Collisional energy transfer in polyatomic molecules

A study of anharmonicity effects in Kr+CO2

George C Schatz*, Thomas Mulloney

*Corresponding author for this work

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

The importance of anharmonicity in determining the rates of collisional energy transfer in Kr+CO2 is studied by combining the usual classical trajectory method with an accurate characterization of the semiclassical stationary "states" of the CO2 molecules (i.e., the "good" action variables) before and after each collision. A linear model of the collision dynamics is assumed, which means that only energy transfer involving the symmetric and asymmetric stretch modes of CO2 is described. Most of our studies focus upon analyzing the average changes in symmetric and asymmetric stretch good actions, and the average T→V energy transfer. For Kr+CO2, comparison of these collisional energy transfer moments using an anharmonic force field for CO2 with those using the corresponding harmonic force field indicates that anharmonicity effects are very important in the collisional energy transfer process, with errors in moments by factors of 10 or more incurred when the harmonic approximation is used. At high collision energies, where the primary energy transfer process is T→V, the anharmonic molecule behaves as a "stiffer" oscillator when compressed than harmonic with the result that a factor of 10 less energy is absorbed. At low collision energy where the energy transfer is primarily V→V and is dominated by the low frequency components of the collisional interaction force, energy transfer is much larger for the anharmonic molecule since the frequencies associated with the harmonic molecule (i.e., the fundamental frequencies) are much higher than one particular combination frequency (2ω13) which exists in the anharmonic molecule. This single frequency then dominates all energy transfer properties, causing all energy transfer moments to have the same dependence on collision energy. One can summarize these results by the statement that diagonal anharmonicity effects dominate in the high collision energy impulsive limit while off diagonal anharmonicities control energy transfer at low collision energies. We also examine the dependence of collisional energy transfer in Kr+CO2 on the level of sophistication of the anharmonic force field, with the conclusion that (at least for the low vibrational states of CO 2), a quartic force field is necessary but apparently also sufficient to quantitatively describe the collision dynamics. In addition, the effect of initially exciting CO2 to the states (N100) with N 1=0,1,2,3,8, and 16 is investigated with the conclusion that anharmonic coupling becomes increasingly important as the amount of vibrational excitation is increased, with its effect on T→V energy transfer generally much smaller than that on V→V transfer.

Original languageEnglish (US)
Pages (from-to)5257-5267
Number of pages11
JournalThe Journal of Chemical Physics
Volume71
Issue number12
DOIs
StatePublished - Jan 1 1979

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polyatomic molecules
Energy transfer
energy transfer
Molecules
collisions
field theory (physics)
harmonics
molecules
moments
energy
Carbon Monoxide
vibrational states
Trajectories
oscillators
trajectories

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

Cite this

@article{31d00fdb81fc44bab14c18f90e97f74b,
title = "Collisional energy transfer in polyatomic molecules: A study of anharmonicity effects in Kr+CO2",
abstract = "The importance of anharmonicity in determining the rates of collisional energy transfer in Kr+CO2 is studied by combining the usual classical trajectory method with an accurate characterization of the semiclassical stationary {"}states{"} of the CO2 molecules (i.e., the {"}good{"} action variables) before and after each collision. A linear model of the collision dynamics is assumed, which means that only energy transfer involving the symmetric and asymmetric stretch modes of CO2 is described. Most of our studies focus upon analyzing the average changes in symmetric and asymmetric stretch good actions, and the average T→V energy transfer. For Kr+CO2, comparison of these collisional energy transfer moments using an anharmonic force field for CO2 with those using the corresponding harmonic force field indicates that anharmonicity effects are very important in the collisional energy transfer process, with errors in moments by factors of 10 or more incurred when the harmonic approximation is used. At high collision energies, where the primary energy transfer process is T→V, the anharmonic molecule behaves as a {"}stiffer{"} oscillator when compressed than harmonic with the result that a factor of 10 less energy is absorbed. At low collision energy where the energy transfer is primarily V→V and is dominated by the low frequency components of the collisional interaction force, energy transfer is much larger for the anharmonic molecule since the frequencies associated with the harmonic molecule (i.e., the fundamental frequencies) are much higher than one particular combination frequency (2ω1-ω3) which exists in the anharmonic molecule. This single frequency then dominates all energy transfer properties, causing all energy transfer moments to have the same dependence on collision energy. One can summarize these results by the statement that diagonal anharmonicity effects dominate in the high collision energy impulsive limit while off diagonal anharmonicities control energy transfer at low collision energies. We also examine the dependence of collisional energy transfer in Kr+CO2 on the level of sophistication of the anharmonic force field, with the conclusion that (at least for the low vibrational states of CO 2), a quartic force field is necessary but apparently also sufficient to quantitatively describe the collision dynamics. In addition, the effect of initially exciting CO2 to the states (N100) with N 1=0,1,2,3,8, and 16 is investigated with the conclusion that anharmonic coupling becomes increasingly important as the amount of vibrational excitation is increased, with its effect on T→V energy transfer generally much smaller than that on V→V transfer.",
author = "Schatz, {George C} and Thomas Mulloney",
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Collisional energy transfer in polyatomic molecules : A study of anharmonicity effects in Kr+CO2. / Schatz, George C; Mulloney, Thomas.

In: The Journal of Chemical Physics, Vol. 71, No. 12, 01.01.1979, p. 5257-5267.

Research output: Contribution to journalArticle

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N2 - The importance of anharmonicity in determining the rates of collisional energy transfer in Kr+CO2 is studied by combining the usual classical trajectory method with an accurate characterization of the semiclassical stationary "states" of the CO2 molecules (i.e., the "good" action variables) before and after each collision. A linear model of the collision dynamics is assumed, which means that only energy transfer involving the symmetric and asymmetric stretch modes of CO2 is described. Most of our studies focus upon analyzing the average changes in symmetric and asymmetric stretch good actions, and the average T→V energy transfer. For Kr+CO2, comparison of these collisional energy transfer moments using an anharmonic force field for CO2 with those using the corresponding harmonic force field indicates that anharmonicity effects are very important in the collisional energy transfer process, with errors in moments by factors of 10 or more incurred when the harmonic approximation is used. At high collision energies, where the primary energy transfer process is T→V, the anharmonic molecule behaves as a "stiffer" oscillator when compressed than harmonic with the result that a factor of 10 less energy is absorbed. At low collision energy where the energy transfer is primarily V→V and is dominated by the low frequency components of the collisional interaction force, energy transfer is much larger for the anharmonic molecule since the frequencies associated with the harmonic molecule (i.e., the fundamental frequencies) are much higher than one particular combination frequency (2ω1-ω3) which exists in the anharmonic molecule. This single frequency then dominates all energy transfer properties, causing all energy transfer moments to have the same dependence on collision energy. One can summarize these results by the statement that diagonal anharmonicity effects dominate in the high collision energy impulsive limit while off diagonal anharmonicities control energy transfer at low collision energies. We also examine the dependence of collisional energy transfer in Kr+CO2 on the level of sophistication of the anharmonic force field, with the conclusion that (at least for the low vibrational states of CO 2), a quartic force field is necessary but apparently also sufficient to quantitatively describe the collision dynamics. In addition, the effect of initially exciting CO2 to the states (N100) with N 1=0,1,2,3,8, and 16 is investigated with the conclusion that anharmonic coupling becomes increasingly important as the amount of vibrational excitation is increased, with its effect on T→V energy transfer generally much smaller than that on V→V transfer.

AB - The importance of anharmonicity in determining the rates of collisional energy transfer in Kr+CO2 is studied by combining the usual classical trajectory method with an accurate characterization of the semiclassical stationary "states" of the CO2 molecules (i.e., the "good" action variables) before and after each collision. A linear model of the collision dynamics is assumed, which means that only energy transfer involving the symmetric and asymmetric stretch modes of CO2 is described. Most of our studies focus upon analyzing the average changes in symmetric and asymmetric stretch good actions, and the average T→V energy transfer. For Kr+CO2, comparison of these collisional energy transfer moments using an anharmonic force field for CO2 with those using the corresponding harmonic force field indicates that anharmonicity effects are very important in the collisional energy transfer process, with errors in moments by factors of 10 or more incurred when the harmonic approximation is used. At high collision energies, where the primary energy transfer process is T→V, the anharmonic molecule behaves as a "stiffer" oscillator when compressed than harmonic with the result that a factor of 10 less energy is absorbed. At low collision energy where the energy transfer is primarily V→V and is dominated by the low frequency components of the collisional interaction force, energy transfer is much larger for the anharmonic molecule since the frequencies associated with the harmonic molecule (i.e., the fundamental frequencies) are much higher than one particular combination frequency (2ω1-ω3) which exists in the anharmonic molecule. This single frequency then dominates all energy transfer properties, causing all energy transfer moments to have the same dependence on collision energy. One can summarize these results by the statement that diagonal anharmonicity effects dominate in the high collision energy impulsive limit while off diagonal anharmonicities control energy transfer at low collision energies. We also examine the dependence of collisional energy transfer in Kr+CO2 on the level of sophistication of the anharmonic force field, with the conclusion that (at least for the low vibrational states of CO 2), a quartic force field is necessary but apparently also sufficient to quantitatively describe the collision dynamics. In addition, the effect of initially exciting CO2 to the states (N100) with N 1=0,1,2,3,8, and 16 is investigated with the conclusion that anharmonic coupling becomes increasingly important as the amount of vibrational excitation is increased, with its effect on T→V energy transfer generally much smaller than that on V→V transfer.

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