Examining the order-of-limits problem and lattice constant performance of the Tao–Mo functional

In their recent communication, Tao and Mo [Phys. Rev. Lett. 117, 073001 (2016)] presented a semi-local density functional derived from the density matrix expansion of the exchange hole localized by a general coordinate transformation. We show that the order-of-limits problem present in the functional, dismissed as harmless in the original publication, causes severe errors in predicted phase transition pressures. We also show that the claim that lattice volume prediction accuracy exceeds that of existing similar functionals was based on comparison to reference data that miss anharmonic zero-point expansion and consequently overestimates accuracy. By highlighting these omissions, we give a more accurate assessment of the Tao-Mo functional and show a possible direction for resolving the order-of-limits problem.