Abstract
The use of a generalized exponential function r v−1 exp(−ζr μ) as a radial basis function in atomic calculations is studied with our special interest in the variationally optimum value of the parameter μ, since special cases of μ = 1 and μ = 2 correspond respectively to the radial parts of commonly-used Slater-type and Gaussian-type functions. Roothaan-Hartree-Fock calculations are performed for ground-state neutral atoms with atomic number Z = 2–54, singly-charged cations with Z = 3–55, and anions with Z = 1–53 within the single-zeta (or minimal basis) framework. For all the species examined, the optimtum μ values are found to be smaller than unity and increase towards unity as the atomic number increases. The present results support the use of Slater-type functions when μ is restricted to be an integer, but suggest from the variational point of view that even the exponential decay of Slater-type functions is too “strong” within the single-zeta approximation.
Similar content being viewed by others
References
Zener, C.: Phys. Rev. 36, 51 (1930)
Slater, J.C.: Phys. Rev. 36, 57 (1930)
Boys, S.F.: Proc. Roy. Soc. A 200, 542 (1950)
Koga, T., Kanayama, K., Thakkar, A.J.: Int. J. Quantum Chem. 62, 1 (1997)
Koga, T., Kanayama, K.: Chem. Phys. Lett. 266, 123 (1997)
Koga, T., Kanayama, K.: J. Phys. B 30, 1623 (1997)
Parr, R.G. Joy, H.W.: J. Chem. Phys. 26, 424 (1957)
Saturno, A.F., Parr, R.G.: J. Chem. Phys. 29, 490 (1958)
Snyder, L.C.: J. Chem. Phys. 33, 1711 (1960)
Allouche, A.: Theor. Chim. Acta 34,79 (1974)
Koga, T., Thakkar, A.J.: Theor. Chim. Acta 85, 391 (1993)
Pitzer, R.M.: QCPE Bull. 10, 14 (1990)
Powen, M.J.D.: Comp. J. 7, 155 (1964)
Chong, D.P.: J. Chem. Phys. 47, 4907 (1967)
Handy, N.C., Marron, M.T., Silverstone, H.J.: Phys. Rev. 180, 45 (1969)
Handler, G.S., Smith, D.W., Silverstone, H.J.: J. Chem. Phys. 73, 3936 (1980)
Ishida, T., Ohno, K.: Theor. Chim. Acta 81, 355 (1992)
Bunge, C.F., Barrientos, J.A., Bunge, A.V., Cogordan, J.A.: Phys. Rev. A 469, 3691 (1992)
Koga, T., Tatewaki, H., Thakkar, A.J.: J. Chem. Phys. 100, 8140 (1994)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Aschenauer, E.C., Markushin, V.E. Generalized exponential functions applied to atomic calculations. Z Phys D - Atoms, Molecules and Clusters 41, 111–115 (1997). https://doi.org/10.1007/s004600050297
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s004600050297