Orbital functionals and other nonlocal approximations hybrids, Meta-GGA, SIC, OEP, etc

Orbital Functionals and Other Nonlocal Approximations Hybrids, Meta-GGA, SIC, OEP, etc. 

The construction of a hybrid functional involves a certain amount of empiricism in the choice of functionals that are mixed and in the optimization of the weight factors given to the mixed functionals. Formally, this might be considered a drawback, but in practice B3LYP has proven to be the most successful approximate functional for chemical applications. 

More extreme examples of this semiempirical mode of construction of functionals are Becke s 1997 hybrid functional, which contains ten adjustable parameters, and the functionals in Refs. [116, 117], each of which contains more than 20 parameters. A more recent example is DF07, which promises a unified treatment of long-range (static) and short-range (dynamical) correlations, with a special correction added to account for dispersion (van der Waals) interactions. This functional contains five mixing parameters, in addition to three parameters contained in the input functionals. 

Another recent beyond-GGA development is the emergence of so-called meta-GGAs, which depend, in addition to the density 

As we have seen in the case of T, it can be much easier to represent a functional in terms of single-particle orbitals than directly in terms of the density. Such functionals are known as orbital functionals, and (45) constitutes a simple example. Another important orbital-dependent functional is the exchange energy (Fock term) of (47). The meta-GGAs and hybrid functionals mentioned above are also orbital functionals, because they depend on the kinetic energy density (79), and on a combination of the orbital functional (47) with ordinary GGAs, respectively. 

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