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Improved treatment for matrix elements of spin‐dependent operators
Author(s) -
Qianer Zhang,
Xiangzhu Li
Publication year - 1989
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.560360305
Subject(s) - matrix (chemical analysis) , product (mathematics) , coupling (piping) , tensor product , representation (politics) , spin (aerodynamics) , tensor (intrinsic definition) , physics , mathematics , pure mathematics , expression (computer science) , symmetric group , matrix representation , element (criminal law) , quantum mechanics , mathematical physics , group (periodic table) , algebra over a field , chemistry , computer science , materials science , geometry , chromatography , politics , political science , law , metallurgy , thermodynamics , programming language
In this paper a general method for the evaluation of the matrix elements of spin‐dependent operators is proposed to improve the treatment primitively suggesteed by Cooper and Musher. This approach is largely based on the recent results which the present authors have achieved in the representation theory for the inner‐ and outer‐product reduction of the symmetric group. It is shown that the so‐called outer‐product coupling coefficients ( OPCC ) can be used to generalize the method for constructing the irreducible tensor operators of group S n . Together with the use of inner‐product coupling coefficients ( IPCC ), an expression for the matrix elements of spin‐dependent operators is presented as the product of a Racah coefficient for S n and a reduced matrix element which can be expressed in terms of IPCC, OPCC , and the related integrals. The treatment for one‐ and two‐electron spin‐dependent operators is discussed in detail.