The correlation factor model for the exchange-correlation energy and its application to transition metal compounds

In the recently developed correlation factor (CF) model [Precechtelova et al., J. Chem. Phys. 143, 144102 (2015)], the exchange-correlation (XC) hole is approximated. Since various constraints satisfied by the XC-hole are known, approximations to it can be designed which largely avoid empirical adjustments. In the CF approach, the XC-hole is written as a product of an exchange hole times a CF. An important constraint satisfied by the CF model is that it correctly reproduces the exact exchange energy in the high density limit. This is achieved by employing the exact exchange-energy per particle (ϵ_Xr) as an input variable, i.e., the CF model builds on exact exchange. Variations of the initial CF model are proposed which ensure that the exact answer is obtained in the homogeneous limit. Furthermore, we apply a correction to the depth of the XC-hole that is designed to capture strong correlation. EC functionals that build on exact exchange, such as hybrids, often fail for systems that exhibit sizeable electron correlation. Despite this fact and despite the reduction of empiricism to a single parameter within CF, accurate atomization energies are obtained for strongly-correlated transition metal compounds. The CF model significantly improves upon widely used functionals such as Perdew-Burke-Ernzerhof (PBE), PBE hybrid, and Tao-Perdew-Staroverov-Scuseria (TPSS).