Density functionals from the extended G2 test set: Second-order gradient corrections

In a recent paper [H. L. Schmider and A. D. Becke, J. Chem. Phys. 108, 9624 (1998)], we applied a systematic method for the determination of exchange-correlation functionals within the generalized gradient approximation (GGA) to the extended G2 test set of standard heats of formation of Curtiss et al. [J. Chem. Phys. 106, 1063 (1997)]. In the present work, we apply a similar methodology that goes beyond the GGA by taking second-order gradients and the (noninteracting) kinetic-energy density into account. The resulting improvement in the reproduction of thermochemical data brings us very close to the quality of G2 theory itself. Our lowest mean absolute error for standard heats of formation, 1.60 kcal/mol, is only marginally greater than the G2 value (1.58 kcal/mol). The corresponding largest deviation is 9.97 kcal/mol, as compared to 8.2 kcal/mol for G2 theory.