Nonadiabatic instanton rate theory beyond the golden-rule limit

Abstract

Fermi's golden rule describes the leading-order behaviour of the reaction rate as a function of the diabatic coupling. Its asymptotic $(\hslash \to 0)$ limit is the semiclassical golden-rule instanton rate theory, which rigorously approximates nuclear quantum effects, lends itself to efficient numerical computation and gives physical insight into reaction mechanisms. However the golden rule by itself becomes insufficient as the strength of the diabatic coupling increases, so higher-order terms must be additionally considered. In this work we give a first-principles derivation of the next-order term beyond the golden rule, represented as a sum of three components. Two of them lead to new instanton pathways that extend the golden-rule case and, among other factors, account for the effects of recrossing on the full rate. The remaining component derives from the equilibrium partition function and accounts for changes in potential energy around the reactant and product wells due to diabatic coupling. The new semiclassical theory demands little computational effort beyond a golden-rule instanton calculation. It makes it possible to rigorously assess the accuracy of the golden-rule approximation and sets the stage for future work on general semiclassical nonadiabatic rate theories.

References in corpus (22)

• Mapping Variable Ring Polymer Molecular Dynamics: A Path-Integral Based Method for Nonadiabatic Processes
• Derivation of a true (t->0+) quantum transition-state theory. Part I: Uniqueness and equivalence to ring-polymer molecular dynamics transition-state-theory
• Kinetically Constrained Ring-Polymer Molecular Dynamics for Non-adiabatic Chemical Reactions
• Elucidating the NuclearQuantum Dynamics of Intramolecular Double Hydrogen Transfer in Porphycene
• Derivation of instanton rate theory from first principles
• Path-Integral Isomorphic Hamiltonian for Including Nuclear Quantum Effects in Non-adiabatic Dynamics
• Coherent State Mapping Ring-Polymer Molecular Dynamics for Non-Adiabatic quantum propagations
• Semiclassical Green's functions and an instanton formulation of electron-transfer rates in the nonadiabatic limit
• Ring-polymer instanton theory of electron transfer in the nonadiabatic limit
• Instanton formulation of Fermi's golden rule in the Marcus inverted regime
• Analytic continuation of Wolynes theory into the Marcus inverted regime
• On the calculation of quantum mechanical electron transfer rates
• Reaction Rates and Kinetic Isotope Effects of H${}_2$ + OH $\to$ H${}_2$O + H
• Semiclassical instanton formulation of Marcus-Levich-Jortner theory
• Non-oscillatory flux correlation functions for efficient nonadiabatic rate theory
• Effects of tunnelling and asymmetry for system-bath models of electron transfer
• Semiclassical analysis of the quantum instanton approximation
• An analysis of isomorphic RPMD in the golden rule limit
• Nonadiabatic quantum transition-state theory in the golden-rule limit. I. Theory and application to model systems
• Nonadiabatic quantum transition-state theory in the golden-rule limit. II. Overcoming the pitfalls of the saddle-point and semiclassical approximations
• Multistate ring polymer instantons and nonadiabatic reaction rates
• A general non-adiabatic quantum instanton approximation

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• Extending non-adiabatic rate theory to strong electronic couplings in the Marcus inverted regime
• Semiclassical Spin Exchange via Temperature-Dependent Transition States