Comparative study of unscreened and screened molecular static linear polarizability in the Hartree-Fock, hybrid-density functional, and density functional models

摘要

The sum-over-states (SOS) polarizabilities are calculated within theapproximate independent electron theories such as the Hartree-Fockapproximation and density functional models using the eigenvalues and orbitalsobtained from the self-consistent solution of single-particle equations. TheSOS polarizabilities are then compared with those calculated using thefinite-field method within three widely used single particle models: (1) theHartree-Fock (HF) method, (2) the three parameter hybrid generalized gradientapproximation (B3LYP), and (3) the parameter free generalized gradientapproximation due to Perdew-Burke-Ernzerhof (PBE). The comparison is carriedout 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. Theresults show that the SOS method almost always overestimate the FFpolarizabilities in the PBE and B3LYP models. This trend is reversed in the HFmethod however exception to the trend do exist. The mean absolute errors (MAE)in the screened (FF) and unscreened (SOS) polarizability are 0.78 \AA$^3$ forthe 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 aresmaller than those predicted by the PBE and B3LYP models. Finally, a simplescheme is devised to obtain FF quality estimate of polarizability from thoseobtained using the SOS method by exploiting the observed trends.