Rehabilitation of the Perdew-Burke-Ernzerhof generalized gradient approximation for layered materials

The structural and energetic properties of layered materials present a challenge to density functional theory with common semilocal approximations to the exchange-correlation energy. By combining the most widely used semilocal generalized gradient approximation (GGA), the Perdew-Burke-Ernzerhof (PBE) one, with the revised Vydrov--van Voorhis nonlocal correlation functional (rVV10), both excellent structural and energetic properties of 28 layered materials have been recovered with a judicious parameter selection. We term the resulting functional PBE+rVV10L, with the ``L'' indicating that it is for layered materials. Such a combination is not new, and only involves refitting a single global parameter. However, the resulting excellent accuracy suggests such a dispersion-corrected PBE for many aspects of theoretical studies on layered materials. For comparison, we also present the results for PBE+rVV10 where the parameter is determined by 22 interaction energies between molecules.