A new inhomogeneity parameter in density-functional theory

Density-functional exchange–correlation approximations depending on spin densities and their gradients have proven remarkably accurate in recent thermochemical tests e.g., A. D. Becke, J. Chem. Phys. 107, 8554 (1997). With the inherent limitations of first-order gradient corrections now in sight, however, we investigate here a class of inhomogeneity corrections based on a new second-order gradient parameter. The new parameter is logically motivated by previous work on Taylor expanded exchange hole densities, and generates exchange–correlation functionals more accurate than those containing first-order gradients only.