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Force correcting atom centered potentials for generalized gradient approximated density functional theory: Approaching hybrid functional accuracy for geometries and harmonic frequencies in small chlorofluorocarbons

Generalized gradient approximated (GGA) density functional theory (DFT) typically overestimates polarizability and bond-lengths, and underestimates force constants of covalent bonds. To overcome this problem we show that one can use empirical force correcting atom centered potentials (FCACPs), parameterized for every nuclear species. Parameters are obtained through minimization of a penalty functional that explicitly encodes hybrid DFT forces and static polarizabilities of reference molecules. For hydrogen, fluorine, chlorine, and carbon the respective reference molecules consist of H$_2$, F$_2$, Cl$_2$, and CH$_4$. The transferability of this approach is assessed for harmonic frequencies in a small set of chlorofluorocarbon molecules. Numerical evidence, gathered for CF$_4$, CCl$_4$, CCl$_3$F, CCl$_2$F$_2$, CClF$_3$, ClF, HF, HCl, CFH$_3$, CF$_2$H$_2$, CF$_3$H, CHCl$_3$, CH$_2$Cl$_2$, CH$_3$Cl indicates that the GGA+FCACP level of theory yields harmonic frequencies that are significantly more consistent with hybrid DFT values, as well as slightly reduced molecular polarizability.