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New derivation and a k ‐particle generalization of SCF ‐type theories
Author(s) -
Kutzelnigg Werner
Publication year - 1980
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560180103
Subject(s) - generalization , unitary state , constructive , type (biology) , density matrix , hierarchy , mathematics , particle (ecology) , matrix (chemical analysis) , mathematical physics , hartree–fock method , physics , quantum mechanics , pure mathematics , quantum , mathematical analysis , chemistry , ecology , oceanography , process (computing) , chromatography , political science , computer science , economics , law , market economy , biology , geology , operating system
A hierarchy of necessary conditions that an exact density matrix of a pure state or an ensemble has to satisfy is derived, namely the hermiticity of certain operators F ( k ) . For k = 1 this reduces to the well‐known Hartree‐Fock condition. It is then shown that the k th set of conditions is equivalent to stationarity of the energy with respect to unitary k ‐particle transformations. k ‐Particle generalizations of Hartree‐Fock theory are then discussed both in the spirit of k ‐particle pseudoeigenvalue equations and in the framework of a Newton–Raphson‐type constructive scheme.