An asymptotically corrected (AC) exchange potential proposed by van Leeuwen and
Baerends is^{vanLeeuwen:1994}

$${v}_{x}^{\text{LB}}=-\beta \left(\frac{{x}^{2}}{1+3\beta {\text{sinh}}^{-1}(x)}\right)$$ | (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:^{vanLeeuwen:1994}

$${v}_{xc}^{\text{LB94}}={v}_{xc}^{\text{LDA}}+{v}_{x}^{\text{LB}}.$$ | (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. Casida:1998 and Hirata:1999b, 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^{Levy:1985} 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