PBE0

PBE0 is a hybrid exchange–correlation functional used in density functional theory. It was introduced by Adamo and Barone in 1999. The functional mixes 25% exact Hartree–Fock exchange with 75% exchange from the PBE functional and retains the PBE correlation energy, so E_xc^PBE0 = 0.25 E_x^HF + 0.75 E_x^PBE + E_c^PBE. The 0.25 fraction is non-empirical, derived from theoretical constraints rather than system-specific fitting.

This construction aims to reduce self-interaction errors and improve thermochemical and kinetic properties relative to PBE, while maintaining computational efficiency closer to a generalized gradient approximation with an added cost for exact exchange. PBE0 typically delivers improved reaction energies, barrier heights, and noncovalent interaction energies for many molecules, and can provide better description of certain properties than PBE.

In practice, performance depends on the system; band gaps and spectroscopic properties can be more accurate than PBE but still underestimate exact gaps. The method is more computationally demanding than pure GGA functionals due to the inclusion of HF exchange, and the scaling of typical implementations is higher.

Limitations include occasional overcorrections and slower scaling; dispersion forces are not inherently treated, so van der Waals corrections may be needed. For solids, alternative hybrids such as screened functionals (for example, HSE06) can offer favorable cost–accuracy trade-offs. PBE0 remains a widely used, non-empirical hybrid for general-purpose electronic structure calculations across chemistry and materials science.