### Abstract

The importance of anharmonicity in determining the rates of collisional energy transfer in Kr+CO_{2} is studied by combining the usual classical trajectory method with an accurate characterization of the semiclassical stationary "states" of the CO_{2} 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 CO_{2} 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+CO_{2}, comparison of these collisional energy transfer moments using an anharmonic force field for CO_{2} 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 (2ω_{1}-ω_{3}) 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+CO_{2} 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 CO_{2} to the states (N_{1}00) 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 language | English (US) |
---|---|

Pages (from-to) | 5257-5267 |

Number of pages | 11 |

Journal | The Journal of Chemical Physics |

Volume | 71 |

Issue number | 12 |

DOIs | |

State | Published - Jan 1 1979 |

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### ASJC Scopus subject areas

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

### Cite this

_{2}.

*The Journal of Chemical Physics*,

*71*(12), 5257-5267. https://doi.org/10.1063/1.438336

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_{2}',

*The Journal of Chemical Physics*, vol. 71, no. 12, pp. 5257-5267. https://doi.org/10.1063/1.438336

**Collisional energy transfer in polyatomic molecules : A study of anharmonicity effects in Kr+CO _{2}.** / Schatz, George C; Mulloney, Thomas.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Collisional energy transfer in polyatomic molecules

T2 - A study of anharmonicity effects in Kr+CO2

AU - Schatz, George C

AU - Mulloney, Thomas

PY - 1979/1/1

Y1 - 1979/1/1

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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UR - http://www.scopus.com/inward/citedby.url?scp=36749121443&partnerID=8YFLogxK

U2 - 10.1063/1.438336

DO - 10.1063/1.438336

M3 - Article

VL - 71

SP - 5257

EP - 5267

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 12

ER -

_{2}. The Journal of Chemical Physics. 1979 Jan 1;71(12):5257-5267. https://doi.org/10.1063/1.438336