  The sum-over-states (SOS) polarizabilities are calculated within the
approximate independent electron theories such as the Hartree-Fock
approximation and density functional models using the eigenvalues and orbitals
obtained from the self-consistent solution of single-particle equations. The
SOS polarizabilities are then compared with those calculated using the
finite-field method within three widely used single particle models: (1) the
Hartree-Fock (HF) method, (2) the three parameter hybrid generalized gradient
approximation (B3LYP), and (3) the parameter free generalized gradient
approximation due to Perdew-Burke-Ernzerhof (PBE). The comparison is carried
out for polarizabilities of 142 molecules calculated using the 6-311++G(d,p)
orbital basis at the geometries optimized at the B3LYP/6-311G** level. The
results show that the SOS method almost always overestimate the FF
polarizabilities in the PBE and B3LYP models. This trend is reversed in the HF
method however exception to the trend do exist. The mean absolute errors (MAE)
in the screened (FF) and unscreened (SOS) polarizability are 0.78 \AA$^3$ for
the HF method, 1.87 \AA$^3$ for the B3LYP, and 3.44 \AA$^3$ for the PBE-GGA.
The Hartree-Fock approximation predicts finite-field polarizabilities that are
smaller than those predicted by the PBE and B3LYP models. Finally, a simple
scheme is devised to obtain FF quality estimate of polarizability from those
obtained using the SOS method by exploiting the observed trends.
