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We demonstrate that collective vibrational strong coupling of molecules inthermal equilibrium can give rise to significant local electronic polarizationsin the thermodynamic limit. We do so by first showing that the fullnon-relativistic Pauli-Fierz problem of an ensemble of strongly-coupledmolecules in the dilute-gas limit reduces in the cavity Born-Oppenheimerapproximation to a cavity-Hartree equation. Consequently, each moleculeexperiences a self-consistent coupling to the dipoles of all other molecules.The here derived cavity-Hartree equations allow for a computationally efficientimplementation in an ab-initio molecular dynamics setting. For a randomlyoriented ensemble of slowly rotating model molecules, we observe a red shift ofthe cavity resonance due to the polarization field, which is in agreement withexperiments. We then demonstrate that the back-action on the local polarizationtakes a non-negligible value in the thermodynamic limit and hence thecollective vibrational strong coupling can polarize individual molecules. Theobserved local polarization pattern with zero net polarization resembles acontinuous form of a spin-glass (or better polarization-glass) phase. Thecontinuous polarization distribution implies the existence of hotspots withinthe molecular ensemble, where the collective coupling can strongly alter localmolecular properties. For atomic ensembles, however, these local polarizationmechanism is absent, since room temperature cannot induce any disorder in thedilute limit. Overall, our findings suggest that the thorough understanding ofpolaritonic chemistry, such as the modification of chemical reactions, requiresa self-consistent treatment of the cavity induced polarization and the usuallyapplied restrictions to the displacement field effects are insufficient.

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