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Unitary group approach to the many‐electron problem. II. Adjoint tensor operators for U ( n )
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.560250312
Subject(s) - tensor (intrinsic definition) , matrix (chemical analysis) , basis (linear algebra) , rank (graph theory) , unitary transformation , mathematics , antisymmetric relation , unitary group , pure mathematics , spin (aerodynamics) , unitary state , group (periodic table) , physics , quantum mechanics , mathematical physics , combinatorics , chemistry , geometry , quantum , political science , law , chromatography , thermodynamics
In this paper we present a derivation of the U ( n ) adjoint coupling coefficients for the representations appropriate to many‐electron systems. Since the states of a many‐fermion system are to comprise the totally antisymmetric N th rank tensor representation of U (2 n ), the work of this paper enables the matrix elements of the U (2 n ) generators to be evaluated directly in the U ( n ) × U (2) (i.e., spin orbit) basis using their transformation properties as adjoint tensor operators. A connection between the adjoint coupling coefficients, as derived in this paper, and the matrix elements of certain (spin independent) two‐body operators is also presented. This indicates that in CI calculations, one may obtain the matrix elements of spin‐dependent operators from the known matrix elements of certain spin‐independent two‐body operators. In particular this implies a segment‐level formula for the matrix elements of the U (2 n ) generators in the spin‐orbit basis.