Atomic Integrals Containing rijp Correlation Factors with Unlinked Indices

The S states of multielectron atoms can be calculated by use of Rayleigh–Ritz expansions, each term of which is a product of Slater-type functions, riaexp(− αri), and a single two-electron correlation factor of the form rijp. This requires convenient (preferably algebraic, rather than numerical integration) methods for evaluating the five types of energy and normalization integrals which arise. Formulas for some of these integrals, including the relatively difficult linked-index three-electron integral, have been given previously. For each of the four nonlinked-index integrals, there is given herein an explicit, computer-programmable formula in which the expansion parameters are treated as input arguments. Practicality of the formulas was demonstrated by preparation of a fortran computer program which was used to evaluate sample integrals. Some differencing error is involved, but typically results in loss of only two or three significant figures.