Matrix elements of U(2n) generators in a multishell spin–orbit basis. II. The two-shell nonzero shift ACCs and U(2n) generator MEs

✍ Scribed by P. J. Burton; M. D. Gould

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 239 KB
• Volume: 66
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/(sici)1097-461x(1998)66:5<345::aid-qua2>3.0.co;2-v

✦ Synopsis

This is the second in a series of articles whose ultimate goal is the Ž . Ž . 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 Ž . 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 Ž . 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 Ž . 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.