Comparison of master equation and trajectory simulation of the relaxation of an ensemble of highly vibrationally excited molecules

György Lendvay, George C Schatz

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56 Citations (Scopus)

Abstract

We present the results of master equation simulations of the collisional relaxation of highly excited CS2 in a CO bath, using a rate coefficient matrix that is derived from trajectory calculations simulating individual collisions. The energy distribution from the master equation solutions is compared with distributions derived from trajectory simulations, and the results are used to assess sensitivity of the energy relaxation process to details of the rate coefficient matrix. We find that excellent agreement between master equation and trajectory energy distributions is obtained when the rate coefficients are represented using a biexponential form as a function of the magnitude of the energy change |ΔE|. This biexponential form consists of strong and weak collision components, with the average energy transfer 〈ΔE〉 being mostly determined by the strong component. We find that it is very important to let the parameters in these two components vary with the energy in the excited molecule in order to obtain realistic energy distributions from the master equation. These parameters have a roughly linear dependence on energy, but if this is ignored, then the energy distribution can switch from unimodal to bimodal as the relaxation proceeds. Only unimodal distributions are found in the accurate master equation simulations. Master equation simulations which use rate coefficients based on the strong component of the energy transfer distribution (i.e., a single rather than biexponential function with energy-dependent parameters) are in reasonable agreement with the biexponential results. Other single-exponential approximations are in poor agreement with accurate results.

Original languageEnglish
Pages (from-to)6530-6536
Number of pages7
JournalJournal of Physical Chemistry
Volume98
Issue number26
Publication statusPublished - 1994

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Trajectories
trajectories
Energy transfer
Molecules
energy distribution
molecules
simulation
Relaxation processes
Carbon Monoxide
coefficients
energy transfer
Switches
energy
collisions
baths
switches
sensitivity
approximation

ASJC Scopus subject areas

  • Physical and Theoretical Chemistry

Cite this

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title = "Comparison of master equation and trajectory simulation of the relaxation of an ensemble of highly vibrationally excited molecules",
abstract = "We present the results of master equation simulations of the collisional relaxation of highly excited CS2 in a CO bath, using a rate coefficient matrix that is derived from trajectory calculations simulating individual collisions. The energy distribution from the master equation solutions is compared with distributions derived from trajectory simulations, and the results are used to assess sensitivity of the energy relaxation process to details of the rate coefficient matrix. We find that excellent agreement between master equation and trajectory energy distributions is obtained when the rate coefficients are represented using a biexponential form as a function of the magnitude of the energy change |ΔE|. This biexponential form consists of strong and weak collision components, with the average energy transfer 〈ΔE〉 being mostly determined by the strong component. We find that it is very important to let the parameters in these two components vary with the energy in the excited molecule in order to obtain realistic energy distributions from the master equation. These parameters have a roughly linear dependence on energy, but if this is ignored, then the energy distribution can switch from unimodal to bimodal as the relaxation proceeds. Only unimodal distributions are found in the accurate master equation simulations. Master equation simulations which use rate coefficients based on the strong component of the energy transfer distribution (i.e., a single rather than biexponential function with energy-dependent parameters) are in reasonable agreement with the biexponential results. Other single-exponential approximations are in poor agreement with accurate results.",
author = "Gy{\"o}rgy Lendvay and Schatz, {George C}",
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journal = "Journal of Physical Chemistry",
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N2 - We present the results of master equation simulations of the collisional relaxation of highly excited CS2 in a CO bath, using a rate coefficient matrix that is derived from trajectory calculations simulating individual collisions. The energy distribution from the master equation solutions is compared with distributions derived from trajectory simulations, and the results are used to assess sensitivity of the energy relaxation process to details of the rate coefficient matrix. We find that excellent agreement between master equation and trajectory energy distributions is obtained when the rate coefficients are represented using a biexponential form as a function of the magnitude of the energy change |ΔE|. This biexponential form consists of strong and weak collision components, with the average energy transfer 〈ΔE〉 being mostly determined by the strong component. We find that it is very important to let the parameters in these two components vary with the energy in the excited molecule in order to obtain realistic energy distributions from the master equation. These parameters have a roughly linear dependence on energy, but if this is ignored, then the energy distribution can switch from unimodal to bimodal as the relaxation proceeds. Only unimodal distributions are found in the accurate master equation simulations. Master equation simulations which use rate coefficients based on the strong component of the energy transfer distribution (i.e., a single rather than biexponential function with energy-dependent parameters) are in reasonable agreement with the biexponential results. Other single-exponential approximations are in poor agreement with accurate results.

AB - We present the results of master equation simulations of the collisional relaxation of highly excited CS2 in a CO bath, using a rate coefficient matrix that is derived from trajectory calculations simulating individual collisions. The energy distribution from the master equation solutions is compared with distributions derived from trajectory simulations, and the results are used to assess sensitivity of the energy relaxation process to details of the rate coefficient matrix. We find that excellent agreement between master equation and trajectory energy distributions is obtained when the rate coefficients are represented using a biexponential form as a function of the magnitude of the energy change |ΔE|. This biexponential form consists of strong and weak collision components, with the average energy transfer 〈ΔE〉 being mostly determined by the strong component. We find that it is very important to let the parameters in these two components vary with the energy in the excited molecule in order to obtain realistic energy distributions from the master equation. These parameters have a roughly linear dependence on energy, but if this is ignored, then the energy distribution can switch from unimodal to bimodal as the relaxation proceeds. Only unimodal distributions are found in the accurate master equation simulations. Master equation simulations which use rate coefficients based on the strong component of the energy transfer distribution (i.e., a single rather than biexponential function with energy-dependent parameters) are in reasonable agreement with the biexponential results. Other single-exponential approximations are in poor agreement with accurate results.

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