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The nonlocal potential contributes an extra term to the velocity operator; Ishow here that such term affects the formal expression of the Drude weight in anontrivial way. Notably, the present main result fixes a disturbing discrepancyin the Dreyer-Coh-Stengel sum rule [Phys. Rev. Lett. {\bf 128}, 095901 (2022)].

Drude weight in presence of nonlocal potentials