Overlap integrals between irregular solid harmonics and STOs via the Fourier transform methods

Oztekin E., Ozcan S.

JOURNAL OF MATHEMATICAL CHEMISTRY, cilt.42, sa.3, ss.337-351, 2007 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 3
  • Basım Tarihi: 2007
  • Doi Numarası: 10.1007/s10910-006-9104-y
  • Dergi Adı: JOURNAL OF MATHEMATICAL CHEMISTRY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.337-351
  • Anahtar Kelimeler: overlap integrals, slater type orbitals, irregular solid harmonics, gegenbauer polynomials, SLATER-TYPE ORBITALS, 2-CENTER NUCLEAR ATTRACTION, REDUCED BESSEL-FUNCTIONS, MOLECULAR INTEGRALS, SCREENING PARAMETERS, COULOMB INTEGRALS, MULTICENTER INTEGRALS, ASYMPTOTIC-BEHAVIOR, QUANTUM-MECHANICS, CONVOLUTION
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

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.