  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.
