Why Does the B3LYP Hybrid Functional Fail for Metals?

The B3LYP hybrid functional has shown to successfully predict a wide range of molecular properties. For periodic systems, however, the failure to attain the exact homogeneous electron gas limit as well as the semiempirical construction turns out to be a major drawback of the functional. We rigorously assess the B3LYP functional for solids through calculations of lattice parameters, bulk moduli, and thermochemical properties (atomization energies and reaction energies). The theoretical lattice constants overestimate the experimental ones by approximately 1%, and hence behave similarly to the PBE gradient-corrected exchange-correlation functional. B3LYP atomization energies of solids are drastically worse than those of nonempirical hybrid Hartree-Fock/density functionals (HF/DFT) such as PBE0 and HSE03. These large errors can be traced back to the lack of a proper description of "free-electron-like" systems with a significant itinerant character (metals and small gap semiconductors). Similar calculations using the popular semiempirical B3PW91 hybrid functional, which fulfills the uniform electron gas limit, show a clear improvement over B3LYP regarding atomization energies. Finally, theoretical values for heats of formation for both the B3LYP as well as the B3PW91 functionals are presented. These document a most likely fortuitously good agreement with experiment for the B3LYP hybrid functional.