Faster Exact Exchange for Solids via occ-RI-K: Application to Combinatorially Optimized Range-Separated Hybrid Functionals for Simple Solids with Pseudopotentials Near the Basis Set Limit

In this work, we developed and showcased the occ-RI-K
algorithm
to compute the exact exchange contribution in density functional calculations
of solids near the basis set limit. Within the Gaussian planewave
(GPW) density fitting, our algorithm achieves a 1–2 orders
of magnitude speedup compared to conventional GPW algorithms. Since
our algorithm is well suited for simulations with large basis sets,
we applied it to 12 hybrid density functionals with pseudopotentials
and a large uncontracted basis set to assess their performance on
band gaps of 25 simple solids near the basis set limit. The largest
calculation performed in this work involves 16 electrons and 350 basis
functions in the unit cell utilizing a 6 × 6 × 6 k-mesh. With 20–27% exact exchange, global hybrid
functionals (B3LYP, PBE0, revPBE0, B97-3, SCAN0) perform similarly
with a root-mean-square deviation (RMSD) of 0.61–0.77 eV, while
other global hybrid functionals such as M06-2X (2.02 eV) and MN15
(1.05 eV) show higher RMSD due to their increased fraction of exact
exchange. A short-range hybrid functional, HSE achieves a similar
RMSD (0.76 eV) but shows a notable underestimation of band gaps due
to the complete lack of long-range exchange. We found that two combinatorially
optimized range-separated hybrid functionals, ωB97X-rV (3.94
eV) and ωB97M-rV (3.40 eV), and the two other range-separated
hybrid functionals, CAM-B3LYP (2.41 eV) and CAM-QTP01 (4.16 eV), significantly
overestimate the band gap because of their high fraction of long-range
exact exchange. Given the failure of ωB97X-rV and ωB97M-rV,
we have yet to find a density functional that offers consistent performance
for both molecules and solids. Our algorithm development and density
functional assessment will serve as a stepping stone toward developing
more accurate hybrid functionals and applying them to practical applications.