Unitary group approach to the many‐electron problem. III. Matrix elements of spin‐dependent Hamiltonians

Abstract

Abstract This is the final paper in a series of three directed toward the evaluation of spin‐dependent Hamiltonians. In this paper we derive the reduced matrix elements of the U (2 n ) generators in a basis symmetry adapted to the subgroup U ( n ) × U (2) (i.e., spin‐orbit basis), for the representations appropriate to many‐electron systems. This enables a direct evaluation of the matrix elements of spin‐dependent Hamiltonians in the spin‐orbit basis. An alternative (indirect) method, which employs the use of U (2 n ) ↓ U ( n ) × U (2) subduction coefficients, is also discussed.