Beyond the GGA functionals

AU these efforts point out how the GGA form is severely limited, and in practice some compromise must be done between molecular applications, which require more nonlocal functionals [57], and soUd-state uses, for which local functionals always provide good results [58]. One general way to go beyond the GGA is to construct a fiUly nonlocal density functional. This goal is quite ambitious and trials might lead to functionals useless for practical purpose [59]. A more practical way is to construct a functional casting additional semilocal information. This can be done, for instance, including the kinetic energy density of the occupied KS orbitals  

It is interesting to note that early x-fiinctionals preceded most GGA s[60,61]. These x-functionals (sometimes referred to as Meta-GGA s [62]), seem to be quite promising, as demonstrated by recent constructions [63-65] based upon fits to chemical data. They have also some important properties. In particular, the PBE fimctional, as well as other GGAs, is not self-interaction free, that is the correlation energy does not vanish for a one-electron density. In this sense, nonlocal functionals, using the kinetic energy density, are Self Interaction Correlation (SIC) free by construction. 

As usual, the parameter D is estimated by minimizing the mean absolute error in the atomization energies of a standard set of molecules (D=0.113). 

The correlation counterpart is nothing else the PBE correlation functional with an additional contribution, which leads to a vanishing correlation for one-electron systems. 

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