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Molecular correlation integrals. Two center one electron integrals containing a function of interparticle distance in one center expansion approximation
Author(s) -
Joshi Bhairav D.,
Kapoor K. L.
Publication year - 1969
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560030403
Subject(s) - slater integrals , center (category theory) , fortran , multiple integral , order of integration (calculus) , function (biology) , volume integral , wave function , correlation function (quantum field theory) , mathematics , electron , trigonometric integral , mathematical analysis , physics , quantum mechanics , integral equation , chemistry , computer science , evolutionary biology , dielectric , trigonometry , biology , crystallography , operating system
Two‐center one‐electron integrals needed in certain molecular correlated wave function calculations, using one‐center expansion approximation, have been studied. The form of the basic correlated function used in this study is\documentclass{article}\pagestyle{empty}\begin{document}$$ h(r_{12}) = r_{12}^n e^{ - \zeta r_{12} } $$\end{document}The parent integral is expressed in terms of an angular integral, and an auxiliary radial integral depending upon the variables r 1 , r 2 , and r 12 . Several analytical formulas, and a recursive formula are derived for the auxiliary integral, and other related integrals. All these formulas are given in computationally useful forms. Logical flow charts and FORTRAN programs were constructed for computing the basic integrals discussed in the paper. Numerical values of some integrals, thus obtained, are tabulated for comparisons.