Improved constraint satisfaction in a simple generalized gradient approximation exchange functional.

Though there is fevered effort on orbital-dependent approximate exchange-correlation functionals, generalized gradient approximations, especially the Perdew-Burke-Ernzerhof (PBE) form, remain the overwhelming choice in calculations. A simple generalized gradient approximation (GGA) exchange functional [A. Vela, V. Medel, and S. B. Trickey, J. Chem. Phys. 130, 244103 (2009)] was developed that improves substantially over PBE in energetics (on a typical test set) while being almost as simple in form. The improvement came from constraining the exchange enhancement factor to be below the Lieb-Oxford bound for all but one value of the exchange dimensionless gradient, s, and to go to the uniform electron gas limit at both s = 0 and s → ∞. Here we discuss the issue of asymptotic constraints for GGAs and show that imposition of the large s constraint, lim(s→∞)s(1/2)F(xc)(n,s)<∞, where F(xc)(n, s) is the enhancement factor and n is the electron density, upon the Vela-Medel-Trickey (VMT) exchange functional yields modest further improvement. The resulting exchange functional, denoted VT{8,4}, is only slightly more complicated than VMT and easy to program. Additional improvement is obtained by combining VT{8,4} or VMT exchange with the Lee-Yang-Parr correlation functional. Extensive computational results on several datasets are provided as verification of the overall performance gains of both versions.