Semiclassical analysis of the quantum instanton approximation

Vaillant, Christophe L.; Thapa, Manish; Vaníček, Jiří; Richardson, Jeremy O.

doi:10.1063/1.5123800

Cited by 21 publications

(36 citation statements)

References 60 publications

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“…Nonetheless, a good understanding of the instanton paths has helped in the development of a number of methods based on path-integral sampling which are applicable to reactions in solution. 61,62,104 We hope that the information obtained on the instanton in this work will help derive novel path-integral-based rate theories which can describe the inverted regime more rigorously.…”

Section: Discussionmentioning

confidence: 94%

Instanton formulation of Fermi’s golden rule in the Marcus inverted regime

Heller

Richardson

2020

The Journal of Chemical Physics

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Fermi's golden rule defines the transition rate between weakly coupled states and can thus be used to describe a multitude of molecular processes including electron-transfer reactions and light-matter interaction. However, it can only be calculated if the wave functions of all internal states are known, which is typically not the case in molecular systems. Marcus theory provides a closed-form expression for the rate constant, which is a classical limit of the golden rule, and indicates the existence of a normal regime and an inverted regime. Semiclassical instanton theory presents a more accurate approximation to the golden-rule rate including nuclear quantum effects such as tunnelling, which has so far been applicable to complex anharmonic systems in the normal regime only. In this paper we extend the instanton method to the inverted regime and study the properties of the periodic orbit, which describes the tunnelling mechanism via two imaginary-time trajectories, one of which now travels in negative imaginary time. It is known that tunnelling is particularly prevalent in the inverted regime, even at room temperature, and thus this method is expected to be useful in studying a wide range of molecular transitions occurring in this regime.

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Section: Discussionmentioning

confidence: 94%

Instanton formulation of Fermi’s golden rule in the Marcus inverted regime

Heller

Richardson

2020

The Journal of Chemical Physics

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“…The resulting expressions only involve time-independent quantities, which can be evaluated by sampling imaginary time paths. Recently, Vaillant et al 48 have suggested a slight modification of the original adiabatic quantum instanton, which they have called the projected quantum instanton (PQI). This enforces sampling of paths close to the semiclassical instanton and results in an expression that is even more closely related to Wolynes theory.…”

Section: Introductionmentioning

confidence: 99%

A general non-adiabatic quantum instanton approximation

Lawrence

Manolopoulos

2020

The Journal of Chemical Physics

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“…The transition state theory (TST) proposed around 1930s was the first attempt for a balance between accuracy and efficiency [10,11]. At the same time, some of its approximate semi-empirical revisions can also capture the quantum effects in the reaction, such as quantum transient theory [8,12], but those methods still have many non-negligible shortcomings. The TST method assumes that there is a dividing surface separating the reactants and products, so it ignores the recrossing in dynamical effects, and it is also difficult to find an accurate dividing surface, especially for high-dimensional or barrier-less reactions.…”

Section: Introductionmentioning

confidence: 99%

Rate Coefficients and Kinetic Isotope Effects of the XCl + Cl (X=H, D, Mu) Reactions from Ring Polymer Molecular Dynamics

fang¹,

Fan²,

Ye³

et al. 2020

Preprint

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<p>The ring-polymer molecular dynamics (RPMD) was used to calculate the thermal rate coefficients and kinetic isotope effects of the heavy-light-heavy abstract reaction Cl + XCl ® XCl + Cl (X=H, D, Mu). For the Cl + HCl reaction, the excellent agreement between the RPMD and experimental values provides a strong proof for the accuracy of the RPMD theory. And the RPMD results also consistent with results from other theoretical methods including improved-canonical-variational-theory and quantum dynamics. The most novel finding is there is a double peak in Cl + MuCl reaction near the transition state, leaving a free energy well. It comes from the mode softening of the reaction system at the peak of the potential energy surface. Such an explicit free energy well suggests strongly there is an observable resonance. And for the Cl + DCl reaction, the RPMD rate coefficient again gives very accurate results comparing with experimental values. The only exception is at the temperature of 312.5 K, at this temperature, results from RPMD and all other theoretical methods are close to each other but slightly lower than the experimental value, which indicates experimental or potential energy surface deficiency.</p><div><br></div>

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Semiclassical analysis of the quantum instanton approximation

Cited by 21 publications

References 60 publications

Instanton formulation of Fermi’s golden rule in the Marcus inverted regime

Instanton formulation of Fermi’s golden rule in the Marcus inverted regime

A general non-adiabatic quantum instanton approximation

Rate Coefficients and Kinetic Isotope Effects of the XCl + Cl (X=H, D, Mu) Reactions from Ring Polymer Molecular Dynamics

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