Functional form of the generalized gradient approximation for exchange:   The PBE$\alpha$ functional
  A new functional form for the exchange enhancement in the generalized gradient approximation within density functional theory is given. The functional form satisfies the constraints used to construct the Perdew-Burke-Ernzerhof (PBE) functional but can be systematically varied using one parameter. This gives the possibility to estimate the reliability of a computational result or to fit the parameter for a certain problem. Compared to other semi-empirical functionals, the present has the advantage that only one physically transparent parameter is used and that the fitted functional will obey the same exact conditions as PBE functional. Furthermore the simple form of the exchange enhancement means that oscillating terms in the exchange potential are avoided. 
Georg K. H. Madsen