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

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.

arXiv comment6 pages, 2 figures

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Cited by in corpus (6)

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• Deorbitalized meta-GGA Exchange-Correlation Functionals in Solids
• Semilocal exchange-correlation potentials for solid-state calculations: Current status and future directions
• Shortcomings of meta-GGA functionals when describing magnetism
• Orbital-free approximations to the kinetic-energy density in exchange-correlation MGGA functionals: tests on solids
• On the calculation of the bandgap of periodic solids with MGGA functionals using the total energy