Confirming the role of nuclear tunneling in aqueous ferrous–ferric electron transfer

Lawrence, Joseph E.; Manolopoulos, David E.

doi:10.1063/5.0022678

Cited by 14 publications

(12 citation statements)

References 203 publications

(168 reference statements)

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“…For now, LGR provides an accurate approach to calculating reaction rates in the golden-rule limit, which is straightforward to apply to condensed phase systems in both the normal and inverted regimes. In a forthcoming paper, 41 we shall apply it to an atomistic model of aqueous ferrous-ferric electron transfer and compare the results to those of Wolynes theory and GR-QTST. This will allow us to assess the recent suggestion that…”

Section: Discussionmentioning

confidence: 99%

“…We shall show in a forthcoming paper that, for a realistic atomistic simulation of aqueous ferrous-ferric electron transfer, the solvent degrees of freedom that are uncoupled from the reaction do indeed dominate the GR-QTST approximation to ρ λ (E), leading to a spurious prediction of the rate. 41 Unfortunately, even in relatively small systems, where all degrees of freedom are significantly coupled to the diabatic electronic states, the lack of size consistency in GR-QTST can lead to large errors in the predicted rates, as we shall illustrate for a spin-boson model in Sec. VI.…”

Section: B Size Inconsistencymentioning

confidence: 95%

“…Although the error in the normal regime is not as pronounced, it is important to stress that since the GR-QTST rates do not converge as f → ∞, it is possible to obtain an arbitrarily large error by going to sufficiently large f. We shall demonstrate in a forthcoming paper that, for more realistic atomistic models of condensed phase electron transfer with thousands of degrees of freedom rather than only 32, the error even in the normal regime can become very significant. 41…”

Section: B Multidimensional Spin-boson Modelmentioning

confidence: 99%

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An improved path-integral method for golden-rule rates

Lawrence

Manolopoulos

2020

The Journal of Chemical Physics

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We present a simple method for the calculation of reaction rates in the Fermi golden-rule limit, which accurately captures the effects of tunneling and zero-point energy. The method is based on a modification of the recently proposed golden-rule quantum transition state theory (GR-QTST) of Thapa, Fang, and Richardson [J. Chem. Phys. 150, 104107 (2019)]. While GR-QTST is not size consistent, leading to the possibility of unbounded errors in the rate, our modified method has no such issue and so can be reliably applied to condensed phase systems. Both methods involve path-integral sampling in a constrained ensemble; the two methods differ, however, in the choice of constraint functional. We demonstrate numerically that our modified method is as accurate as GR-QTST for the one-dimensional model considered by Thapa and co-workers. We then study a multidimensional spin-boson model, for which our method accurately predicts the true quantum rate, while GR-QTST breaks down with an increasing number of boson modes in the discretization of the spectral density. Our method is able to accurately predict reaction rates in the Marcus inverted regime without the need for the analytic continuation required by Wolynes theory.

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Section: Discussionmentioning

confidence: 99%

Section: B Size Inconsistencymentioning

confidence: 95%

Section: B Multidimensional Spin-boson Modelmentioning

confidence: 99%

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An improved path-integral method for golden-rule rates

Lawrence

Manolopoulos

2020

The Journal of Chemical Physics

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“…Recently, Chowdhury and Huo [70] have developed 'non-adiabatic Matsubara dynamics', which treats the mapping variables quantum mechanically and the nuclear coordinates by Matsubara dynamics. Progress has also been made in the treatment of charge-transfer reactions, with the development of Golden-rule ring-polymer transition-state approaches [157][158][159][160] and analytic continuations of instanton [161] and Wolynes theory [162,163,172], capable of treating the Marcus-inverted regime. However, it would be premature to say more at present about these rapidly developing areas: we leave this task to future review articles.…”

Section: Conclusion and Recent Developmentsmentioning

confidence: 99%

Path-integral approximations to quantum dynamics

Althorpe

2021

Eur. Phys. J. B

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Imaginary-time path-integral or ‘ring-polymer’ methods have been used to simulate quantum (Boltzmann) statistical properties since the 1980s. This article reviews the more recent extension of such methods to simulate quantum dynamics, summarising the chain of approximations that links practical path-integral methods, such as centroid molecular dynamics (CMD) and ring-polymer molecular dynamics (RPMD), to the exact quantum Kubo time-correlation function. We focus on single-surface Born–Oppenheimer dynamics, using the infrared spectrum of water as an illustrative example, but also survey other recent applications and practical techniques, as well as the limitations of current methods and their scope for future development. Graphic abstract

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“…We shall demonstrate in a forthcoming paper that, for more realistic atomistic models of condensed phase electron transfer with thousands of degrees of freedom rather than only 32, the error even in the normal regime can become very significant. 41…”

Section: B Multi-dimensional Spin Boson Modelmentioning

confidence: 99%

An improved path-integral method for golden-rule rates

Lawrence,

Manolopoulos

2020

Preprint

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We present a simple method for the calculation of reaction rates in the Fermi golden-rule limit, which accurately captures the effects of tunnelling and zero-point energy. The method is based on a modification of the recently proposed golden-rule quantum transition state theory (GR-QTST) of Thapa, Fang and Richardson. While GR-QTST is not size consistent, leading to the possibility of unbounded errors in the rate, our modified method has no such issue and so can be reliably applied to condensed phase systems. Both methods involve path-integral sampling in a constrained ensemble; the two methods differ, however, in the choice of constraint functional. We demonstrate numerically that our modified method is as accurate as GR-QTST for the one-dimensional model considered by Thapa and coworkers. We then study a multi-dimensional spin-boson model, for which our method accurately predicts the true quantum rate, while GR-QTST breaks down with an increasing number of boson modes in the discretisation of the spectral density. Our method is able to accurately predict reaction rates in the Marcus inverted regime, without the need for the analytic continuation required by Wolynes theory.

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Confirming the role of nuclear tunneling in aqueous ferrous–ferric electron transfer

Abstract: Note: This paper is part of the JCP Special Topic on 65 Years of Electron Transfer.

Cited by 14 publications

References 203 publications

An improved path-integral method for golden-rule rates

An improved path-integral method for golden-rule rates

Path-integral approximations to quantum dynamics

An improved path-integral method for golden-rule rates

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