Generalized energy gap law: An open system dynamics approach to non-adiabatic phenomena in molecules

TL;DR

This paper extends the energy gap law to include vibrational relaxation, dephasing, and radiative loss, providing a unified open system dynamics approach to non-adiabatic phenomena in molecules.

Contribution

It develops a closed analytical solution linking non-radiative rates with vibrational relaxation and dephasing, advancing the theoretical understanding of non-adiabatic molecular processes.

Findings

Non-radiative rate proportional to vibrational relaxation at low temperatures.

Non-radiative rate proportional to dephasing rate at high temperatures.

Unified analytical framework connecting quantum optics and molecular physics.

Abstract

Non-adiabatic molecular phenomena, arising from the breakdown of the Born-Oppenheimer approximation, govern the fate of virtually all photo-physical and photochemical processes and limit the quantum efficiency of molecules and other solid-state embedded quantum emitters. A simple and elegant description, the energy gap law, was derived five decades ago, predicting that the non-adiabatic coupling between the excited and ground potential landscapes lead to non-radiative decay with a quasi-exponential dependence on the energy gap. We revisit and extend this theory to account for crucial aspects such as vibrational relaxation, dephasing, and radiative loss. We find a closed analytical solution with general validity which indicates a direct proportionality of the non-radiative rate with the vibrational relaxation rate at low temperatures, and with the dephasing rate of the electronic transition at high temperatures. Our work establishes a connection between nanoscale quantum optics, open quantum system dynamics and non-adiabatic molecular physics.