The computation of electron transfer rates: The nonadiabatic instanton solution

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Nonadiabatic instanton calculation of multistate electron transfer reaction rate: Interference effects in three and four states systemsIn this paper semiclassical low-temperature rate theory is extended to treat nonadiabatic transitions which are typically important in electron transfer reactions. This theory is appropriate for arbitrary coupling strength between electronic states. As in adiabatic semiclassical tunneling theory, it is found that the leading order contribution to the tunneling rate is due to periodic orbits which exist in the barrier region of configuration space between reactant and product. In the current case, these orbits move on effective potentials generated from upside-down ͑nuclear͒ potentials of the coupled electronic states. A stable method of finding these mixed quantum/classical ''trajectories'' is developed using a Newton-Raphson method. Examples employing model systems demonstrate that the current nonadiabatic theory well-reproduces the known adiabatic and Golden Rule limits and that the theory can indeed be applied to systems with more than one degree of freedom.

Section: Introductionsupporting

confidence: 61%

Section: Discussionmentioning

confidence: 79%

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The semiclassical calculation of nonadiabatic tunneling rates

Schwieters¹,

Voth²

1998

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“…For these, a more general approach is needed which correctly gives the limiting cases in both the strong-and weak-coupling regimes. Some suggestions have been given as to how instanton theory could be extended to describe these reactions, 104 but as they are based on the "Im F" premise, they do not appear to give a reasonable classical high-temperature limit. Further work is needed to benchmark these approaches and to apply them to realistic problems.…”

Section: Further Developmentsmentioning

confidence: 99%

Perspective: Ring-polymer instanton theory

Richardson

2018

124

Since the earliest explorations of quantum mechanics, it has been a topic of great interest that quantum tunneling allows particles to penetrate classically insurmountable barriers. Instanton theory provides a simple description of these processes in terms of dominant tunneling pathways. Using a ring-polymer discretization, an efficient computational method is obtained for applying this theory to compute reaction rates and tunneling splittings in molecular systems. Unlike other quantum-dynamics approaches, the method scales well with the number of degrees of freedom, and for many polyatomic systems, the method may provide the most accurate predictions which can be practically computed. Instanton theory thus has the capability to produce useful data for many fields of low-temperature chemistry including spectroscopy, atmospheric and astrochemistry, as well as surface science. There is however still room for improvement in the efficiency of the numerical algorithms, and new theories are under development for describing tunneling in nonadiabatic transitions.

“…͑However, encouraging progress in the latter arena has been been reported by Wolynes, 17 and we will make contact with and extend this intriguing point of view from a different perspective.͒ In a recent paper, it was shown that significant progress toward the calculation of ET rate constants for general systems can be achieved by exploring the structure of instanton theory in systems influenced by nonadiabatic transitions. 18 To briefly review this perspective, the approach 18 is based on the instanton expression for quantum rate constants [19][20][21][22][23] combined with a nonadiabatic dynamics formalism 24,25 adapted to treat the imaginary time instanton trajectory undergoing nonadiabatic transitions. As will be discussed later, this mathematical formalism is also contained within the um-brella of a unified theoretical framework for quantum activated rate constants, as was developed in Ref.…”

Section: Introductionmentioning

confidence: 99%

A unified framework for quantum activated rate processes. II. The nonadiabatic limit

Cao

Voth

1997

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Quantum mechanical canonical rate theory: A new approach based on the reactive flux and numerical analytic continuation methods Erratum: "A unified framework for quantum activated rate processes.A recently proposed unified theoretical framework for quantum activated rate constants is further developed and explored. The case of electronically nonadiabatic rate processes is considered, and the weak coupling limit explicitly investigated by an expansion of the rate constant expression. By virtue of this approach, a semiclassical Golden Rule expression is derived after a series of steepest descent approximations. The semiclassical analysis in turn reveals a closed form path integral expression for the quantum activated rate constant in the nonadiabatic ͑Golden Rule͒ limit which is free of harmonic and/or classical approximations for the many-dimensional nuclear ͑vibronic͒ modes. The latter expression is amenable to direct calculation in realistic systems through computer simulation.