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
$-{\epsilon}_{\mathrm{HOMO}}$ 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.