An asymptotically corrected (AC) exchange potential proposed by van Leeuwen and
Baerends is^{931}

$${v}_{x}^{\text{LB}}=-\beta \left(\frac{{x}^{2}}{1+3\beta {\text{sinh}}^{-1}(x)}\right)$$ | (5.57) |

where $x=\parallel \widehat{\mathbf{\nabla}}\rho \parallel /{\rho}^{4/3}$ is the reduced
density gradient. For an exponentially-decaying density, this potential
reduces to $-1/r$ in the asymptotic region of molecular systems. The LB94 xc
potential is formed by a linear combination of LDA XC potential and the LB
exchange potential:^{931}

$${v}_{xc}^{\text{LB94}}={v}_{xc}^{\text{LDA}}+{v}_{x}^{\text{LB}}.$$ | (5.58) |

The parameter $\beta $ in Eq. (5.57) was determined by fitting to the exact XC potential for Be atom. As mentioned in Refs. 150 and 378, for TDDFT calculations, it is sufficient to include the AC XC potential for ground-state calculations followed by TDDFT calculations with an adiabatic LDA XC kernel. The implementation of the LB94 XC potential in Q-Chem takes this approach, using the LB94 XC potential for the ground state calculations, followed by a TDDFT calculation with an adiabatic LDA XC kernel. This TDLDA/LB94 approach has been widely applied to study excited-state properties of large molecules.

Since the LB exchange potential in Eq. (5.57) does not come from the
functional derivative of an exchange energy functional, the Levy-Perdew virial
relation^{562} is used instead to obtain the exchange energy:

$${E}_{x}^{\text{LB}}=-\int {v}_{x}^{\text{LB}}[\rho ](\text{\mathbf{r}})\left[3\rho (\mathbf{r})+\mathbf{r}\mathbf{\cdot}\widehat{\mathbf{\nabla}}\rho (\mathbf{r})\right]\mathit{d}\mathbf{r}$$ | (5.59) |

An LB94 calculation is requested by setting EXCHANGE = LB94
in the *$rem* section. Additional job control and examples appear below.

LB94_BETA

Sets the $\beta $ parameter for the LB94 XC potential

TYPE:

INTEGER

DEFAULT:

500

OPTIONS:

$n$
Corresponding to $\beta =n/10000$.

RECOMMENDATION:

Use the default.

$comment TDLDA/LB94 calculation is performed for excitation energies. $end $molecule 0 1 N 0.0000 0.0000 0.0000 N 1.0977 0.0000 0.0000 $end $rem JOBTYPE = sp EXCHANGE = lb94 BASIS = 6-311(2+,2+)G** CIS_N_ROOTS = 30 RPA = true $end