On collisional energy transfer in recombination and dissociation reactions: A Wiener–Hopf problem and the effect of a near elastic peak

Zhu, Zhaoyan; Marcus, R. A.

doi:10.1063/1.3026605

Cited by 11 publications

(47 citation statements)

References 61 publications

(86 reference statements)

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“…To describe the transport of chemical recombination dissociation reaction AB ↔ C with the vibrationally excited intermediate AB * , we model the quantum system interacting with two chemical reservoirs or leads with different chemical potentials which provide the effective chemical pumping for the system by collisions 44 . The three quantum states are denoted by |AB , |AB * and |C as schematically shown in Fig.1.…”

Section: B Coupled To Chemical (Fermionic) Reservoirsmentioning

confidence: 99%

“…In this paper, we will establish a theoretical framework in terms of curl flux, population landscape and coherence at steady state for the first time for the non-equilibrium quantum dynamical systems and associated thermodynamics, by exploring the energy transport between different sites in single molecules 45,46 and chemical reaction process (also charge transfer in molecules) 40,44,47,54,56 . The former is coupled to the two heat environments (bosonic) with different temperatures while the latter is coupled to the two chemical environments (fermionic such as electronic baths) with different chemical potentials.…”

Section: Introductionmentioning

confidence: 99%

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Curl flux, coherence, and population landscape of molecular systems: Nonequilibrium quantum steady state, energy (charge) transport, and thermodynamics

Zhang

Wang

2014

The Journal of Chemical Physics

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We established a theoretical framework in terms of the curl flux, population landscape and coherence for non-equilibrium quantum systems at steady state, through exploring the energy and charge transport in molecular processes. The curl quantum flux plays the key role in determining transport properties and the system reaches equilibrium when flux vanishes. The novel curl quantum flux reflects the degree of nonequilibriumness and the time-irreversibility. We found an analytical expression for the quantum flux and its relationship to the environmental pumping (non-equilibriumness quantified by the voltage away from the equilibrium) and the quantum tunnelling. Furthermore, we investigated another quantum signature, the coherence, quantitatively measured by the non-zero off diagonal element of the density matrix. Populations of states give the probabilities of individual states and therefore quantify the population landscape. Both curl flux and coherence depend on steady state population landscape. Besides the environment-assistance which can give dramatic enhancement of coherence and quantum flux with high voltage at a fixed tunnelling strength, the quantum flux is promoted by the coherence in the regime of small tunnelling while reduced by the coherence in the regime of large tunneling, due to the non-monotonic relationship between the coherence and tunneling. This is in contrast to the previously found linear relationship. For the systems coupled to bosonic (photonic and phononic) reservoirs the flux is significantly promoted at large voltage while for fermionic (electronic) reservoirs the flux reaches a saturation after a significant enhancement at large voltage due to the Pauli exclusion principle. In view of the system as a quantum heat engine, we studied the nonequilibrium thermodynamics and established the analytical connections of curl quantum flux to the transport quantities such as energy (charge) transfer efficiency (ETE or CTE), chemical reaction efficiency (CRE), energy dissipation, heat and electric currents observed in the experiments. We observed a perfect transfer efficiency in chemical reactions at high voltage (chemical potential difference). Our theoretical predicted behavior of the electric current with respect to the voltage is in good agreements with the recent experiments on electron transfer in single molecules.

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Section: B Coupled To Chemical (Fermionic) Reservoirsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Curl flux, coherence, and population landscape of molecular systems: Nonequilibrium quantum steady state, energy (charge) transport, and thermodynamics

Zhang

Wang

2014

The Journal of Chemical Physics

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“…15 The recombination rate constant may also be determined directly, upon using the populations acquired from the analytic solution of the master equation. 27 In previous works, approximate analytic solutions, distribution functions for populations, for a master equation for a unimolecular process for a strong collision model, 1 and solutions for the low pressure limit unimolecular master equation based on various energy transfer models have been derived for their dissociation rate constants. 1,27,28 In one study, a Wiener-Hopf method was used to derive analytic solutions, considered for the energy transfer part of the master equation.…”

Section: -17mentioning

confidence: 99%

“…27 In previous works, approximate analytic solutions, distribution functions for populations, for a master equation for a unimolecular process for a strong collision model, 1 and solutions for the low pressure limit unimolecular master equation based on various energy transfer models have been derived for their dissociation rate constants. 1,27,28 In one study, a Wiener-Hopf method was used to derive analytic solutions, considered for the energy transfer part of the master equation. 27 For a bimolecular reaction in discrete matrix form, analytic solutions for populations have been derived.…”

Section: -17mentioning

confidence: 99%

“…1,27,28 In one study, a Wiener-Hopf method was used to derive analytic solutions, considered for the energy transfer part of the master equation. 27 For a bimolecular reaction in discrete matrix form, analytic solutions for populations have been derived. 1 In the present work, the exact analytic solutions (i.e., populations) are derived for the K-adiabatic and K-active based continuum master equation for a bimolecular process, which includes the dissociation, recombination, and energy transfer steps, considered for a bimolecular recombination rate constant using properties of linear inhomogeneous integral equations [29][30][31][32] ( …”

Section: -17mentioning

confidence: 99%

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Bimolecular recombination reactions: K-adiabatic and K-active forms of the bimolecular master equations and analytic solutions

Ghaderi

2016

The Journal of Chemical Physics

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Expressions for a K-adiabatic master equation for a bimolecular recombination rate constant k rec are derived for a bimolecular reaction forming a complex with a single well or complexes with multiple well, where K is the component of the total angular momentum along the axis of least moment of inertia of the recombination product. The K-active master equation is also considered. The exact analytic solutions, i.e., the K-adiabatic and K-active steady-state population distribution function of reactive complexes, g(E JK) and g(E J), respectively, are derived for the K-adiabatic and K-active master equation cases using properties of inhomogeneous integral equations (Fredholm type). The solutions accommodate arbitrary intermolecular energy transfer models, e.g., the single exponential, double exponential, Gaussian, step-ladder, and near-singularity models. At the high pressure limit, the k rec for both the K-adiabatic and K-active master equations reduce, respectively, to the K-adiabatic and K-active bimolecular Rice-Ramsperger-Kassel-Marcus theory (high pressure limit expressions). Ozone and its formation from O + O 2 are known to exhibit an adiabatic K. The ratio of the K-adiabatic to the K-active recombination rate constants for ozone formation at the high pressure limit is calculated to be ∼0.9 at 300 K. Results on the temperature and pressure dependence of the recombination rate constants and populations of O 3 will be presented elsewhere. C 2016 AIP Publishing LLC. [http://dx

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Bimolecular Master Equations for a Single and Multiple Potential Wells with Analytic Solutions

Ghaderi

2018

J. Phys. Chem. A

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The analytic solutions, that is, populations, are derived for the K-adiabatic and K-active bimolecular master equations, separately, for a single and multiple potential wells and reaction channels, where K is the component of the total angular momentum J along the axis of least moment of inertia of the recombination products at a given energy E. The analytic approach provides the functional dependence of the population of molecules on its K-active or K-adiabatic dissociation, association rate constants and the intermolecular energy transfer, where the approach may complement the usual numerical approaches for reactions of interest. Our previous work, Part I, considered the solutions for a single potential well, whereby an assumption utilized there is presently obviated in the derivation of the exact solutions and farther discussed. At the high-pressure limit, the K-adiabatic and K-active bimolecular master equations may each reduce, respectively, to the K-adiabatic and K-active bimolecular Rice-Ramsperger-Kassel-Marcus theory (high-pressure limit expressions) for bimolecular recombination rate constant, for a single potential well, and augmented by isomerization terms when multiple potential wells are present. In the low-pressure limit, the expression for population above the dissociation limit, associated with a single potential well, becomes equivalent to the usual presumed detailed balance between the association and dissociation rate constants, where the multiple well case is also considered. When the collision frequency of energy transfer, Z, between the chemical intermediate and bath gas is sufficiently less than the dissociation rate constant k( E' J' K') for postcollision ( E' J' K), then the solution for population, g( EJK), above the critical energy further simplifies such that depending on Z, the dissociation and association rate constant k( EJK), as g( EJK) = k( EJK)A·BC/[ Z+ k( EJK)], where A and BC are the reactants, for example, relevant for O formation from O + O + Ar up to ∼100 bar; otherwise, additional contributions from postcollision are present and especially relevant at high pressures. In the aforementioned regime Z < k( E' J' K) the physical connection of recombination rate constants, k based on either utilizing population from the master equation approach or a collision based bimolecular RRKM theory is traced and elucidated analytically that the rate constants are equal. Recombination rate constants, k, based on the population, are also given and considered for an adiabatic or active K. For example, for O formation in Ar bath gas, the K-adiabatic-based k for O yields 4.0 × 10 cm molecule s at T = 300 K and 1 bar, in agreement with the experimental value, where the contribution from the population of metastable ozone is discussed and the adiabaticity of K highlighted. A facile numerical implementation of the formalism for g( EJK) and k for O is noted. The application of the expressions to ozone recombination as a function of pressure and temperature is given elsewhere, beyond the selection ...

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On collisional energy transfer in recombination and dissociation reactions: A Wiener–Hopf problem and the effect of a near elastic peak

Cited by 11 publications

References 61 publications

Curl flux, coherence, and population landscape of molecular systems: Nonequilibrium quantum steady state, energy (charge) transport, and thermodynamics

Curl flux, coherence, and population landscape of molecular systems: Nonequilibrium quantum steady state, energy (charge) transport, and thermodynamics

Bimolecular recombination reactions: K-adiabatic and K-active forms of the bimolecular master equations and analytic solutions

Bimolecular Master Equations for a Single and Multiple Potential Wells with Analytic Solutions

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