Hyperbolic cosine functions applied to atomic Roothaan–Hartree–Fock wave functions

Abstract

A hyperbolic cosine function cosh ( βr) is incorporated into a Slater-type radial function r n−1 exp (− αr) with noninteger principal quantum number n. The new radial basis functions r n−1 exp (− αr)cosh ( βr) are applied to Roothaan–Hartree–Fock calculations of atoms within the minimal-basis framework. The results of a systematic study on the neutral atoms from He ( Z=2) to Lr ( Z=103) in their ground state show that the total energy errors of the parent Slater-type functions, relative to the numerical Hartree–Fock values, are reduced to half or less by the addition of cosh ( βr). Orbital energies are also improved. The present accuracy of the minimal-basis description of atoms supersedes the previous one achieved in the literature.