Reversible and irreversible formulation of unimolecular reactions

Aguda, Baltazar D.; Pritchard, H. O.

doi:10.1063/1.462689

Cited by 15 publications

(16 citation statements)

References 16 publications

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“…This is an important difference between the master equation, eqn (2), and the phenomenological description of the chemical kinetics, eqn (12). This point has been made several times in the past, 1,[17][18][19][20] but it cannot be overemphasized. Most importantly, general proofs of detailed balance for Hamiltonian systems, such as those given by van Kampen and Wigner, 21,22 do not apply to eqn (12), because these proofs require that the transition probabilities in the ME be flux coefficients.…”

Section: Some Properties Of the Rate Constant Matrixmentioning

confidence: 99%

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Detailed balance in multiple-well chemical reactions

Miller

Klippenstein

Robertson

et al. 2009

Phys. Chem. Chem. Phys.

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Chemical reactions that involve multiple, interconnected potential wells are of paramount importance in applications of chemical kinetics, particularly combustion and atmospheric chemistry. The only accurate way of determining phenomenological rate constants theoretically for this type of reaction is from the solution of a time-dependent, multiple-well master equation. In this Perspective we address the issue of whether or not (and to what extent) detailed balance is satisfied by rate constants obtained from such solutions. In addressing this issue we discuss a number of related topics, including necessary and sufficient conditions for a system of first-order rate equations to evolve to chemical equilibrium and the relationship between detailed balance and Wegscheider conditions. The assumption of a "near-Boltzmann" distribution in the wells sheds considerable light on the issue at hand. We discuss this approximation in some detail and suggest a quantitative measure of "near-Boltzmann". It is extremely unlikely that the rate constants of interest satisfy detailed balance exactly (there is no reason to believe that they do). However, the discrepancies are expected to be vanishingly small, as observed in practice.

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Section: Some Properties Of the Rate Constant Matrixmentioning

confidence: 99%

“…Now let us look explicitly at what the approximation (41) implies and how it impacts the rate constants. From eqn (18), after the IEREs relax to zero, one obtains jwi ¼ X…”

Section: The ''Near-boltzmann'' Approximationmentioning

confidence: 99%

Detailed balance in multiple-well chemical reactions

Miller

Klippenstein

Robertson

et al. 2009

Phys. Chem. Chem. Phys.

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“…If we further assume that the observed steady-state population ( ∼ 4) is dynamic and controlled by an effective equilibrium constant, K eq , for the unimolecular reaction then the forward ( k f ) and reverse ( k r ) unimolecular reaction rates that govern the exchange kinetics follow the usual constraint: . Solving the kinetic response equations yields the predicted time-dependent populations of the two sites in Figure . These curves describe the limiting regime II case where the local population in one site is completely removed by the pump laser and is then partially restored as the remaining ion ensemble relaxes back to the steady state.…”

mentioning

confidence: 99%

“…This model leads to the time evolution of the reactant population AD( t ): where ΔAD( t ) = AD( t ) – AD(∞). AD(0) is the population immediately after depletion by the pump, and AD(∞) denotes that upon re-equilibration …”

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Unmasking Rare, Large-Amplitude Motions in D₂-Tagged I^–·(H₂O)₂ Isotopomers with Two-Color, Infrared–Infrared Vibrational Predissociation Spectroscopy

Yang

Duong

Kelleher

et al. 2018

J. Phys. Chem. Lett.

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We describe a two-color, isotopomer-selective infrared-infrared population-labeling method that can monitor very slow spectral diffusion of OH oscillators in H-bonded networks and apply it to the I·(HDO)·(DO) and I·(HO)·(DO) systems, which are cryogenically cooled and D-tagged at an ion trap temperature of 15 K. These measurements reveal very large (>400 cm), spontaneous spectral shifts despite the fact that the predissociation spectra in the OH stretching region of both isotopologues are sharp and readily assigned to four fundamentals of largely decoupled OH oscillators held in a cyclic H-bonded network. This spectral diffusion is not observed in the untagged isotopologues of the dihydrate clusters that are generated under the same source conditions but does become apparent at about 75 K. These results are discussed in the context of the large-amplitude "jump" mechanism for H-bond relaxation dynamics advanced by Laage and Hynes in an experimental scenario where rare events can be captured by following the migration of OH groups among the four available positions in the quasi-rigid equilibrium structure.

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Unimolecular decomposition of large organic radicals with low reaction thresholds: Decomposition and reversible isomerization of n‐pentyl radicals

Tsang

Bedanov

Zachariah

1997

Ber Bunsenges Phys Chem

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The decomposition kinetics of n-pentyl radicals in the high temperature regime where steady state distributions are not achieved and reversible isomerization to decomposing 2-pentyl radicals is of importance has been analyzed through the solution of the time-dependent master equation. The reactions are characterized by low activation thresholds and lead to large rate constants that vary with time. Particular attention is paid to branching ratios for direct decomposition of the n-pentyl radical and the decomposition that follows reversible isomerization to the 2-pentyl species. The behavior of the system under a variety of conditions is described and the use of branching ratios as a possible means of characterizing the reactions in a manner that is compatible with present methods for employing kinetic data for simulating complex chemical phenomenon is considered. At higher temperatures, rate constants and branching ratios collapse to limiting values. The combination of limiting and the onset of steady state behavior complicates the situation at lower temperatures. The overall behavior of such systems is highly dependent on the magnitude of the barrier to isomerization. The extent of departures from the high pressure-branching ratios are defined.

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Reversible and irreversible formulation of unimolecular reactions

Cited by 15 publications

References 16 publications

Detailed balance in multiple-well chemical reactions

Detailed balance in multiple-well chemical reactions

Unmasking Rare, Large-Amplitude Motions in D₂-Tagged I^–·(H₂O)₂ Isotopomers with Two-Color, Infrared–Infrared Vibrational Predissociation Spectroscopy

Unimolecular decomposition of large organic radicals with low reaction thresholds: Decomposition and reversible isomerization of n‐pentyl radicals

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Reversible and irreversible formulation of unimolecular reactions

Cited by 15 publications

References 16 publications

Detailed balance in multiple-well chemical reactions

Detailed balance in multiple-well chemical reactions

Unmasking Rare, Large-Amplitude Motions in D2-Tagged I–·(H2O)2 Isotopomers with Two-Color, Infrared–Infrared Vibrational Predissociation Spectroscopy

Unimolecular decomposition of large organic radicals with low reaction thresholds: Decomposition and reversible isomerization of n‐pentyl radicals

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Unmasking Rare, Large-Amplitude Motions in D₂-Tagged I^–·(H₂O)₂ Isotopomers with Two-Color, Infrared–Infrared Vibrational Predissociation Spectroscopy