The Perdew Burke Ernzerhof (PBE) functional is a widely used generalized gradient approximation (GGA) method in density functional theory (DFT). It was developed by John Perdew, Kieron Burke, and Matthias Ernzerhof in 1996. The PBE functional is designed to improve the exchange-correlation energy calculations by including the gradient of the electron density, providing more accurate results for a broad range of systems compared to the local density approximation (LDA).