Divide-and-Conquer Method for Instanton Rate Theory

Winter, Pierre; Richardson, Jeremy O.

doi:10.1021/acs.jctc.8b01267

Cited by 11 publications

(14 citation statements)

References 72 publications

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“…The corresponding kinetic isotope effects (KIE), defined as k Mu+Y /k H+Y , are also given alternative methods exist for reducing the computational cost of this procedure. 103 3 Results for the low-temperature regime A representation of the instanton optimised for the Mu + CH 4 reaction is shown in Fig. 3.…”

Section: Details Of the Instanton Calculationsmentioning

confidence: 99%

Calculations of quantum tunnelling rates for muonium reactions with methane, ethane and propane

Laude

Calderini

Welsch

et al. 2020

Phys. Chem. Chem. Phys.

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Section: Details Of the Instanton Calculationsmentioning

confidence: 99%

Calculations of quantum tunnelling rates for muonium reactions with methane, ethane and propane

Laude

Calderini

Welsch

et al. 2020

Phys. Chem. Chem. Phys.

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“…The efficient evaluation of the fluctuation prefactor is also important for instanton theories of dynamical quantities such as temperature-dependendent 51,52 and energy-dependent reaction rates 53,54 , where several methods have been proposed to speed up the RPI calculations [54][55][56][57] .…”

Section: Introductionmentioning

confidence: 99%

Instanton theory of ground-state tunneling splittings with general paths

Eraković

Vaillant

Cvitaš

2020

The Journal of Chemical Physics

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We derive a multidimensional instanton theory for calculating ground-state tunneling splittings in Cartesian coordinates for general paths. It is an extension of the method by Mil'nikov and Nakamura [J. Chem. Phys. 115, 6881 (2001)] to include asymmetric paths that are necessary for calculating tunneling splitting patterns in multi-well systems, such as water clusters. The approach avoids multiple expensive matrix diagonalizations to converge the fluctuation prefactor in the ring-polymer instanton (RPI) method, and instead replaces them by an integration of a Riccati differential equation. When combined with the string method for locating instantons, we avoid the need to converge the calculation with respect to the imaginary-time period of the semiclassical orbit, thereby reducing the number of convergence parameters of the optimized object to just one: the number of equally-spaced system replicas used to represent the instanton path. The entirety of the numerical effort is thus concentrated in optimizing the shape of the path and evaluating hessians along the path, which is a dramatic improvement over RPI. In addition to the standard instanton approximations, we neglect the coupling of vibrational modes to external rotations. The method is tested on the model potential of malonaldehyde and on the water dimer and trimer, giving close agreement with RPI at a much-reduced cost.

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“…3.11, 3.12, and 4.18 one must find the instanton trajectory as well as the stability parameters and the matrix C ξ,η for each considered energy. [59][60][61] The instanton trajectory search is facilitated by the following considerations. One can start from the vicinity of the saddle point where the instanton trajectory is well known and corresponds to the motion along the unstable vibrational mode, the vectors q i and p i correspond to the transverse normal modes vectors with the appropriate normalization, and the stability parameters are u i = 2πω i /ω b .…”

Section: Numerical Implementationmentioning

confidence: 99%

Entanglement Effect and Angular Momentum Conservation in a Non-separable Tunneling Treatment

Georgievskii

Klippenstein

2021

Preprint

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The important, and often dominant, role of tunneling in low temperature kinetics has resulted in numerous theoretical explorations into the methodology for predicting it. Nevertheless, there are still key aspects of the derivations that are lacking, particularly for non-separable systems in the low temperature regime, and further explorations of the physical factors affecting the tunneling rate are warranted. In this work we obtain a closed-form rate expression for the tunneling rate constant that is a direct analog of the rigid-rotor-harmonic-oscillator expression. This expression introduces a novel "entanglement factor" that modulates the reaction rate. Furthermore, we are able to extend this expression, which is valid for non-separable systems at low temperatures, to properly account for the conservation of angular momentum. In contrast, previous calculations have considered only vibrational transverse modes and so effectively employ a decoupled rotational partition function for the orientational modes. We also suggest a simple theoretical model to describe the tunneling effects in the vicinity of the crossover temperature (the temperature where tunneling becomes the dominating mechanism). This model allows one to naturally classify, interpret, and predict experimental data. Among other things, it quantitatively explains in simple terms the so-called "quantum bobsled" effect, also known as the negative centrifugal effect, which is related to curvature of the reaction path. Taken together, the expressions obtained here allow one to predict the thermal and E-resolved rate constants over broad ranges of temperatures and energies.

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Divide-and-Conquer Method for Instanton Rate Theory

Cited by 11 publications

References 72 publications

Calculations of quantum tunnelling rates for muonium reactions with methane, ethane and propane

Calculations of quantum tunnelling rates for muonium reactions with methane, ethane and propane

Instanton theory of ground-state tunneling splittings with general paths

Entanglement Effect and Angular Momentum Conservation in a Non-separable Tunneling Treatment

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