Electronic wave functions III. Some theorems on integrals of antisymmetric functions of equivalent orbital form

Abstract A fresh formulation of the Slater methods of constructing antisymmetric functions is given. This formulation enables a systematic reduction scheme to be found for the integrals of all antisymmetric functions which occur in a completely convergent variational procedure. The theorems are purely mathematical, but the types of integral considered are those which would be obtained from functions representing both equal and different numbers of equivalent electrons. There have not previously been theorems which reduce the antisymmetry operators in the latter cases. These relations are a practical necessity for the calculations of atomic wave functions which are being reported in the present series. The theorems are equally applicable to functions which might be used for atoms, molecules, or nuclei.