A self-consistent systematic optimization of range-separated hybrid functionals from first principles

In this communication, we represent a self-consistent systematic optimization procedure for the development of optimally tuned (OT) range-separated hybrid (RSH) functionals from \emph{first principles}. This is an offshoot of our recent work, which employed a purely numerical approach for efficient computation of exact exchange contribution in the conventional global hybrid functionals through a range-separated (RS) technique. We make use of the size-dependency based ansatz i.e., RS parameter, $\gamma$, is a functional of density, $\rho(\mathbf{r})$, of which not much is known. To be consistent with this ansatz, a novel procedure is presented that relates the characteristic length of a given system (where $\rho(\mathbf{r})$ exponentially decays to zero) with $\gamma$ self-consistently via a simple mathematical constraint. In practice, $\gamma_{\mathrm{OT}}$ is obtained through an optimization of total energy as follows: $\gamma_{\mathrm{OT}} \equiv \underset{\gamma }{\mathrm{opt}} \ E_{\mathrm{tot},\gamma}$. It is found that the parameter $\gamma_{\mathrm{OT}}$, estimated as above can show better performance in predicting properties (especially from frontier orbital energies) than conventional respective RSH functionals, of a given system. We have examined the nature of highest fractionally occupied orbital from exact piece-wise linearity behavior, which reveals that this approach is sufficient to maintain this condition. A careful statistical analysis then illustrates the viability and suitability of the current approach. All the calculations are done in a Cartesian-grid based pseudopotential (G)KS-DFT framework.