Generalized Gradient Approximation Made Simple: Theoretical Review

The Generalized Gradient Approximation Made Simple—better known as PBE after Perdew, Burke, and Ernzerhof—provides a non-empirical density-functional for exchange-correlation (XC) that depends only on the local electron density and its gradient. It was designed to obey exact constraints and recover key limits of many-electron physics, while remaining simple and computationally efficient. This exposition situates PBE within Kohn–Sham DFT, details the mathematics behind its exchange and correlation terms, derives the primary reduced gradients and enhancement factors, and explains how exact conditions (uniform scaling, linear response of the uniform gas, Lieb–Oxford bound, spin scaling, and correct high-density behavior) fix the PBE formulas and parameters. Extensions such as PBEsol are briefly discussed.