Nonadiabatic transition paths from quantum jump trajectories

Abstract

We present a means of studying rare reactive pathways in open quantum systems using transition path theory and ensembles of quantum jump trajectories. This approach allows for the elucidation of reactive paths for dissipative, nonadiabatic dynamics when the system is embedded in a Markovian environment. We detail the dominant pathways and rates of thermally activated processes and the relaxation pathways and photoyields following vertical excitation in a minimal model of a conical intersection. We find that the geometry of the conical intersection affects the electronic character of the transition state as defined through a generalization of a committor function for a thermal barrier crossing event. Similarly, the geometry changes the mechanism of relaxation following a vertical excitation. Relaxation in models resulting from small diabatic coupling proceeds through pathways dominated by pure dephasing, while those with large diabatic coupling proceed through pathways limited by dissipation. The perspective introduced here for the nonadiabatic dynamics of open quantum systems generalizes classical notions of reactive paths to fundamentally quantum mechanical processes.

On the Mechanism of Polaritonic Rate Suppression from Quantum Transition Paths

“…To elucidate the source of resonant effects in polaritonic systems, we have employed a simple Pauli–Fierz quantum electrodynamics Hamiltonian , for a single photon mode coupled to a reactive proton coordinate solvated in a bath and have employed QTPT to extract barrier crossing rates and mechanisms. QTPT and related quantum path sampling techniques have been recently developed and used to extract mechanistic information from quantum dynamical processes, including energy transfer , and nonadiabatic relaxation through conical intersections. , Here we have used QTPT to extract the dominant reactive pathways of a thermally induced proton-transfer event under conditions where the proton was resonantly coupled to a cavity photon mode, whose natural frequency we could adjust. These pathways are given by a series of jumps through energy eigenstates of the combined proton–cavity system.…”

“…From the committors, we found the barrier crossing rate, k , ,, as a function of ω c /ω s , where ω s is the approximate harmonic frequency of the proton, to look for resonance rate modification effects. In Figure a), the barrier crossing rate relative to a reference k 0 (η c ) is provided for three different light–matter coupling strengths, η c .…”

“…QTPT and related quantum path sampling techniques have been recently developed and used to extract mechanistic information from quantum dynamical processes, including energy transfer 24,25 and nonadiabatic relaxation through conical intersections. 4,26 Here we have used QTPT to extract the dominant reactive pathways of a thermally induced proton-transfer event under conditions where the proton was resonantly coupled to a cavity photon mode, whose natural frequency we could adjust. These pathways are given by a series of jumps through energy eigenstates of the combined proton−cavity system.…”

“…The rates of ground-state bond-breaking reactions of molecules in such cavities have been shown to be significantly modulated from their values outside of the cavity. − This phenomenon of polaritonic chemistry holds promise for selective catalysis; however, the mechanisms of rate enhancement and suppression remain unclear. Here, we have applied quantum transition path theory (QTPT) to a simple model in order to elucidate the underlying quantum mechanical source of the rate modification. We find that the origin of sharp rate decreases under cavity resonance conditions is due to poor bath-mediated tunneling between polariton wave functions.…”