PerdewBurkeErnzerhof

Perdew–Burke–Ernzerhof (PBE) is a widely used exchange-correlation functional within density functional theory. It belongs to the generalized gradient approximation (GGA) class and was developed by John P. Perdew, Kieron Burke, and Matthias Ernzerhof. The functional was introduced in 1996 as a non-empirical, constraint-based form designed to improve upon the local density approximation while maintaining simplicity and robustness.

PBE constructs the exchange-correlation energy by incorporating the gradient of the electron density to satisfy known exact conditions of the exchange-correlation functional. It uses a simple, parameter-free form for the exchange enhancement factor and a corresponding correlation part, ensuring the correct uniform electron gas limit and reasonable behavior for slowly varying densities. The design emphasizes transferability across a broad range of systems, including atoms, molecules, and solids, without resorting to system-specific fitting.

Performance and usage: PBE is one of the most commonly used functionals in solid-state and molecular calculations, providing reliable geometries and energetics with modest computational cost. However, it has limitations: lattice constants predicted by PBE tend to be slightly larger than experiment, and cohesive energies and reaction barriers can be underestimated. By itself, PBE does not account for dispersion interactions; in practice, practitioners often apply dispersion corrections (e.g., D3) or pair PBE with van der Waals functionals for weak interactions.

Variants and related forms: The PBE family includes PBEsol, a variant optimized for condensed-phase solids and lattice constants, and RPBE (revised PBE) with modified exchange to improve adsorption energetics. PBE also has spin-polarized versions for open-shell systems and serves as a common baseline for many hybrid and meta-GGA methods when combined with additional corrections.