5 Density Functional Theory

5.10 Asymptotically Corrected Exchange-Correlation Potentials

No GGA exchange functional can simultaneously produce the correct contribution to the exchange energy density and exchange potential in the asymptotic region of molecular systems,vanLeeuwen:1994 and existing GGA exchange-correlation (XC) potentials decay much faster than the correct -1/r XC potential in the asymptotic region.Casida:2000 High-lying occupied orbitals and low-lying virtual orbitals are therefore too loosely bound, and -εHOMO becomes far smaller than the ionization energy, despite the exact condition that these should be the same for the exact functional.vanGisbergen:1996, Wu:2003 Moreover, response properties may be poorly predicted from TDDFT calculations with GGA functionals.vanGisbergen:1996 Long-range corrected hybrid DFT (LRC-DFT), described in Section 5.6, has greatly remedied this situation, but is more expensive that KS-DFT with GGA functionals due to the use of Hatree-Fock exchange. The asymptotic corrections described in this section are designed to remedy the same problems but within the GGA framework.