Instanton formulation of Fermi's golden rule in the Marcus inverted regime

Abstract

Fermi's golden rule defines the transition rate between weakly coupled states and can thus be used to describe a multitude of molecular processes including electron-transfer reactions and light-matter interaction. However, it can only be calculated if the wave functions of all internal states are known, which is typically not the case in molecular systems. Marcus theory provides a closed-form expression for the rate constant, which is a classical limit of the golden rule, and indicates the existence of a normal regime and an inverted regime. Semiclassical instanton theory presents a more accurate approximation to the golden-rule rate including nuclear quantum effects such as tunnelling, which has so far been applicable to complex anharmonic systems in the normal regime only. In this paper we extend the instanton method to the inverted regime and study the properties of the periodic orbit, which describes the tunnelling mechanism via two imaginary-time trajectories, one of which now travels in negative imaginary time. It is known that tunnelling is particularly prevalent in the inverted regime, even at room temperature, and thus this method is expected to be useful in studying a wide range of molecular transitions occurring in this regime.

References in corpus (2)

• Analytic continuation of Wolynes theory into the Marcus inverted regime
• Effects of tunnelling and asymmetry for system-bath models of electron transfer

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• An improved path-integral method for golden-rule rates
• A general non-adiabatic quantum instanton approximation
• Semiclassical instanton theory for reaction rates at any temperature: How a rigorous real-time derivation solves the crossover temperature problem
• Evaluation of transition rates from nonequilibrium instantons
• Nonadiabatic transition paths from quantum jump trajectories
• Extending non-adiabatic rate theory to strong electronic couplings in the Marcus inverted regime
• Instanton Theory for Nonadiabatic Tunneling through Near-Barrier Crossings
• The onset time of Fermi's golden rule
• Fewest switches surface hopping with decoherence in the Marcus inverted regime: correct rates but wrong thermal populations
• Semiclassical Spin Exchange via Temperature-Dependent Transition States