Molecular integrals with Slater basis. V. Recurrence algorithm for the exchange integrals

The numerical and analytical procedures, used for calculating exchange integrals with Slater functions, fail to give high accuracy for large quantum numbers and some values of the parameters. We propose here an algorithmic approach based on recurrence relations which start from some simple functions. An extensive study in which exponents, interatomic distances, and quantum numbers were varied proves that the new procedure is fully reliable. Finally, the cost of the procedure is analyzed, including the effect of the number of terms needed to attain a given accuracy.