Hybrid or hyper-GGA methods

In the crudest approximation (taking to be linear in A), the integral is given as the average of the values at the two end-points. 

b and c parameters are determined by fitting to experimental data and depend on the chosen forms for and E°°, with typical values being a 0.2, b 0.7 and c 0.8. Subsequent versions denoted B97 and B98 employed ten fitting parameters, but the improvements were rather marginal relative to the three parameters version. 

The t-HCTH functional has been augmented with exact exchange to produce the acronym r-HCTH-hybrid. The PBE functional has also been improved by addition 

Inclusion of exact HE exchange is often found to improve the calculated results, although the optimum fraction to include depends on the specific property of interest. The improvement of new functionals by inclusion of a suitable fraction of exact exchange is now a standard feature. At least part of the improvement may arise from reducing the self-interaction error, since HE theory is completely selfinteraction-free. 

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