An extension of the pairing theorem

Peter Karadakov

doi:10.1002/qua.560270607

An extension of the pairing theorem

Peter Karadakov

Chemistry

Research output: Contribution to journal › Article › peer-review

Abstract

An extended pairing scheme is presented which ensures the fulfillment of pairing conditions not only between the sets of occupied orbitals for spin α and for spin β, but also between their orthogonal complements, i.e., the sets of virtual orbitals for spin α and spin β, as well as between occupied orbitals for spin α and virtual orbitals for spin β and between virtual orbitals for spin α and occupied orbitals for spin β. It is shown that the extended pairing properties are suggested by some aspects of the construction of alternant molecular orbitals. The algorithm for singular value decomposition of rectangular matrices is proposed for use in practical implementations of the (extended) pairing scheme.

Original language	English
Pages (from-to)	699-707
Number of pages	9
Journal	INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY
Volume	27
Issue number	6
DOIs	https://doi.org/10.1002/qua.560270607
Publication status	Published - 1985

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10.1002/qua.560270607

http://dx.doi.org/10.1002/qua.560270607

Cite this

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title = "An extension of the pairing theorem",

abstract = "An extended pairing scheme is presented which ensures the fulfillment of pairing conditions not only between the sets of occupied orbitals for spin α and for spin β, but also between their orthogonal complements, i.e., the sets of virtual orbitals for spin α and spin β, as well as between occupied orbitals for spin α and virtual orbitals for spin β and between virtual orbitals for spin α and occupied orbitals for spin β. It is shown that the extended pairing properties are suggested by some aspects of the construction of alternant molecular orbitals. The algorithm for singular value decomposition of rectangular matrices is proposed for use in practical implementations of the (extended) pairing scheme.",

author = "Peter Karadakov",

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AU - Karadakov, Peter

PY - 1985

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N2 - An extended pairing scheme is presented which ensures the fulfillment of pairing conditions not only between the sets of occupied orbitals for spin α and for spin β, but also between their orthogonal complements, i.e., the sets of virtual orbitals for spin α and spin β, as well as between occupied orbitals for spin α and virtual orbitals for spin β and between virtual orbitals for spin α and occupied orbitals for spin β. It is shown that the extended pairing properties are suggested by some aspects of the construction of alternant molecular orbitals. The algorithm for singular value decomposition of rectangular matrices is proposed for use in practical implementations of the (extended) pairing scheme.

AB - An extended pairing scheme is presented which ensures the fulfillment of pairing conditions not only between the sets of occupied orbitals for spin α and for spin β, but also between their orthogonal complements, i.e., the sets of virtual orbitals for spin α and spin β, as well as between occupied orbitals for spin α and virtual orbitals for spin β and between virtual orbitals for spin α and occupied orbitals for spin β. It is shown that the extended pairing properties are suggested by some aspects of the construction of alternant molecular orbitals. The algorithm for singular value decomposition of rectangular matrices is proposed for use in practical implementations of the (extended) pairing scheme.

U2 - 10.1002/qua.560270607

DO - 10.1002/qua.560270607

M3 - Article

SN - 1097-461X

VL - 27

SP - 699

EP - 707

JO - INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY

JF - INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY

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