MATRIX-ELEMENTS OF U(2N) GENERATORS IN A MULTISHELL SPIN-ORBIT BASIS - III - GENERAL FORMULAS

This is the third and final article in a series directed toward the ev aluation of the U(2n) generator matrix elements (MEs) in a multishell spin/orbit basis. Such a basis is required for many-electron systems p ossessing a partitioned orbital space and where spin-dependence is imp ortant. The approach taken is based on the transformation properties o f the U(2n) generators as an adjoint tensor operator of U(n) x U(2) an d application of the Wigner-Eckart theorem. A complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis (which is appropriate to the many-electron problem) were obtained in the first and second articles of this series. Ln the first article we defined zero-shift coupling coefficients. These are proportional to th e corresponding two-shell del-operator matrix elements. See P. J. Burt on and and M. D. Gould, J. Chem. Phys., 104, 5112 (1996), for a discus sion of the del-operator and its properties. Ln the second article of the series, the nonzero shift coupling coefficients were derived. Havi ng obtained all the necessary coefficients, we now apply the formalism developed above to obtain the U(2n) generator MEs in a multishell spi n-orbit basis. The methods used are based on the work of Gould et al. (see the above reference). (C) 1998 John Wiley & Sons, Inc.