Nonadiabatic quantum transition-state theory in the golden-rule limit. II. Overcoming the pitfalls of the saddle-point and semiclassical approximations

Abstract

We describe a path-integral molecular dynamics implementation of our recently developed golden-rule quantum transition-state theory (GR-QTST). The method is applied to compute the reaction rate in various models of electron transfer and benchmarked against exact results. We demonstrate that for systems exhibiting two or more transition states, rates computed using Wolynes theory [P. G. Wolynes, J.\ Chem.\ Phys.\ 87, 6559 (1987)] can be overestimated by orders of magnitude, whereas the GR-QTST predictions are numerically accurate. This is the case both at low temperature, where nuclear tunneling makes a considerable contribution, and also in the classical limit, where only GR-QTST rigorously tends to the correct result. Analysis shows that the saddle-point approximation employed by Wolynes theory is not valid in this case, which results in predictions of unphysical reaction pathways, whilst the energy constraint employed by GR-QTST resolves this problem. The GR-QTST method is also seen to give accurate results for a strongly anharmonic system by sampling configurations around the instanton pathway without making the semiclassical approximation. These promising results indicate that the GR-QTST method could be an efficient and accurate approach for simulating electron-transfer reactions in complex molecular systems.

References in corpus (17)

• Parallel Tempering: Theory, Applications, and New Perspectives
• Nuclear quantum effects enter the mainstream
• Exact factorization of the time-dependent electron-nuclear wavefunction
• 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
• Derivation of instanton rate theory from first principles
• High Order Path Integrals Made Easy
• Semiclassical Green's functions and an instanton formulation of electron-transfer rates in the nonadiabatic limit
• Cayley modification for strongly stable path-integral and ring-polymer molecular dynamics
• Ring-polymer instanton theory of electron transfer in the nonadiabatic limit
• Analytic continuation of Wolynes theory into the Marcus inverted regime
• On the calculation of quantum mechanical electron transfer rates
• Non-oscillatory flux correlation functions for efficient nonadiabatic rate theory
• Effects of tunnelling and asymmetry for system-bath models of electron transfer
• Path integral molecular dynamics with surface hopping for thermal equilibrium sampling of nonadiabatic systems
• Semiclassical analysis of the quantum instanton approximation
• Nonadiabatic quantum transition-state theory in the golden-rule limit. I. Theory and application to model systems

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• Confirming the role of nuclear tunnelling in aqueous ferrous-ferric electron transfer
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• An improved path-integral method for golden-rule rates
• A general non-adiabatic quantum instanton approximation
• Nonadiabatic transition paths from quantum jump trajectories