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

摘要

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, 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, weexpect the presented technique to become a powerful tool in the computation ofreaction paths, intermediates, and transition states of medium sized molecules.