An asymptotically corrected (AC) exchange potential proposed by van Leeuwen and Baerends isvanLeeuwen:1994
where is the reduced density gradient. For an exponentially-decaying density, this potential reduces to 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
The parameter 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 relationLevy:1985 is used instead to obtain the exchange energy:
An LB94 calculation is requested by setting EXCHANGE = LB94 in the $rem section. Additional job control and examples appear below.
$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