The evaluation of integrals occurring in the theory of molecular structure. Parts I & II
- 20 March 1951
- journal article
- Published by The Royal Society in Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
- Vol. 243 (864) , 221-249
- https://doi.org/10.1098/rsta.1951.0003
Abstract
Part I : A new technique is developed for evaluating the integrals which occur in molecular theory. The method is based on the expansion of exponentials in terms of the so-called £ functions. These involve modified Bessel functions. In this part we list the properties of these £ functions needed for the two-centre integrals. A table is provided of the I ’s and K ’s used in their tabulation. An account is given of the properties of certain integrals of the £ functions and some numerical examples are provided. Part II : Methods are described for the evaluation of the two-centre, one-electron Coulomb, overlap and resonance integrals, for the two-electron Coulomb and hybrid (Coulomb-exchange) integrals, and for the penetration integrals. Formulae are listed for more than 180 distinct integrals.Keywords
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