The completeness properties of Gaussian-type orbitals in quantum chemistry

In this work, I extend results on the convergence of Gaussian basis sets in quantum chemistry, previously shown for ground-state hydrogenic wavefunctions, to orbitals of arbitrary angular momentum. I give rigorous proofs of their asymptotic behavior, and demonstrate for methods with regular potential operators-in particular, Hartree-Fock and Kohn-Sham density functional theory-that the assumption of completeness is correct under fairly lenient conditions. The final result under the correct norm is that the convergence in energy followsexp mml:mfenced close=")" open="("-kM, whereMis the number of Gaussians andkis a positive constant, generalizing previous results due to Kutzelnigg. This then yields prescriptions for accelerated convergence using even-tempered Gaussians, which could be used as initial guesses in future basis set optimizations.