Comment on "Unraveling a Cavity-Induced Molecular Polarization Mechanism from Collective Vibrational Strong Coupling"

Sidler et al. [J. Phys. Chem. Lett. 15, 5208 (2024)] simulate N Shin–Metiu molecules coupled to one cavity mode with coupling λ_c/√N and report a nonzero large-N saturation of the cavity-induced local polarization. In their cavity-Hartree equations each molecule couples to the cavity and to all other molecules only through one scalar s, the transverse electric field divided by λ, up to a self term of order 1/N. At fixed molecular orientations, with the photon coordinate in the canonical equilibrium stated in the caption of their aligned-molecule figure, we prove E[s²|R] ≤ k_BT for every nuclear configuration R; for gapped molecules in a finite basis the mean and the expected maximum over molecules of the induced dipole are then O(N^(−1/2)). For the rotating molecules of their main figure a linear-response calculation, supported by simulations, gives the same scaling. The published points decrease over N = 10³–10⁴ as expected from N^(−1/2), but a plateau approached as 1/N fits them about as well, so the case against a nonzero limit rests on the theory, not on the points. Their mean amplitude, 4.6 and 4.4 times the canonical value, is consistent with a photon coordinate that was not thermalized and, for the rotating molecules, with the rotational driving of the protocol.