MOLECULAR MULTICENTER INTEGRALS OF SPHERICAL GAUSSIAN FUNCTIONS BY GENERALIZED GRADIENT OPERATOR METHOD
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Date
1996
Journal Title
Journal ISSN
Volume Title
Publisher
Ohio State University
Abstract
The spherical Laguerre Gaussian type function (LGTF) centered at nucleus $A$, $L_{n}^{l+1/2}(ar_{u}^{2})\cal{Y}_{m}(r_{u})\exp(-ar^{2}_{u})$: can be generated by operating on the Gaussian exponential, exp ($-ar^{2}_{u}$) with a generalized gradient operator, $\cal{Y}_{n|m}(\nabla_{A})$.$^{1}$ Through the vector coupling of the gradient operators, the Talmi coefficient of transforming the product of two LGTFs, one centered at $A$ and the other centered at $B$, into a linear combination of the products of two different LGTFs, one centered at $P$ (center of mass of $A$ and $B$) and the other made of the internuclear coordinates, has been obtained. Multicenter molecular integrals of the overlap, the Coulomb repulsion, the spin-spin interaction and the spin-other-orbit interaction can be evaluated analytically. The integral results are simpler than those obtained by Fourier transform convolution $theorem.^{2}$
Description
$^{1}$. G. Fieck, Theoret. Chim. Acta 54, 323 (1980). $^{2}$. M. Moharenzadeh and L.-Y. Chow Chiu, J. Chem. Phys. 104, 616 (1996).
Author Institution: Department of Chemistry, Howard University; Natural Sciences and Mathematics Department, Bowie State University
Author Institution: Department of Chemistry, Howard University; Natural Sciences and Mathematics Department, Bowie State University