Configuration interaction matrix elements. I. Algebraic approach to the relationship between unitary group generators and permutations

Matrix elements of unitary group generators between spin‐adapted antisymmetric states are shown to be proportional to spin matrix elements of so‐called “line‐up” permutations. The proportionality factor is given explicitly as a simple function of the orbital occupation numbers. If one bases the theory on ordered orbital products, the line‐up permutations are given a priori. The final formulas have a very simple structure; this is a direct consequence of the fact that the spin functions have been taken to be geminally antisymmetric.