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When the enhanced electromagnetic field of a confined light mode interacts with photoactive molecules, the system can be driven into the regime of strong coupling, where new hybrid light-matter states, polaritons, are formed. Polaritons, manifested by the Rabi split in the dispersion, have shown potential for controlling the chemistry of the coupled molecules. Here, we show by angle-resolved steady-state experiments accompanied by multi-scale molecular dynamics simulations that the molecular Stokes shift plays a significant role in the relaxation of polaritons formed by organic molecules embedded in a polymer matrix within metallic Fabry-Pérot cavities. Our results suggest that in the case of Rhodamine 6G, a dye with a significant Stokes shift, excitation of the upper polariton leads to a rapid localization of the energy into the fluorescing state of one of the molecules, from where the energy scatters into the lower polariton (radiative pumping), which then emits. In contrast, for excitonic J-aggregates with a negligible Stokes shift, the fluorescing state does not provide an efficient relaxation gateway. Instead, the relaxation is mediated by exchanging energy quanta matching the energy gap between the dark states and lower polariton into vibrational modes (vibrationally assisted scattering). To understand better how the fluorescing state of a molecule that is not strongly coupled to the cavity can transfer its excitation energy to the lower polariton in the radiative pumping mechanism, we performed multi-scale molecular dynamics simulations. The results of these simulations suggest that non-adiabatic couplings between uncoupled molecules and the polaritons are the driving force for this energy transfer process.

It is included two versions of this item: the Accepted Version which is already Open Access and the Published Version which is under an embargo period till 2022-03-09., Coupling molecules to the confined light modes of an optical cavity is showing great promise for manipulating chemical reactions. However, to fully exploit this principle and use cavities as a new tool for controlling chemistry, a complete understanding of the effects of strong light-matter coupling on molecular dynamics and reactivity is required. While quantum chemistry can provide atomistic insight into the reactivity of uncoupled molecules, the possibilities to also explore strongly coupled systems are still rather limited due to the challenges associated with an accurate description of the cavity in such calculations. Despite recent progress in introducing strong coupling effects into quantum chemistry calculations, applications are mostly restricted to single or simplified molecules in ideal lossless cavities that support a single light mode only. However, even if commonly used planar mirror micro-cavities are characterized by a fundamental mode with a frequency determined by the distance between the mirrors, the cavity energy also depends on the wave vector of the incident light rays. To account for this dependency, called cavity dispersion, in atomistic simulations of molecules in optical cavities, we have extended our multi-scale molecular dynamics model for strongly coupled molecular ensembles to include multiple confined light modes. To validate the new model, we have performed simulations of up to 512 Rhodamine molecules in red-detuned Fabry-Pérot cavities. The results of our simulations suggest that after resonant excitation into the upper polariton at a fixed wave vector, or incidence angle, the coupled cavity-molecule system rapidly decays into dark states that lack dispersion. Slower relaxation from the dark state manifold into both the upper and lower bright polaritons causes observable photo-luminescence from the molecule-cavity system along the two polariton dispersion branches that ultimately evolves toward the bottom of the lower polariton branch, in line with experimental observations. We anticipate that the more realistic cavity description in our approach will help to better understand and predict how cavities can modify molecular properties, This work was supported by the Academy of Finland (Grant No. 323996 to G.G.) as well as the European Research Council (Grant No. ERC-2016-StG-714870 to J.F.) and the Spanish Ministry for Science, Innovation, and Universities—AEI (Grant No. RTI2018-099737-B-I00 to J.F.). We thank the Center for Scientific Computing (CSC-IT Center for Science) for generous computational resources

We discovered a sign error in our implementation of the (correct) expression for the exchange interaction between the Auger electron and the bound electrons (Eq. (2)). As a consequence, the Auger rates reported in the aforementioned article 1 are not correct. We have corrected the error in our implementation and recomputed the single and double core Auger rates for all molecules. After correcting the sign of the exchange potential the computed Auger decay rates are slightly smaller. The deviation to previously published values is slightly larger, but still comparable to the deviations between the two theoretical works 2, 3 and experiments. 4–6 Since both single and double core Auger rates were overestimated, the conclusions we draw, which were concerned with the ratio between the double and single-core Auger rates, remain unaltered. Therefore, with this correction Tables I–III and Figure 1 of the original article need to be replaced by the tables and the figure in this erratum. The tables and figures can be found in the supplemental material. 7