Constant denominator perturbative schemes and the partitioning technique

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10 Citations (Scopus)

Abstract

With the aid of Löwdin's partitioning theory, an infinite series for the eigenvalue of the Schrödinger equation is derived which does not contain energy differences in denominators. The resulting formulae are compared to those of constant denominator methods, such as perturbation theory within the Unsøld approximation and the connected moment expansion (CMX). The Unsold formulae are easily obtained from partitioning theory by a suitable choice of the zero order Hamiltonian. Optimizing the value of the energy denominator using the first order wave function in a size-consistent way, the third order Unsold correction vanishes, and the corresponding energy correction formula of the CMX is recovered at the second order.

Original languageEnglish
Pages (from-to)20-26
Number of pages7
JournalInternational Journal of Quantum Chemistry
Volume90
Issue number1
DOIs
Publication statusPublished - okt. 5 2002

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Hamiltonians
Wave functions
moments
expansion
energy
eigenvalues
perturbation theory
wave functions
approximation

ASJC Scopus subject areas

  • Physical and Theoretical Chemistry

Cite this

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title = "Constant denominator perturbative schemes and the partitioning technique",
abstract = "With the aid of L{\"o}wdin's partitioning theory, an infinite series for the eigenvalue of the Schr{\"o}dinger equation is derived which does not contain energy differences in denominators. The resulting formulae are compared to those of constant denominator methods, such as perturbation theory within the Uns{\o}ld approximation and the connected moment expansion (CMX). The Unsold formulae are easily obtained from partitioning theory by a suitable choice of the zero order Hamiltonian. Optimizing the value of the energy denominator using the first order wave function in a size-consistent way, the third order Unsold correction vanishes, and the corresponding energy correction formula of the CMX is recovered at the second order.",
keywords = "Connected moment expansion, Constant-denominator perturbation theory, Multi-reference perturbation theory, Optimized partitioning, Quasi-degeneracy perturbation theory",
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AU - Surján, P.

AU - Szabados, A.

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N2 - With the aid of Löwdin's partitioning theory, an infinite series for the eigenvalue of the Schrödinger equation is derived which does not contain energy differences in denominators. The resulting formulae are compared to those of constant denominator methods, such as perturbation theory within the Unsøld approximation and the connected moment expansion (CMX). The Unsold formulae are easily obtained from partitioning theory by a suitable choice of the zero order Hamiltonian. Optimizing the value of the energy denominator using the first order wave function in a size-consistent way, the third order Unsold correction vanishes, and the corresponding energy correction formula of the CMX is recovered at the second order.

AB - With the aid of Löwdin's partitioning theory, an infinite series for the eigenvalue of the Schrödinger equation is derived which does not contain energy differences in denominators. The resulting formulae are compared to those of constant denominator methods, such as perturbation theory within the Unsøld approximation and the connected moment expansion (CMX). The Unsold formulae are easily obtained from partitioning theory by a suitable choice of the zero order Hamiltonian. Optimizing the value of the energy denominator using the first order wave function in a size-consistent way, the third order Unsold correction vanishes, and the corresponding energy correction formula of the CMX is recovered at the second order.

KW - Connected moment expansion

KW - Constant-denominator perturbation theory

KW - Multi-reference perturbation theory

KW - Optimized partitioning

KW - Quasi-degeneracy perturbation theory

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