Exact exchange (EXX) methods, via the optimized effective
potential (OEP), are techniques for making "true" density
functionals out of orbital-dependent functionals such as
Hartree-Fock or MC-SCF wave functions. Typically, EXX
methods have much better band gaps. The figure below shows
atomic Helium excitation spectra for HF, LDA, BLYP, B3LYP,
along with two OEP methods, as compared to the essentially
exact QMC results. The OEP methods are almost quantitative.
By putting in some wave-function-dependent correlation we
can obtain other properties. Below we have based an OEP
potential on the generalized valence bond (GVB) wave
function, which allows proper dissociation of molecular
hydrogen, something that eludes the best DFT techniques.
