A simple quality test for self-consistent-field atomic orbitals

A quality test is proposed for SCF atomic orbitals, approximated as finite linear combinations of suitable basis functions The key is in a function, readily derived from the Hartree-Fock equation which is identically zero for true Hartree-Fock spin orbitals and not so for approximate orbitals. In this way, our test measures how closely approximate orbital descriptions approach the true Hartree-Fock limit and thus provides a quality ordering of orbital bases with respect to one another and with respect to that limit, in a scale uniquely defined by the latter. Moreover, this analysis also holds for atomic subspaces of our choice, e.g., the valence region. Examples are offered for representative collections of Slater- and Gaussian-type orbital expansions.