Coupling coefficients for systems with two open electronic shells: Transition metal ions with p^M d^N configuration

Abstract

We derived the necessary conditions to wh ich the vector coupling coefficients (vcc) am• and bmn , describing atomic L,S-multiplets of pMd N and dNs' configurations (1 ",; N ",; 9, 1 ",; M ",; 5), should satisfy. It is shown that for two-open-shell systems under consideration the unknown vcc should satisfy not only usual restrictions resulting from the spheric symmetry, but also some addi· tional equation introduced in the present paper in the form of a postulate. vcc obtained were used for the ab initio calculations (by the general SCF coupling operator method) of several transition· metal atoms and ions with electronic configurations 3d'4p', 3p