Efficient treatment of local meta-generalized gradient density functionals via auxiliary density expansion: the density fitting (DF) J+X approximation.
We report an efficient technique to treat density functionals of the meta-generalized gradient approximation (mGGA) class in conjunction with density 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 a DF-JX calculation, we show that the Laplacian of the density $\upsilon$ can be computed with almost no extra cost. With this technique, $\upsilon$-form mGGAs become only slightly more expensive (10%--20%) than GGAs in DF-JX treatment---and several times faster than regular $\tau$-based mGGA calculations with DF-J and regular treatment of the density functional. We investigate the translation of $\upsilon$-form mGGAs into $\tau$-form mGGAs by employing a kinetic energy functional, but find this insufficiently reliable at this moment. However, since $\upsilon$ and $\tau$ carry equivalent information, a reparameterization of accurate mGGAs from the $\tau$-form into the $\upsilon$-form should be possible. Once such functionals become available, we expect the presented technique to become a powerful tool in the computation of reaction paths, intermediates, and transition states of medium sized molecules.
Publisher URL: http://arxiv.org/abs/1710.10049