# Exact Potential Energy Surface for Molecules in Cavities

## TL;DR

This paper derives and analyzes the exact time-dependent potential energy surface for proton motion in molecules within cavities, revealing how cavity effects influence proton dynamics and challenge traditional polaritonic surface approaches.

## Contribution

It introduces the exact potential energy surface for cavity-molecule systems, providing insights into cavity-induced suppression of proton transfer beyond polaritonic approximations.

## Key findings

- Exact potential energy surface correlates with proton dynamics.
- Cavity modifications alter the structure of the potential energy surface.
- Traditional polaritonic surfaces may be insufficient for accurate dynamics.

## Abstract

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 discuss cavity-modifications of its structure responsible for the suppression. The results highlight the interplay between non-adiabatic effects from coupling to photons and coupling to electrons, and suggest caution is needed when applying traditional dynamics methods based on polaritonic surfaces.