Abstract
The series expansion formulae in terms of complete orthonormal sets of Ψα-exponential type orbitals introduced by the author are derived for the two-center charge densities of integer and noninteger n generalized exponential functions. The expansion coefficients arising in these relations are the multicenter overlap integrals of three Ψα-functions. The charge density expansion formulae obtained are utilized for the evaluation of multicenter multielectron integrals appearing in the Hartree–Fock–Roothaan and explicitly correlated theories when the generalized exponential type orbitals are employed as basis functions.
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Zener C. (1930) Phys. Rev. 36: 51
Slater J.C. (1930) Phys. Rev. 36: 57
Boys S.F. (1950) Proc. Roy. Soc. A200: 542
Guseinov I.I. (2002) Int. J. Quantum Chem. 90: 114
Guseinov I.I. (2007) J. Math. Chem. 42: 415
Guseinov I.I. (1998) J. Mol. Struct. (Theochem) 422: 75
Guseinov I.I. (2003) J. Mol. Model. 9: 190
Guseinov I.I. (2008) J. Math. Chem. 43: 427
Koga T., Kanayama K. (1997) Z. Phys. D 41: 111
Condon E.U., Shortley G.H. (1970) The Theory of Atomic Spectra. Cambridge University, Cambridge
Guseinov I.I., Ertürk M. (2009) MATCH Commun. Math. Comput. Chem. 61: 603
Gradshteyn I.S., Ryzhik I.M. (1980) Tables of Integrals, Sums, Series and Products, 4th ed. Academic Press, New York
Guseinov I.I. (2007) J. Math. Chem. 42: 991
Whittaker E.T., Watson G.N. (1952) A Course of Modern Analysis. Cambridge University Press, Cambridge
Guseinov I.I. (2008) J. Math. Chem. 43: 1024
Guseinov I.I., Mamedov B.A. (2007) Z. Naturforsch. 62a(9): 467
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Guseinov, I.I. Expansion formulae for two-center charge densities of integer and noninteger n generalized exponential type orbitals applied to evaluation of multicenter multielectron integrals. J Math Chem 47, 384–390 (2010). https://doi.org/10.1007/s10910-009-9578-5
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DOI: https://doi.org/10.1007/s10910-009-9578-5