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Matrix elements of U (2 n ) generators in a multishell spin–orbit basis. II. The two‐shell nonzero shift ACCs and U (2 n ) generator MEs
Author(s) -
Burton P. J.,
Gould M. D.
Publication year - 1998
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/(sici)1097-461x(1998)66:5<345::aid-qua2>3.0.co;2-v
Subject(s) - basis set , basis (linear algebra) , series (stratigraphy) , shell (structure) , generator (circuit theory) , matrix (chemical analysis) , spin–orbit interaction , open shell , unitary group , orbit (dynamics) , perturbation theory (quantum mechanics) , quantum mechanics , physics , mathematics , unitary state , chemistry , geometry , density functional theory , materials science , paleontology , power (physics) , engineering , chromatography , political science , law , composite material , biology , aerospace engineering
This is the second in a series of articles whose ultimate goal is the evaluation of the matrix elements (MEs) of the U (2 n ) generators in a multishell spin–orbit basis. This extends the existing unitary group approach to spin‐dependent configuration interaction (CI) and many‐body perturbation theory calculations on molecules to systems where there is a natural partitioning of the electronic orbital space. As a necessary preliminary to obtaining the U (2 n ) generator MEs in a multishell spin–orbit basis, we must obtain a complete set of adjoint coupling coefficients for the two‐shell composite Gelfand–Paldus basis. The zero‐shift coefficients were obtained in the first article of the series. In this article, we evaluate the nonzero shift adjoint coupling coefficients for the two‐shell composite Gelfand–Paldus basis. We then demonstrate that the one‐shell versions of these coefficients may be obtained by taking the Gelfand–Tsetlin limit of the two‐shell formulas. These coefficients, together with the zero‐shift types, then enable us to write down formulas for the U (2 n ) generator matrix elements in a two‐shell spin–orbit basis. Ultimately, the results of the series may be used to determine the many‐electron density matrices for a partitioned system. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 345–363, 1998