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

TL;DR

This paper introduces an efficient method for treating meta-GGA density functionals using auxiliary density expansion, significantly reducing computational costs and enabling faster calculations of reaction pathways in medium-sized molecules.

Contribution

The authors develop a nearly cost-free way to compute the Laplacian of the density for mGGA functionals, improving computational efficiency in density functional theory calculations.

Findings

Laplace of density can be computed with minimal extra cost.

mGGA calculations become only 10-20% more expensive with the new method.

The technique is promising for studying reaction pathways and transition states.

Abstract

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, $\upsilon$ and $\tau$ are believed to carry essentially equivalent 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 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.