Calculation of ω Coefficients in the Guseinov’s Serial Expansion Method by Using Recursive Relations

Year 2016, Volume: 42 Issue: 1, 37 - 41, 01.06.2016

Erhan Akın

Abstract

: In this study, analytical expressions in the recursive form have been obtained for ω coefficients, arising in Guseinov’s serial expansion method. ω coefficients defined in terms of binomial coefficients can be easily calculated by recursive relations obtained in this work without using binomial coefficient. Calculations for both recursive relations and relation in terms of binomial coefficient are in agreement with each other.

Keywords

Slater-type atom orbitals, Guseinov’s serial expansion method

Guseinov’un STO’ları Taşıma Bağıntısındaki ω Katsayılarının Tekrarlama Bağıntılarıyla Hesaplanması

Abstract

Bu çalışmada Guseinov’un Slater-tipi atom orbitallerini bir merkezden başka bir merkeze taşıma yönteminde gerekli olan ω katsayıları için tekrarlama bağıntıları elde edilmiştir. Binom katsayıları cinsinden ifade edilen ω katsayıları bu çalışmadaki tekrarlama bağıntıları ile binom katsayıları kullanılmaksızın kolaylıkla hesaplanabilir. Yapılan böyle bilgisayar hesaplamaları, her iki bağıntıdan elde edilen sonuçların aynı olduğunu göstermiştir.

Keywords

Slater-tipi atom orbitalleri, Guseinov’un seri açılım yöntemi

References

• Barnett MP, Coulson CA (1951). The evaluation of integrals occurring in the theory of molecular structure Parts I & II., Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 243, 221–249.
• Guseinov II (1970). Analytical evaluation of two-centre Coulomb, hybrid and one-electron integrals for Slater-type orbitals, Journal of Physics B: Atomic and Molecular Physics 3(11), 1399–1406.
• Guseinov II (1985). Expansion of slater-type orbitals about a displaced center and the evaluation of multicenter electron-repulsion integrals, Physical Review A 31(5), 2851– 2853.
• Guseinov II, Ozmen A, Atav U, Yuksel H (1998). Computation of overlap integrals over Slater-type orbitals using auxiliary functions, International Journal of Quantum Chemistry 67(4), 199–204.
• Jones, HW (1992). Lowdin alpha-function, overlap integral, and computer algebra, International Journal of Quantum Chemistry 41(5), 749–754.
• Roothaan CCJ (1951). New developments in molecular orbital theory, Reviews of Modern Physics 23, 69–89.
• Silverstone HJ (1966). On the evaluation of two‐center overlap and coulomb integrals with noninteger‐n slater‐type orbitals, The Journal of Chemical Physics 45(11), 4337–4341.