Generalized quadratic model for charge transfer

We present a two-parabola interpolation model that reproduces the observed behavior for the total energy as a function of fractional occupation for known density functional approximations to the Kohn-Sham exchange-correlation energy. The model is based on the second-order Taylor series expansion of the energy as a function of the electron number for a reference chemical species, and it correctly reduces to a linear regime for density functionals satisfying the ionization theorems. The use of this generalized quadratic model results in revised definitions of electrodonating and electroaccepting powers that correctly diverge for the exact functional. Further application to charge transfer processes using two hydration reaction sets shows that this quadratic generalization unequivocally distinguishes between electrophilic and nucleophilic reaction mechanisms. This distinction was unattainable with previous approximations based on one- and two-parabolas.