Generating Exchange-Correlation Functionals with a Simplified, Self-Consistent Correlation Factor Model

We focus on the spherically averaged exchange-correlation hole ρ_XC(r, u) of density functional theory, which describes the reduction in the electron density at a distance u due to the reference electron localized at position r. The correlation factor (CF) approach, where the model exchange hole ρ_X^model(r, u) is multiplied by a CF (f_C(r, u)) to yield an approximation to the exchange-correlation hole ρ_XC(r, u) = f_C(r, u) ρ_X^model(r, u), has proven to be a powerful tool for the development of new approximations. One of the remaining challenges within the CF approach is the self-consistent implementation of the resulting functionals. To address this issue, here we propose a simplification of the previously developed CFs such that self-consistent implementations become feasible. As an illustration of the simplified CF model, we develop a new meta-GGA functional, and using only a minimum of empiricism, we provide an easy derivation of an approximation that is of an accuracy similar to more involved meta-GGA functionals.