A state‐to‐state statistical‐dynamical theory for large molecule collisional energy transfer

Barker, John R.

doi:10.1002/bbpc.19971010332

Cited by 23 publications

(7 citation statements)

References 38 publications

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“…The empirical trends described by eq are consistent with the variety of fundamental theories for collisional energy transfer have been advanced ,− since Landau and Teller. , These theories, which typically involve assumptions such as treating collisions as isotropic, nearly vibrationally adiabatic, and impulsive, are rarely quantitative, but instead their goal is typically to provide mechanistic insights into collisional energy transfer and to discover dependencies on masses, frequencies, collision times, and other properties, as briefly outlined next.…”

Section: Resultsmentioning

confidence: 73%

Microcanonical Rate Constants for Unimolecular Reactions in the Low-Pressure Limit

Jasper

2020

J. Phys. Chem. A

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Low-pressure-limit microcanonical rate constants, κ 0 (E,J), describe the rate of activating bath gas collisions in a unimolecular reaction and are calculated here using classical trajectories and quantized thresholds for reaction. The resulting semiclassical rate constants are twodimensional (in total energy E and total angular momentum J) and are intermediate in complexity between the four-dimensional state-to-state collisional energy and angular momentum transfer rate constant, R(E′,J′;E,J), and the highly averaged thermal rate constant, k 0 . Results are presented for CH 4 (+M), C 2 H x (+M), x = 3−6, and H 2 O (+M), where κ 0 (E,J) is shown generally to be a sensitive function of the bath gas, temperature, and initial state of the unimolecular reactant. Strong variations in κ 0 with respect to E and J lead to complex trends in relative microcanonical bath gas efficiencies. This underlying complexity may complicate the search for simple explanations for observed trends in relative thermal bath gas efficiencies. A different measure of the microcanonical collision efficiency that describes the energy range of activating collisions is introduced that supports the empirical decomposition of collisional activation into separable translational-to-vibrational and rotational-to-vibrational activation mechanisms. The two mechanisms depend differently on mass, temperature, and the J-dependence of the threshold energy for reaction, with rotational-to-vibrational activation favored for heavier baths and for reactions with rigid transition states. Finally, κ 0 is used to test the accuracy of several two-dimensional models for R that were proposed for use in master equation studies.

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Section: Resultsmentioning

confidence: 73%

Microcanonical Rate Constants for Unimolecular Reactions in the Low-Pressure Limit

Jasper

2020

J. Phys. Chem. A

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“…Early work by Barker applied SSH theory to the energy transfer process. 34 More recent work includes the approach by Nordholm and colleagues, 35−42 who apply ergodic collision theory to the energy transfer problem. Their model, when adjusted to reflect the fact that not all collisions are strong, gives good agreement with a variety of experiments.…”

Section: ■ Introductionmentioning

confidence: 99%

A Model For Energy Transfer in Collisions of Atoms with Highly Excited Molecules

2015

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A model for energy transfer in the collision between an atom and a highly excited target molecule has been developed on the basis of classical mechanics and turning point analysis. The predictions of the model have been tested against the results of trajectory calculations for collisions of five different target molecules with argon or helium under a variety of temperatures, collision energies, and initial rotational levels. The model predicts selected moments of the joint probability distribution, P(Jf,ΔE) with an R(2) ≈ 0.90. The calculation is efficient, in most cases taking less than one CPU-hour. The model provides several insights into the energy transfer process. The joint probability distribution is strongly dependent on rotational energy transfer and conservation laws and less dependent on vibrational energy transfer. There are two mechanisms for rotational excitation, one due to motion normal to the intermolecular potential and one due to motion tangential to it and perpendicular to the line of centers. Energy transfer is found to depend strongly on the intermolecular potential and only weakly on the intramolecular potential. Highly efficient collisions are a natural consequence of the energy transfer and arise due to collisions at "sweet spots" in the space of impact parameter and molecular orientation.

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“…Such an exponential dependence is often referred to as weak collider model, since the probability density has a maximum value for elastic collisions, ⌬E ϭ 0. This dependence has been reproduced by a state-to-state statistical dynamical theory developed by Barker [7] and is used for the down-step side in most thermal energy transfer models [17,18]. Other approaches that could have been employed are a double exponential dependence [20] or a Gaussian dependence [1] of the probability density on the step size.…”

Section: Theory and Implementationmentioning

confidence: 99%

“…Therefore it cannot be expected to describe every detail of the energy transfer process accurately. In particular, microscopic models that take into account the individual interaction potential, such as the implementation of a state-to-state statistical dynamical theory using the SSH model [7] seem to be too complex and specialized for this purpose, while classical trajectory calculations and quantum mechanical close coupling calculations are computationally very expensive. Rather, the most appropriate model may be a semi-empirical model that fulfills the fundamental physical requirements, but relies on additionally adjustable parameters that are chosen to match the experimentally observed results.…”

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confidence: 99%

A model for energy transfer in inelastic molecular collisions applicable at steady state or non-steady state and for an arbitrary distribution of collision energies

Plaß

Cooks

2003

J. Am. Soc. Mass Spectrom.

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A new model for energy exchange between translational and internal degrees of freedom in atom-molecule collisions has been developed. It is suitable for both steady state conditions (e.g., a large number of collisions with thermal kinetic energies) and non-steady state conditions with an arbitrary distribution of collision energies (e.g., single high-energy collisions). In particular, it does not require that the collision energies be characterized by a quasi-thermal distribution, but nevertheless it is capable of producing a Boltzmann distribution of internal energies with the correct internal temperature under quasi-thermal conditions. The energy exchange is described by a transfer probability density that depends on the initial relative kinetic energy, the internal energy of the molecule, and the amount of energy transferred. The probability density for collisions that lead to excitation is assumed to decrease exponentially with the amount of transferred energy. The probability density for de-excitation is obtained from microscopic reversibility. The model has been implemented in the ion trap simulation program ITSIM and coupled with an Rice-Rampsberger-Kassel-Marcus (RRKM) algorithm to describe the unimolecular dissociation of populations of ions. Monte Carlo simulations of collisional energy transfer are presented. The model is validated for non-steady state conditions and for steady state conditions, and the effect of the kinetic energy dependence of the collision cross-section on internal temperature is discussed. Applications of the model to the problem of chemical mass shifts in RF ion trap mass spectrometry are shown.

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A state‐to‐state statistical‐dynamical theory for large molecule collisional energy transfer

Cited by 23 publications

References 38 publications

Microcanonical Rate Constants for Unimolecular Reactions in the Low-Pressure Limit

Microcanonical Rate Constants for Unimolecular Reactions in the Low-Pressure Limit

A Model For Energy Transfer in Collisions of Atoms with Highly Excited Molecules

A model for energy transfer in inelastic molecular collisions applicable at steady state or non-steady state and for an arbitrary distribution of collision energies

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