5.6 Range-Separated Hybrid Density Functionals

5.6.4 Tuned RSH Functionals Based on the Global Density-Dependent Condition

The value of range-separation parameter based on IP tuning procedure (ωIP) exhibits a troublesome dependence on system size.Uhlig:2014, Garrett:2014, Vazquez:2015, Coons:2016, Oviedo:2016 An alternative method to select ω is the global density-dependent (GDD) tuning procedure,Modrzejewski:2013 in which the optimal value

ωGDD=Cdx2-1/2 (5.18)

is related to the average of the distance dx between an electron in the outer regions of a molecule and the exchange hole in the region of localized valence orbitals. The quantity C is an empirical parameter for a given LRC functional, which was determined for LRC-ωPBE (C=0.90) and LRC-ωPBEh (C=0.75) using the def2-TZVPP basis set.Modrzejewski:2013 (A slightly different value, C=0.885, was determined for Q-Chem’s implementation of LRC-ωPBE.Lao:2018a) Since LRC-ωPBE(ωGDD) provides a better description of polarizabilities in polyacetylene as compared to ωIPHapka:2014, it is anticipated that using ωGDD in place of ωIP may afford more accurate molecular properties, especially in conjugated systems. GDD tuning of an RSH functional is involving by setting the $rem variable OMEGA_GDD = TRUE. The electron density is obviously needed to compute ωGDD in Eq. (5.18) and this is accomplished using the converged SCF density computed using the RSH functional with the value of ω given by the $rem variable OMEGA. The value of ωGDD therefore depends, in principle, upon the value of OMEGA, although in practice it is not very sensitive to this value.

OMEGA_GDD
       Controls the application of ωGDD tuning for long-range-corrected DFT
TYPE:
       LOGICAL
DEFAULT:
       FALSE
OPTIONS:
       FALSE (or 0) Do not apply ωGDD tuning. TRUE (or 1) Use ωGDD tuning.
RECOMMENDATION:
       The $rem variable OMEGA must also be specified, in order to set the initial range-separation parameter.

OMEGA_GDD_SCALING
       Sets the empirical constant C in ωGDD tuning procedure.
TYPE:
       INTEGER
DEFAULT:
       885
OPTIONS:
       n Corresponding to C=n/1000.
RECOMMENDATION:
       The quantity n = 885 was determined by Lao and Herbert in Ref. Lao:2018a using LRC-ωPBE and def2-TZVPP augmented with diffuse functions on non-hydrogen atoms that are taken from Dunning’s aug-cc-pVTZ basis set.

Example 5.9  Sample input illustrating a calculation to determine the ω value for LRC-ωPBE based on the ωGDD tuning procedure.

$comment
The initial omega value has to set.
$end

$molecule
0 1
O   -0.042500   0.091700   0.110000
H    0.749000   0.556800   0.438700
H   -0.825800   0.574700   0.432500
$end


$rem
   EXCHANGE          gen
   BASIS             aug-cc-pvdz
   LRC_DFT           true
   OMEGA             300
   OMEGA_GDD         true
$end

$xc_functional
X   wPBE   1.0
C    PBE   1.0
$end