Accurate Density Functional with Correct Formal Properties: A Step Beyond the Generalized Gradient Approximation

We approximate the exchange-correlation energy of density functional theory as a controlled extrapolation from the slowly varying limit. While generalized gradient approximations (GGA's) require only the local density and its first gradient as input, our meta-GGA also requires the orbital kinetic energy density. Its exchange energy component recovers the fourth-order gradient expansion, while its correlation energy is free of self-interaction error. Molecular atomization energies and metal surface energies are significantly improved over GGA, while lattice constants are little changed.