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New complete orthonormal sets of exponential‐type orbitals and their application to translation of Slater orbitals
Author(s) -
Guseinov I. I.
Publication year - 2002
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.927
Subject(s) - orthonormal basis , exponential type , atomic orbital , laguerre polynomials , slater type orbital , type (biology) , wave function , translation (biology) , quantum mechanics , physics , exponential function , coulomb , computation , mathematical physics , mathematics , linear combination of atomic orbitals , chemistry , mathematical analysis , electron , algorithm , ecology , biochemistry , messenger rna , gene , biology
The new complete orthonormal sets of exponential‐type orbitals (ETOs) are introduced in closed form as functions of the exponential, the complex or real regular solid spherical harmonic, and the generalized Laguerre polynomials,\documentclass{article}\pagestyle{empty}\begin{document}\begin{displaymath}{\Psi^{\alpha}_{nlm}\hbox{\large$\left(\right.$}\!\zeta,\vec{r}\hspace{0.5pt}\!\hbox{\large$\left.\right)$}= (-1)^{\alpha} \biggl[ \frac{(2\zeta)^{3}(n-l-1)!}{(2n)^{\alpha}[(n+l+1-\alpha)!]^{3}} \biggr]^{1/2}} (2\zeta r)^{l}e^{-\zeta r} L_{n+l+1-\alpha}^{2l+2-\alpha}(2\zeta r)S_{lm}(\theta,\varphi),\end{displaymath}\end{document}where α=1,0,−1,−2,−3,… . These Ψ α ‐ETOs are represented as finite linear combinations of Slater‐type orbitals (STOs). The Coulomb Sturmian and Lambda ETOs are the special classes of Ψ α ‐ETOs for α=1 and α=0, respectively. By the use of Ψ α ‐ETOs the simpler expansion formulas for translation of STOs are derived. The translation coefficients are presented by a linear combination of overlap integrals. The final results are especially useful for machine computations of arbitrary multielectron multicenter molecular integrals over STOs that arise in the Hartree–Fock–Roothaan approximation and also in the Hylleraas correlated wave function method which play a significant role in theory and application to quantum mechanics of atoms, molecules, and solids. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002