Gaussian basis sets violate nuclear cusp conditions.Kato:1957, Pack:1966, Rassolov:1996a This may lead to large errors in wave function at nuclei, particularly for spin density calculations.Chipman:1989 This problem can be alleviated by using an averaging operator that compute wave function density based on constraints that wave function must satisfy near Coulomb singularity.Rassolov:1996b, Rassolov:1996c The derivation of operators is based on hyper virial theoremHirschfelder:1960 and presented in Ref. Rassolov:1996b. Application to molecular spin densities for spin-polarizedRassolov:1996c and DFTWang:2000b wave functions show considerable improvement over traditional delta function operator.
One of the simplest forms of such operators is based on the Gaussian weight function that samples the vicinity of a nucleus of charge located at . The parameter has to be small enough to neglect two-electron contributions of the order but large enough for meaningful averaging. The range of values between 0.15–0.3 a.u. has been shown to be adequate, with final answer being relatively insensitive to the exact choice of .Rassolov:1996b, Rassolov:1996c The value of is chosen by RC_R0 keyword in the units of 0.001 a.u. The averaging operators are implemented for single determinant Hartree-Fock and DFT, and correlated SSG wave functions. Spin and charge densities are printed for all nuclei in a molecule, including ghost atoms.