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(June 30, 2021)

Gaussian basis sets violate nuclear cusp conditions.
^{
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Commun. Pure Appl. Math.

(1957),
10,
pp. 151.
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^{,}
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J. Chem. Phys.

(1966),
45,
pp. 556.
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^{,}
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J. Chem. Phys.

(1996),
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pp. 9908.
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This may lead to large errors in wave function at nuclei,
particularly for spin density calculations.
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Theor. Chem. Acc.

(1989),
76,
pp. 73.
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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.
^{
918
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J. Chem. Phys.

(1996),
105,
pp. 1470.
Link
^{,}
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J. Chem. Phys.

(1996),
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pp. 1479.
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The derivation of operators is
based on hyper virial theorem
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J. Chem. Phys.

(1960),
33,
pp. 1462.
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and presented in
Ref. 918. Application to molecular spin densities for
spin-polarized
^{
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J. Chem. Phys.

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pp. 1479.
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and DFT
^{
1146
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Phys. Chem. Chem. Phys.

(2000),
2,
pp. 2131.
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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 ${r}_{0}$.
^{
918
}
J. Chem. Phys.

(1996),
105,
pp. 1470.
Link
^{,}
^{
919
}
J. Chem. Phys.

(1996),
105,
pp. 1479.
Link
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.