Generalized gradient approximations with local parameters

We develop and demonstrate the performance of a nonseparable form of the generalized gradient approximation (GGA) for exchange and correlation that includes locally varying parameters that match second-order gradient expansion behavior. Specifically, the high- and low-density limits are included to recover locally the linear response through inclusion of their dependence on the electron density. This local parametrization allows the GGA form to provide varying behavior depending on the density regime. On the basis of an extensive series of property calculations involving both molecules and solids, we show that this nonempirical methodology can lead to a balanced GGA description of both finite and extended systems.