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

The iso-orbital indicator α = (τ − τvW)/τUEG is a key ingredient of meta-generalized gradient approximation (meta-GGA) functionals but diverges in low-density tails, causing unphysical exchange potentials and systematic bandgap errors as noted in Bartók and Yates [J. Chem. Phys. 150, 161101 (2019)]. We replace the denominator of α with a physically motivated Pauli kinetic energy density drawn from the orbital-free density functional theory 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 r2SCAN 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 bandgap mean absolute error is reduced by 41.1% for r2SCAN@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.