Quantum chemistry with Coulomb Sturmians: Construction and convergence of Coulomb Sturmian basis sets at the Hartree-Fock level

A discussion of basis sets consisting of exponentially decaying Coulomb Sturmian functions for modeling electronic structures is presented. The proposed basis-set construction selects Coulomb Sturmian functions using separate upper limits to their principal, angular momentum, and magnetic quantum numbers. Their common Coulomb Sturmian exponent is taken as a fourth parameter. The convergence properties of such basis sets are investigated taking the second- and third-row atoms at the Hartree-Fock level as examples. Thereby, important relations between the values of the basis-set parameters and the physical properties of the electronic structure are recognized. Furthermore, a connection between the optimal, i.e., minimum-energy, Coulomb Sturmian exponent and the average Slater exponents values obtained by Clementi and Raimondi [J. Chem. Phys. 38, 2686 (1963)] is made. These features of Coulomb Sturmian basis sets emphasize their ability to correctly reproduce the physical features of the Hartree-Fock wave functions. As an outlook, the application of Coulomb Sturmian discretizations for molecular calculations and post-Hartree-Fock methods is briefly discussed.