Electronic wave functions: VI. Some theorems facilitating the evaluation of Schrödinger integrals of vector-coupled functions

Abstract

The theorems reported here provide some powerful additional relations to the general theory of the reduction of Schrodinger integrals completed in part V. One result of these is to establish a number of relations between the various vector-coupling coefficients and thus to reduce considerably the labour of calculation of these. A second result is to provide a method of evaluating the two-electron electrostatic integrals which is a complete alternative to the c ^k method which has generally been used previously. This appears to be simpler and more powerful. A third result is only applicable to a restricted class of integrals and only to particular terms in the formulas for these, but where applicable it makes trivial the evaluation of the terms concerned and actually simplifies about three-quarters of the integrals normally occurring. These methods have been found to be extremely useful in the convergent variational calculations of atomic wave functions, and will also be applicable to all problems which require the evaluation of Schrödinger integrals between vector-coupled functions.