From the perspective of perturbation theory, Chai and Chen[Chai and Chen(2013)] 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.

FOA_FUNDGAP

Compute the frozen-orbital approximation of the fundamental gap.

TYPE:

Boolean

DEFAULT:

FALSE

OPTIONS:

FALSE

Do not compute FOA derivative discontinuity and fundamental gap.

TRUE

Compute and print FOA fundamental gap information. Implies KS_GAP_PRINT.

RECOMMENDATION:

Use in conjunction with KS_GAP_UNIT if true.

KS_GAP_PRINT

Control printing of (generalized Kohn-Sham) HOMO-LUMO gap information.

TYPE:

Boolean

DEFAULT:

false

OPTIONS:

false

(default) do not print gap information

true

print gap information

RECOMMENDATION:

Use in conjunction with KS_GAP_UNIT if true.

KS_GAP_UNIT

Unit for KS_GAP_PRINT and FOA_FUNDGAP (see Section 5.11)

TYPE:

INTEGER

DEFAULT:

0

OPTIONS:

0

(default) hartrees

1

eV

RECOMMENDATION:

none

**Example 5.62** frozen-orbital approximation of derivative discontinuity with PBE and LFAs-PBE functionals on carbon atom

$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