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.927, 284, 940, 188, 691 An alternative method to select ω is the global density-dependent (GDD) tuning procedure,642 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.642 (A slightly different value, C=0.885, was determined for Q-Chem’s implementation of LRC-ωPBE.529) Since LRC-ωPBE(ωGDD) provides a better description of polarizabilities in polyacetylene as compared to ωIP343, 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. 529 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 5.7  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