Becke nonlocal-exchange correction

The form of F(p, Vp) varies and often contains empirical parameters. F(p, Vp) is frequently termed a gradient or non-local correction, since the potential is computed not only as a funcion of the location but also as a function of the Laplacian of the charge density, Vp(r). Of course, even these nonlocal functionals are perfectly local in a mathematical sense. The development of nonlocal exchange functionals is dominated by Becke, who has published a number of increasingly refined mathematical expressions for F(p, Vp) since 1983 (B). Nonlocal correlation functionals have been proposed by Perdew (P), Lee, Yang, and Parr (LYP), and Perdew and Wang (PW). The most commonly used nonlocal functional combinations are BP, BLYP and BPW. Earlier correction schemes like the self-interaction correction by Stoll, PreuB, and Pavli-dou (SPP) have been found to be inferior to the gradient-corrected functionals in most cases and seldom appear in the literature. 

A more sophisticated DFT study by Bridgeman and Rothery has also been published [18]. They used a functional consisting of a LSD part with nonlocal corrections from the Becke 1988 functional for exchange and the Perdew 1986 functional for correlation. The results were slightly better than those of Piechota and Suffczynski but the dissociation energies were still systematically overestimated. 

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