For the singly charged cations to and anions to in their ground state, Roothaan - Hartree - Fock calculations are carried out using a single-zeta (or minimal) basis set of extended Slater-type functions whose principal quantum numbers are allowed to be variationally optimum noninteger values. The resultant total energies are substantially lower than those obtained from the conventional single-zeta method which implicitly restricts the quantum numbers to be integer values. In the case of and ions, for example, the improvements amount to 11.4 and 11.0 Hartrees, respectively. The noninteger principal quantum numbers also improve the orbital energies. In particular, unphysical positive orbital energies predicted by the conventional single-zeta method for 56 atomic orbitals change to realistic negative values (with only three exceptions) by the use of noninteger principal quantum numbers without increasing the number of basis functions. Ionization potentials and electron affinities are improved as well within the single-zeta approximation.