Nonadiabatic quantum transition-state theory in the golden-rule limit. I. Theory and application to model systems

Abstract

We propose a new quantum transition-state theory for calculating Fermi's golden-rule rates in complex multidimensional systems. This method is able to account for the nuclear quantum effects of delocalization, zero-point energy and tunnelling in an electron-transfer reaction. It is related to instanton theory but can be computed by path-integral sampling and is thus applicable to treat molecular reactions in solution. A constraint functional based on energy conservation is introduced which ensures that the dominant paths contributing to the reaction rate are sampled. We prove that the theory gives exact results for a system of crossed linear potentials and also the correct classical limit for any system. In numerical tests, the new method is also seen to be accurate for anharmonic systems, and even gives good predictions for rates in the Marcus inverted regime.

arXiv comment18 pages and 6 figures

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Cited by in corpus (11)

• Instanton formulation of Fermi's golden rule in the Marcus inverted regime
• On the calculation of quantum mechanical electron transfer rates
• Semiclassical instanton formulation of Marcus-Levich-Jortner theory
• Semiclassical analysis of the quantum instanton approximation
• Nonadiabatic instanton rate theory beyond the golden-rule limit
• An analysis of isomorphic RPMD in the golden rule limit
• Nonadiabatic quantum transition-state theory in the golden-rule limit. II. Overcoming the pitfalls of the saddle-point and semiclassical approximations
• Revisiting nuclear tunnelling in the aqueous ferrous-ferric electron transfer
• An improved path-integral method for golden-rule rates
• A general non-adiabatic quantum instanton approximation
• Extending non-adiabatic rate theory to strong electronic couplings in the Marcus inverted regime