Configuration interaction matrix elements. II. Graphical approach to the relationship between unitary group generators and permutations

Abstract

AbstractThe explicit expressions for the matrix elements of unitary group generators between geminally antisymmetric spin‐adapted N‐electron configurations in terms of the orbital occupancies and spin factors, given as spin function matrix elements of appropriate orbital permutations, are derived using the many‐body time‐independent diagrammatic techniques. It is also shown how this approach can be conveniently combined with graphical methods of spin algebras to obtain explicit expressions for the spin factors, once a definite coupling scheme is chosen. This method yields explicit expressions for the orbital permutations defining the spin factors. However, if desired, the explicit determination of line‐up permutations can be avoided in this approach, since they are implicitly contained in the orbital diagrams. It also clearly indicates why the geminally antisymmetric spin functions have to be used when a simple formalism is desired.