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We report an efficient technique to treat density functionals of themeta-generalized gradient approximation (mGGA) class in conjunction withdensity fitting of Coulomb terms (DF-J) and exchange-correlation terms (DF-X).While the kinetic energy density $\tau$ cannot be computed in the context of aDF-JX calculation, we show that the Laplacian of the density $\upsilon$ can becomputed with almost no extra cost. With this technique, $\upsilon$-form mGGAsbecome only slightly more expensive (10%--20%) than GGAs in DF-JXtreatment---and several times faster than regular $\tau$-based mGGAcalculations with DF-J and regular treatment of the density functional. Weinvestigate the translation of $\upsilon$-form mGGAs into $\tau$-form mGGAs byemploying a kinetic energy functional, but find this insufficiently reliable atthis moment. However, $\upsilon$ and $\tau$ are believed to carry essentiallyequivalent information beyond $\rho$ and $\Vert\vec\nabla\rho\Vert$ [Phys. Rev.B 2007, 75, 155109], so a reparametrization of accurate mGGAs from the$\tau$-form into the $\upsilon$-form should be possible. Once such functionalsbecome available, we expect the presented technique to become a powerful toolin the computation of reaction paths, intermediates, and transition states ofmedium sized molecules.

journal of chemical theory and computation

Efficient treatment of local meta-generalized gradient density  functionals via auxiliary density expansion: the density fitting (DF) J+X  approximation