Exchange long-range corrections

Likura H, Tsuneda T, Yanai T, Hirao K (2001) A long-range correction scheme for generalized-gradient-approximation exchange functionals, J Chem Phys, 115 3540—3544... 

An approach to address the proper r decay of the exchange-correlation potential is the LC scheme, where LC indicates a long-range correction. HF exchange is only applied to long-range electron correlation, with a functional defined as... 

As mentioned above, various correction schemes have been developed up to the present. However, there is room for further improvement in conventional correction schemes. Conventional hybrid functionals give poor excitation energies in TDDFT calculations as mentioned later. Asymptotic and SICs have little (or worse) effect on reproducibilities of molecular chemical properties. Recently, it has been proved that a long-range correction for exchange functionals obviously brings solutions to various... 

Long-range correction schemes for exchange functionals... 

It is easily confirmed that Eq. (67) reproduces the original GGA exchange functional for fjb = 0. Parameter jx is determined to optimize bond distances of homonuclear diatomic molecules up to the third period as /r = 0.33. This scheme is called long-range correction (EC) scheme . The applicabilities of the EC scheme will be discussed in the later section. 

In Fig. 1 we report the orbital energies for the benzene molecule, comparing HF, GKS, GGA (namely B-LYP ) and exchange-only OEP (namely the LHF method, see seetion 3.7.1) for GKS we consider long-range corrected (LC-BLYP ) and eonventional hybrids (B3-LYP with 20% of HF exehange, BH-LYP with 50% of HF exchange). The exaet vertieal I.P. is at... 

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