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

The value of range-separation parameter based on IP tuning procedure ($\omega_{\rm IP}$) exhibits a troublesome dependence on system size.978, 280, 991, 180, 720 An alternative method to select $\omega$ is the global density-dependent (GDD) tuning procedure,664 in which the optimal value

 $\omega_{\rm GDD}=C\langle d^{2}_{\rm x}\rangle^{-1/2}$ (5.18)

is related to the average of the distance $d_{\rm x}$ 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-$\omega$PBE ($C=0.90$) and LRC-$\omega$PBEh ($C=0.75$) using the def2-TZVPP basis set.664 (A slightly different value, $C=0.885$, was determined for Q-Chem’s implementation of LRC-$\omega$PBE.541) Since LRC-$\omega$PBE($\omega_{\rm GDD}$) provides a better description of polarizabilities in polyacetylene as compared to $\omega_{\rm IP}$346, it is anticipated that using $\omega_{\rm GDD}$ in place of $\omega_{\rm IP}$ 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 $\omega_{\rm GDD}$ in Eq. (5.18) and this is accomplished using the converged SCF density computed using the RSH functional with the value of $\omega$ given by the$rem variable OMEGA. The value of $\omega_{\rm GDD}$ 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 $\omega_{\rm GDD}$ tuning for long-range-corrected DFT
TYPE:
LOGICAL
DEFAULT:
FALSE
OPTIONS:
FALSE (or 0) Do not apply $\omega_{\rm GDD}$ tuning. TRUE (or 1) Use $\omega_{\rm GDD}$ 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 $\omega_{\rm GDD}$ 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. 541 using LRC-$\omega$PBE 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 $\omega$ value for LRC-$\omega$PBE based on the $\omega_{\rm GDD}$ 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