One-parameter optimization of a nonempirical meta-generalized-gradient-approximation for the exchange-correlation energy

The meta-generalized-gradient-approximation (meta-GGA) for the exchange-correlation energy, as constructed by Tao, Perdew, Staroverov, and Scuseria (TPSS) [Phys. Rev. Lett. 91, 146401 (2003)], has achieved usefully consistent accuracy for diverse systems and is the most reliable nonempirical density functional (and the most reliable nonhybrid) in common use. We present here an optimized version of this TPSS functional obtained by empirically fitting a single free parameter that controls the approach of the exchange enhancement factor to its rapidly-varying-density limit, while preserving all the exact constraints that the original TPSS functional satisfies. We find that molecular atomization energies are significantly improved with the optimized version and are even better than those obtained with the best hybrid functionals employing a fraction of exact exchange (e.g., the TPSS hybrid), while energy barrier heights are slightly improved; jellium surface energies remain accurate and almost unchanged. The one-parameter freedom of the TPSS functional may be useful even beyond the meta-GGA level, since the TPSS approximation is a natural starting point for the higher-level hyper-GGA.