  The first discussion of basis sets consisting of exponentially decaying
Coulomb Sturmian functions for modelling electronic structures is presented.
The proposed basis set construction selects Coulomb Sturmian functions using
separate upper limits to their principle, 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 for second and
third row atoms at the Hartree-Fock level. Thereby important relations between
the values of the basis set parameters and the physical properties of the
electronic structure are recognised. For example, an unusually large limit for
the angular momentum quantum number in unrestricted Hartree-Fock calculations
can be linked to the breaking of spherical symmetry in such cases. Furthermore,
a connection between the optimal, i.e. minimum-energy, Coulomb Sturmian
exponent and the average Slater exponents values obtained by Clementi and
Raimondi (E. Clementi and D. L. Raimondi, J. Chem. Phys. 38, 2686 (1963)) is
made. These features of Coulomb Sturmian basis sets emphasise their ability to
correctly reproduce the physical features of Hartree-Fock wave functions.
