5.10.1 Introduction

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, ¹²⁴⁵ van Leeuwen R., Baerends E. J.
Phys. Rev. A
(1994), 49, pp. 2421. Link and existing GGA exchange-correlation (XC) potentials decay much faster than the correct $-1/r$ XC potential in the asymptotic region. ¹⁸⁵ Casida M. E., Salahub D. R.
J. Chem. Phys.
(2000), 113, pp. 8918. Link 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. ¹²⁴⁴ van Gisbergen S. J. A. et al.
J. Chem. Phys.
(1996), 105, pp. 3142. Link ^{, 1343} Wu Q., Ayers P. W., Yang W.
J. Chem. Phys.
(2003), 119, pp. 2978. Link Moreover, response properties may be poorly predicted from TDDFT calculations with GGA functionals. ¹²⁴⁴ van Gisbergen S. J. A. et al.
J. Chem. Phys.
(1996), 105, pp. 3142. Link 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.