.…”

mentioning

confidence: 98%

Equivalence of Saunders' level-shifting method for Hartree-Fock equations and expansion method for modified Hartree-Fock equations

Matsuoka

1975

Molecular Physics

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“…To carry out orbital optimization, we proceed from the energy expression Eq. ( 5 ) where the coefficients are defined by…”

Section: A T H E Cmc Scf Approachmentioning

confidence: 99%

Computation scheme for optimizing multiconfigurational wave‐functions

Kuprievich¹,

Klymenko²

1976

Int J of Quantum Chemistry

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Sciences of the Ukrainian SSR, Metrologicheskaya str. 14-b,252130, Kiev-130, U.S.S.R. AbStTaCt. 5A computation scheme is proposed to determine the wave-functions of molecular systems within the framework of the CMC SCF theory and the APSG SCF approach. The orbital optimization is carried out by the refined first-order one-electron Hamiltonian method. Explicit expressions of the first and second energy derivatives are obtained. In the suggested scheme all the calculations are based on using the matrices of the "partial" Coulomb and the exchange operators constructed over the orbitals at the current iteration cycle.Un proddt de calcul est propost pour dtterminer les fonctions d'onde de systbmes moltculaires dans le cadre de la thtorie CMC SCF et la mtthode APSG SCF. Les orbitales sont optimisdes par la mtthode raffinte du Hamiltonian a un Clectron du premier ordre. Des expressions explicites des dtrivtes premibre et seconde de I'energie sont obtenues. Dans le proctdt propost ici tous les calculs sont basts sur l'ltmploi des matrices des operateurs de Coulomb et d'tchange "partiels", construits a partir des orbitales dans le cycle d'itkration courant.Ein Berechnungsverfahren wird vorgeschlagen um Wellenfunktionen fur molekulare Systeme im Rahmen der CMC scF-Theorie und der APSG scF-Methode zu bestimmen. Die Orbitaloptimisierung wird mittels der verfeinerten Methode mit einem Hamiltonoperator erster Ordnung ausgefuhrt. Explizite Ausdriicke fur die erste und zweite Energieableitungen werden erhalten. In dem hier vorgeschlagenen Verfahren basieren alle Rechnungen auf die Anwendung von Matrizen der "partiellen" Coulomb-und Austauschoperatoren, die mit den Orbitalen in dem laufenden Iterationszyklus konstruiert werden.

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On convergence guarantees for the multi-configuration self-consistent field theory

Abstract: A discussion of the MC-SCF theory of Veillard and Clemenfi is given and the conditions for the guaranteed convergence of the energy formulated. A brief description of the computer programme which has been written is included, together with a simple numerical application of the method.

Cited by 42 publications

References 25 publications

Analytic techniques for the coupled multiconfiguration SCF perturbation theory

Analytic techniques for the coupled multiconfiguration SCF perturbation theory

Equivalence of Saunders' level-shifting method for Hartree-Fock equations and expansion method for modified Hartree-Fock equations

Computation scheme for optimizing multiconfigurational wave‐functions

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