Noninteger principal quantum numbers increase the efficiency of Slater-type basis sets: heavy atoms

For the atoms Cs (Z = 55) through Lr (Z = 103) in their ground state, Roothaan-Hartree-Fock calculations are performed 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 superior to those obtained from the conventional single-zeta method which implicitly restricts the quantum numbers to be integer values. In the case of the Lr atom, the improvement amounts to 56.8 Eh. The noninteger principal quantum numbers improve the orbital energies; unphysical positive d and f orbital energies predicted by the conventional single-zeta method change to realistic negative values by the use of noninteger principal quantum numbers.