Simple Modifications of the SCAN Meta-Generalized Gradient Approximation Functional.

We analyzed various possibilities to improve upon the SCAN meta-generalized gradient approximation density functional obeying all known properties of the exact functional that can be satisfied at this level of approximation. We examined the necessity of locally satisfying a strongly tightened lower bound for the exchange energy density in single-orbital regions, the nature of the error cancellation between the exchange and correlation parts in two-electron regions, and the effect of the fourth-order term in the gradient expansion of the correlation energy density. We have concluded that the functional can be modified to separately reproduce the exchange and correlation energies of the helium atom by locally releasing the strongly tightened lower bound for the exchange energy density in single-orbital regions, but this leads to an unbalanced improvement in the single-orbital electron densities. Therefore, we decided to keep the F ≤ 1.174 exact condition for any single-orbital density, where F is the exchange enhancement factor. However, we observed a general improvement in the single-orbital electron densities by revising the correlation functional form to follow the second-order gradient expansion in a wider range. Our new revSCAN functional provides more-accurate atomization energies for the systems with multireference character, compared to the SCAN functional. The nonlocal VV10 dispersion-corrected revSCAN functional yields more-accurate noncovalent interaction energies than the VV10-corrected SCAN functional. Furthermore, its global hybrid version with 25% of exact exchange, called revSCAN0, generally performs better than the similar SCAN0 for reaction barrier heights. Here, we also analyzed the possibility of the construction of a local hybrid from the SCAN exchange and a specific locally bounded nonconventional exact exchange energy density. We predict compatibility problems since this nonconventional exact exchange energy density does not really obey the strongly tightened lower bound for the exchange energy density in single-orbital regions.