From the perspective of perturbation theory, Chai and Chen
Phys. Rev. Lett.
(2013), 110, pp. 033002. proposed a systematic procedure for the evaluation of the derivative discontinuity of the exchange-correlation energy functional in Kohn-Sham (KS) DFT, wherein the exact derivative discontinuity can in principle be obtained by summing up all the perturbation corrections to infinite order. Truncation of the perturbation series at low order yields an efficient scheme for obtaining the approximate derivative discontinuity. In particular, the first-order correction term is equivalent to the frozen-orbital approximation method. Its implementation in Q-Chem supports only local and GGA functionals at present, not meta-GGA, hybrid, or non-local functionals. Job control variables and examples appear below.
$comment Frozen-orbital derivative discontinuity, C atom, PBE $end $molecule 0 3 C $end $rem BASIS 6-31G* METHOD PBE FOA_FUNDGAP true KS_GAP_UNIT 1 ! print gap info in eV THRESH 14 $end @@@ $comment with LFAs-PBE functional instead $end $molecule READ $end $rem BASIS 6-31G* SCF_GUESS READ EXCHANGE gen FOA_FUNDGAP true KS_GAP_UNIT 1 THRESH 14 $end $xc_functional X PBE 1.0 X LFAs 1.0 C PBE 1.0 $end