Premium
Unitary group approach to the many‐electron problem. I. Matrix element evaluation and shift operators
Author(s) -
Gould M. D.,
Chandler G. S.
Publication year - 1984
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.560250311
Subject(s) - matrix element , matrix (chemical analysis) , formalism (music) , element (criminal law) , unitary state , basis (linear algebra) , group (periodic table) , simple (philosophy) , unitary matrix , algebra over a field , mathematics , unitary group , pure mathematics , physics , quantum mechanics , chemistry , geometry , particle physics , art , musical , philosophy , epistemology , chromatography , political science , law , visual arts
This is the first paper in a series of three directed toward the evaluation of spin‐dependent Hamiltonians directly in the spin‐orbit basis. In this paper we present a new and complete derivation of the matrix elements of the U ( n ) generators in the electronic Gel'fand basis. The approach employed differs from previous treatments in that the matrix elements of nonelementary generators are obtained directly. A general matrix element formula is derived which explicitly demonstrates the segment level formalism obtained previously by Shavitt using different methods. A simple relationship between the matrix elements of raising and lowering generators is determined which indicates that in CI calculations, only the matrix elements of raising generators need be calculated. Some results on the matrix elements of products of two generators are also presented.