Physically motivated iso-orbital indicator for meta-GGA exchange functionals

Abstract

The iso-orbital indicator $α= (τ- τ^\mathrm{vW})/τ^\mathrm{UEG}$ is a key ingredient of meta-generalized gradient approximation (meta-GGA) functionals, but diverges in low-density tails , causing unphysical exchange potentials and systematic band gap errors as noted in [J. Chem. Phys. 150, 161101 (2019)]. We replace the denominator of $α$ with a physically motivated Pauli KED drawn from the orbital-free DFT literature, eliminating the divergence in the low density atomic tail without any empirical regularization parameter. Testing two such enhancement factors: LKT and PGS, within the r$^2$SCAN and MS2 exchange functionals, we find that the modified indicators suppress spurious oscillations in the semilocal exchange potential and restore correct electron localization in atomic tails. For a ten-member cubic semiconductor benchmark, the band gap mean absolute error is reduced by 41.1 % for r$^2$SCAN@PGS and 48.8 % for MS2@PGS, while cohesive energy accuracy is largely preserved. The consistent improvement across two functionals with distinct constructions confirms a physical rather than functional specific origin, and motivates further development of meta-GGA functionals with constraint satisfying iso-orbital indicators.