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,¹¹⁴⁵ and existing GGA exchange-correlation (XC) potentials decay much faster than the correct $-1/r$ XC potential in the asymptotic region.¹⁷³ 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.^{1144, 1237} Moreover, response properties may be poorly predicted from TDDFT calculations with GGA functionals.¹¹⁴⁴ 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.