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 follows urn:x-wiley:00207608:media:qua26264:qua26264-math-0001, where M is the number of Gaussians and k is 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.