where, without loss of generality, we have considered that the N-th molecule is the one that undergoes the reaction (notice that, in accordance with the notation introduced in Eq. ( ), the mode D ðNÞ N is highly localized in P N for sufficiently large N). Furthermore, we can identify the photon (â 0 ), the N-th molecule (â N ), and the bright state that excludes it (â BðNÀ1Þ ) as the normal modes embodying the natural degrees of freedom of the problem, since the modes in reactants and products can be written as Duschinsky transformations of these. Explicitly, for the reactants we have