Extensions of the Hulthén Orbital Concept

Three extensions of the Hulthen representation of atomic orbitals are investigated. In earlier work it was shown that radial functions 0s = N1[exp(− αr) − exp(− βr)](1 / r) and 1p = N2[exp(− γr) − exp(− δr)] excellently represented 1s and 2p radial functions for atoms. In the present paper, investigations are reported (a) using Hulthen orbitals as the starting point for a perturbation calculation of exact Hartree–Fock orbitals, (b) employing a full Dirichlet‐type series [Σiλiexp(− μir)](1 / r) to represent a 1s orbital, and (c) using the Laplace transformation representation for a 1s orbital, 1s(r) =  ∫ 0∞ a(x) exp(− xr)dx.