Study of Two-Center Integrals Useful in Calculations on Molecular Structure. V. General Methods for Diatomic Integrals Applicable to Digital Computers

The calculation of the electronic structure of atomic and molecular systems involves the determination of a number of integrals over the electronic coordinates. These calculations are feasible only by the use of high-speed, large-memory digital computers. This discussion is based on a culmination of experience obtained in this laboratory with regard to methods useful in the evaluation of two-center integrals by means of digital computers. The ground work for this paper, in terms of the analysis employed, is given in a series of papers by Roothaan, Ruedenberg, and Jaunzemis, but significant changes have evolved which offer considerable improvements and more economical calculations. The analysis presented here is especially the result of efforts to take full advantage of the capabilities of present digital computers. The methods advocated here are thought to be near optimal to a completely reliable and automatic computation of the electronic integrals in question with the desired accuracy. A not insignificant aspect of the methods given here is that an approach was sought which is unfailingly reliable and accurate regardless of the AO's involved in the integrals and at the same time as economical as possible.