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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 ($\tau$), i.e. on the laplacian of the orbitals.

$\tau \left( \mathbf{r} \right)=\sum\limits_{i}^{occupied}{\frac{1}{2}\left| \nabla \psi _{i}\left( \mathbf{r} \right) \right|}^{2}$

Some functionals of this type are: tHCTH,TPSS, VSXC and M06L .

References Edit

• Cramer, C. J. (2004) Essentials of Computational Chemistry, 2nd Ed. John Wiley & Sons.