Exact Potential Energy Surface for Molecules in Cavities

We find and analyze the exact time-dependent potential energy surface driving the proton motion for a model of cavity-induced suppression of proton-coupled electron transfer. We show how, in contrast to the polaritonic surfaces, its features directly correlate to the proton dynamics and we discuss cavity modifications of its structure responsible for the suppression. The results highlight the interplay between nonadiabatic effects from coupling to photons and coupling to electrons and suggest caution is needed when applying traditional dynamics methods based on polaritonic surfaces.

Figure 1

Upper panel: the lowest BO surfaces for the PCET model. The initial conditional electronic wave function associated with the initial excitation on the donor side is shown in the inset on the left, showing localization of the electron at negative $r$ values, while those associated with the BO surfaces after a proton transfer are shown on the right. The latter show that on the second surface the electron is localized at negative $r$ values, while on the lower surface the electron becomes localized at positive $r$. Lower panel: the polaritonic surfaces, for coupling strengths indicated.

Figure 2

Snapshots of the nuclear density (scaled by 0.1) and exact TDPES for dynamics inside (red) and outside (black) the cavity. The lowest panels show the electronic and nuclear dipole moments and the photon number over time. Cavity-induced suppression of PCET is evident in the red density as part of the nuclear wave packet becomes trapped on the left, consistent with the structure of the TDPES (see text).

Figure 3

Snapshots of the nuclear density and the components of the TDPES for dynamics in the cavity, $\lambda =0.005$, ${\omega }_{\alpha }=0.1$. The thin lines represent the polaritonic surfaces.

Figure 4

Snapshots of the zero- and one-photon resolved nuclear densities of Eq. (10) (lower panel), along with the BO coefficients of Eq. (11) (upper panel).