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10.6 Spin and Charge Densities at the Nuclei

10.6.1 Overview

(December 20, 2021)

Gaussian basis sets violate nuclear cusp conditions. 553 Kato T.
Commun. Pure Appl. Math.
(1957), 10, pp. 151.
Link
, 853 Pack R. T., Brown W. B.
J. Chem. Phys.
(1966), 45, pp. 556.
Link
, 948 Rassolov V. A., Chipman D. M.
J. Chem. Phys.
(1996), 104, pp. 9908.
Link
This may lead to large errors in wave function at nuclei, particularly for spin density calculations. 201 Chipman D. M.
Theor. Chem. Acc.
(1989), 76, pp. 73.
Link
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. 949 Rassolov V. A., Chipman D. M.
J. Chem. Phys.
(1996), 105, pp. 1470.
Link
, 950 Rassolov V. A., Chipman D. M.
J. Chem. Phys.
(1996), 105, pp. 1479.
Link
The derivation of operators is based on hyper virial theorem 472 Hirschfelder J. O.
J. Chem. Phys.
(1960), 33, pp. 1462.
Link
and presented in Ref.  949 Rassolov V. A., Chipman D. M.
J. Chem. Phys.
(1996), 105, pp. 1470.
Link
. Application to molecular spin densities for spin-polarized 950 Rassolov V. A., Chipman D. M.
J. Chem. Phys.
(1996), 105, pp. 1479.
Link
and DFT 1179 Wang B., Baker J., Pulay P.
Phys. Chem. Chem. Phys.
(2000), 2, pp. 2131.
Link
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 exp[-(Z/r0)2(𝐫-𝐑)2] that samples the vicinity of a nucleus of charge Z located at 𝐑. The parameter r0 has to be small enough to neglect two-electron contributions of the order 𝒪(r04) 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 r0. 949 Rassolov V. A., Chipman D. M.
J. Chem. Phys.
(1996), 105, pp. 1470.
Link
, 950 Rassolov V. A., Chipman D. M.
J. Chem. Phys.
(1996), 105, pp. 1479.
Link
The value of r0 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

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×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 r0 also yield adequate spin density.