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

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In this communication, we represent a self-consistent systematic optimisation procedure for the development of optimally tuned (OT) range-separated hybrid (RSH) functionals from 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, γ, is a functional of density, , 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 exponentially decays to zero) with γ self-consistently via a simple mathematical constraint. In practice, is obtained through an optimisation of total energy as follows: . It is found that the parameter , 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 behaviour, 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.