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# 5.10.1 Introduction

(February 4, 2022)

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 $-\varepsilon_{\rm HOMO}$ 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.