Exchange-correlation density functional beyond the gradient approximation

An exchange-correlation functional is introduced that goes beyond the conventional gradient approximation by including contributions from the Laplacian of the density. The exchange part of this functional reproduces atomic exchange energies from the optimized potential model for main group elements (H-Xe) more accurately than other established exchange functionals. By construction, the exchange functional reproduces the small-gradient expansion for the exchange energy up to the fourth order and possesses the Coulomb asymptote for the exchange potential $v_x.$ In molecular applications, the exchange functional is combined with a modified version of a recently proposed nonlocal correlation functional based on a Coulomb hole model. Detailed results are reported for the molecules from the G2 database. In an overall assessment, the present results for the atomization energies and the molecular geometries for the G2 reference molecules seem comparable in quality to those from the B3LYP hybrid functional. Some illustrative results for transition-metal compounds are also given.