Overlap Integrals Between Irregular Solid Harmonics and STOs Via the Fourier Transform Methods |
| |
Authors: | Emin Öztekin Selda Özcan |
| |
Institution: | (1) Department of Physics, Faculty of Science and Art, Ondokuz Mayis University, 55139 Kurupelit, Samsun, Turkey |
| |
Abstract: | In this paper, a unified analytical and numerical treatment of overlap integrals between Slater type orbitals (STOs) and irregular
Solid Harmonics (ISH) with different screening parameters is presented via the Fourier transform method. Fourier transform
of STOs is probably the simplest to express of overlap integrals. Consequently, it is relatively easy to express the Fourier
integral representations of the overlap integrals as finite sums and infinite series of STOs, ISHs, Gegenbauer, and Gaunt
coefficients. The another mathematical tools except for Fourier transform have used partial-fraction decomposition and Taylor
expansions of rational functions. Our approach leads to considerable simplification of the derivation of the previously known
analytical representations for the overlap integrals between STOs and ISHs with different screening parameters. These overlap
integrals have also been calculated for extremely large quantum numbers using Gegenbauer, Clebsch-Gordan and Binomial coefficients.
The accuracy of the numerical results is quite high for the quantum numbers of Slater functions, irregular solid harmonic
functions and for arbitrary values of internuclear distances and screening parameters of atomic orbitals. |
| |
Keywords: | overlap integrals slater type orbitals irregular solid harmonics gegenbauer polynomials |
本文献已被 SpringerLink 等数据库收录! |
|