Gaussian basis sets violate nuclear cusp conditions.^{454, 694, 768}
This may lead to large errors in wave function at nuclei,
particularly for spin density calculations.^{172} 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.^{769, 770} The derivation of operators is
based on hyper virial theorem^{380} and presented in
Ref. 769. Application to molecular spin densities for
spin-polarized^{770} and DFT^{956} 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 $\mathrm{exp}[-{(Z/{r}_{0})}^{2}{(\mathbf{r}-\mathbf{R})}^{2}]$
that samples the vicinity of a nucleus of charge $Z$ located at $\mathbf{R}$. The parameter ${r}_{0}$
has to be small enough to neglect two-electron contributions of the order
$\mathcal{O}({r}_{0}^{4})$ 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 ${r}_{0}$.^{769, 770}
The value of ${r}_{0}$ 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.

RC_R0

Determines the parameter in the Gaussian weight function used to smooth the
density at the nuclei.

TYPE:

INTEGER

DEFAULT:

0

OPTIONS:

0
Corresponds the traditional delta function spin and charge densities
$n$
corresponding to $n\times {10}^{-3}$ a.u.

RECOMMENDATION:

We recommend value of 250 for a typical spit valence basis. For basis sets
with increased flexibility in the nuclear vicinity the smaller values of ${r}_{0}$
also yield adequate spin density.