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1951•Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical SciencesRequires access

The evaluation of integrals occurring in the theory of molecular structure. Parts I & II

Michael P. Barnett, C. A. Coulson

Open publisher page 353 citations

Abstract

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.

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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.

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Available abstract

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.

Key concepts: Slater integrals, Trigonometric integral, Coulomb, Bessel function, Order of integration (calculus), Coulomb wave function, Mathematics, Volume integral

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