A general non-adiabatic quantum instanton approximation

Lawrence, Joseph E.; Manolopoulos, David E.

doi:10.1063/5.0009109

Cited by 16 publications

(14 citation statements)

References 55 publications

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“…More general methods have also been proposed for arbitrary coupling strengths, 65,[101][102][103][104][105][106][107][108][109] although unlike RPMD in the Born-Oppenheimer case, 4 none has been connected to a rigorous instanton theory. 99,110,111 New path-integral rate theories may thus be inspired by the theoretical developments in this work.…”

Section: Discussionmentioning

confidence: 99%

Nonadiabatic instanton rate theory beyond the golden-rule limit

Trenins,

Richardson

2022

Preprint

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Fermi's golden rule describes the leading-order behaviour of the reaction rate as a function of the diabatic coupling. Its asymptotic ( → 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.

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Section: Discussionmentioning

confidence: 99%

Nonadiabatic instanton rate theory beyond the golden-rule limit

Trenins,

Richardson

2022

Preprint

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“…We have recently shown that Wolynes theory can be generalized to calculate reaction rates beyond the golden-rule limit to give a non-adiabatic quantum instanton approximation, 45 which reduces to the projected quantum instanton in the adiabatic limit. [46][47][48] The development of a generalization of LGR, capable of treating systems with arbitrary couplings, is an important target of future work.…”

Section: Discussionmentioning

confidence: 99%

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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“…We have recently shown that Wolynes theory can be generalised to calculate reaction rates beyond the golden-rule limit, to give a non-adiabatic quantum instanton approximation, 45 which reduces to the projected quantum instanton in the adiabatic limit. [46][47][48] The development of a generalisation of LGR, capable of treating systems with arbitrary couplings, is an important target of future work.…”

Section: Discussionmentioning

confidence: 99%

An improved path-integral method for golden-rule rates

Lawrence,

Manolopoulos

2020

Preprint

Self Cite

View full text Add to dashboard Cite

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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A general non-adiabatic quantum instanton approximation

Abstract: Instanton formulation of Fermi's golden rule in the Marcus inverted regime

Cited by 16 publications

References 55 publications

Nonadiabatic instanton rate theory beyond the golden-rule limit

Nonadiabatic instanton rate theory beyond the golden-rule limit

An improved path-integral method for golden-rule rates

An improved path-integral method for golden-rule rates

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