A meta-GGA DFT functional in its original form includes the second derivative of the electron density (the Laplacian). This is a natural development after the GGA (generalized gradient approximation), that includes only the density and its first derivative in the exchange-correlation potential.
Nowadays a meta-GGA functional is refered more typically to one that includes a dependence on the kinetic energy density (), i.e. on the laplacian of the orbitals.
Some functionals of this type are: tHCTH,TPSS, VSXC and M06L .
- Cramer, C. J. (2004) Essentials of Computational Chemistry, 2nd Ed. John Wiley & Sons.