Title: Unraveling a cavity induced molecular polarization mechanism from collective vibrational strong coupling

Abstract: We demonstrate that collective vibrational strong coupling of molecules in thermal equilibrium can give rise to significant local electronic polarization effects in the thermodynamic limit. We do so by first showing that the full non-relativistic Pauli-Fierz problem of an ensemble of strongly-coupled molecules in the dilute-gas limit reduces in the cavity Born-Oppenheimer approximation to a cavity-Hartree equation. Consequently, each molecule experiences a self-consistent coupling to the dipoles of all other molecules. In the thermodynamic limit, the sum of all molecular dipoles constitutes the macroscopic polarization field and the self-consistency then accounts for the delicate back-action on its heterogeneous microscopic constituents. The here derived cavity-Hartree equations allow for a computationally efficient implementation in an ab-initio molecular dynamics setting. For a randomly oriented ensemble of slowly rotating model molecules, we observe a red shift of the cavity resonance due to the polarization field, which is in agreement with experiments. We then demonstrate that the back-action on the local polarization takes a non-negligible value in the thermodynamic limit and hence the collective vibrational strong coupling can modify individual molecular properties locally. This is not the case, however, for atomic ensembles, where room temperature does not induce any disorder and local polarization effects are absent in the dilute limit. Our findings suggest that the thorough understanding of polaritonic chemistry, such as the modification of chemical reactions, requires self-consistent treatment of the cavity induced polarization and the usually applied restrictions to the displacement field effects may be insufficient.