Hyperbolic cosine functions applied to atomic calculations: singly-charged cations and anions

The radial basis functions rn−1exp(−αr)cosh(βr+γ), proposed recently for Roothaan–Hartree–Fock calculations of neutral atoms, are applied to the 53 singly-charged cations Li+ through Cs+ and 43 anions H− through I− (excluding 10 unstable anions) within the minimal-basis framework. Our systematic study of the 96 ions in their ground states confirms that the basis functions are useful for a compact analytical approximation of Hartree–Fock wavefunctions of ionic species as well. Compared to the values of the conventional Slater-type functions, the total energies are lower by 12.6 hartree for Cs+ and by 12.1 for I−. Orbital energies are also improved; the errors relative to the Hartree–Fock limit values never exceed 0.024 hartree.