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The value of range-separation parameter based on IP tuning procedure
(${\omega}_{\mathrm{IP}}$) 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

$${\omega}_{\mathrm{GDD}}=C{\u27e8{d}_{\mathrm{x}}^{2}\u27e9}^{-1/2}$$ | (5.18) |

is related to the average of the distance ${d}_{\mathrm{x}}$ 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}_{\mathrm{GDD}}$) provides a better description of
polarizabilities in polyacetylene as compared to ${\omega}_{\mathrm{IP}}$^{346}, it is anticipated that using ${\omega}_{\mathrm{GDD}}$ in
place of ${\omega}_{\mathrm{IP}}$ 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 ${\omega}_{\mathrm{GDD}}$ 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 ${\omega}_{\mathrm{GDD}}$ 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 ${\omega}_{\mathrm{GDD}}$ tuning for long-range-corrected DFT

TYPE:

LOGICAL

DEFAULT:

FALSE

OPTIONS:

FALSE (or 0)
Do not apply ${\omega}_{\mathrm{GDD}}$ tuning.
TRUE (or 1)
Use ${\omega}_{\mathrm{GDD}}$ 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 ${\omega}_{\mathrm{GDD}}$ 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.

$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