### Abstract

This paper presents a detailed theoretical analysis of the vibrational relaxation of highly excited CS_{2} (initially 32 640 cm^{-1}) in collinear collisions with a thermal bath of He atoms. The relaxation is simulated by a classical molecular dynamics method in which CS_{2} undergoes successive collisions with thousands of He atoms. In most of our studies the CS_{2} coordinates and momenta at the end of one collision are used as input to the next collision, so it is possible to examine the detailed evolution of the CS_{2} vibrational phase space during the relaxation process. By restricting motion to being collinear, it is possible to characterize this evolution using surfaces of section and other methods. Comparisons of our collinear results with corresponding three-dimensional simulations indicates that the collinear restriction does not alter the relaxation process significantly. Our phase space analysis indicates that individual relaxation sequences can evolve in a variety of different ways depending on the initial location in phase space and on the details of subsequent collisions. Much of the initial phase space is chaotic, and if a sequence starts in such a region then after usually less than 30 collisions, the CS_{2} has moved into a nonlinear resonance zone where the antisymmetric and symmetric stretch modes have frequency ratios of 5:2, 7:3, or 9:4. These nonlinear resonances do not greatly change the ensemble averaged energy transfer per collision 〈ΔE〉 compared to the chaotic regions, but they are collisionally stable relative to these regions. As a result, it takes an energetic collision to kick the molecule out of a nonlinear resonance. If kicked out, then usually within a few more collisions another nonlinear resonance (or perhaps the same) has been entered. As relaxation progresses molecules caught in nonlinear resonances eventually drop down to simple quasiperiodic regions where the frequency ratio is not constrained to be a ratio of integers. We do find a region of phase space that is quasiperiodic even at 32 640 cm^{-1}, corresponding to a "hyperspherical mode" in which most of the vibrational energy is locked up in antisymmetric stretch motion. Molecules in this region of phase space relax much more slowly than in chaotic and resonant regions. In addition, molecules starting initially in a chaotic region can be kicked into this hyperspherical mode region, leading to an additional slowing of the relaxation as the molecule drops down the well. This additional slowing plays an important role in determining the dependence of 〈ΔE〉 on the molecular vibrational energy E. In particular, we find that 〈ΔE〉 varies linearly with E if phase space undergoes forced randomization after each collision, but it shows a stronger than linear dependence when redistribution is not forced. This implies that deviations from linearity in the dependence of 〈ΔE〉 on E provide a measure of the division of phase space into regions that have very different relaxation characteristics.

Original language | English |
---|---|

Pages (from-to) | 6561-6573 |

Number of pages | 13 |

Journal | Journal of Chemical Physics |

Volume | 92 |

Issue number | 11 |

Publication status | Published - 1990 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

_{2}.

*Journal of Chemical Physics*,

*92*(11), 6561-6573.

**The evolution of vibrational phase space during the collisional relaxation of highly excited collinear CS _{2}.** / Bruehl, Margaret; Schatz, George C.

Research output: Contribution to journal › Article

_{2}',

*Journal of Chemical Physics*, vol. 92, no. 11, pp. 6561-6573.

}

TY - JOUR

T1 - The evolution of vibrational phase space during the collisional relaxation of highly excited collinear CS2

AU - Bruehl, Margaret

AU - Schatz, George C

PY - 1990

Y1 - 1990

N2 - This paper presents a detailed theoretical analysis of the vibrational relaxation of highly excited CS2 (initially 32 640 cm-1) in collinear collisions with a thermal bath of He atoms. The relaxation is simulated by a classical molecular dynamics method in which CS2 undergoes successive collisions with thousands of He atoms. In most of our studies the CS2 coordinates and momenta at the end of one collision are used as input to the next collision, so it is possible to examine the detailed evolution of the CS2 vibrational phase space during the relaxation process. By restricting motion to being collinear, it is possible to characterize this evolution using surfaces of section and other methods. Comparisons of our collinear results with corresponding three-dimensional simulations indicates that the collinear restriction does not alter the relaxation process significantly. Our phase space analysis indicates that individual relaxation sequences can evolve in a variety of different ways depending on the initial location in phase space and on the details of subsequent collisions. Much of the initial phase space is chaotic, and if a sequence starts in such a region then after usually less than 30 collisions, the CS2 has moved into a nonlinear resonance zone where the antisymmetric and symmetric stretch modes have frequency ratios of 5:2, 7:3, or 9:4. These nonlinear resonances do not greatly change the ensemble averaged energy transfer per collision 〈ΔE〉 compared to the chaotic regions, but they are collisionally stable relative to these regions. As a result, it takes an energetic collision to kick the molecule out of a nonlinear resonance. If kicked out, then usually within a few more collisions another nonlinear resonance (or perhaps the same) has been entered. As relaxation progresses molecules caught in nonlinear resonances eventually drop down to simple quasiperiodic regions where the frequency ratio is not constrained to be a ratio of integers. We do find a region of phase space that is quasiperiodic even at 32 640 cm-1, corresponding to a "hyperspherical mode" in which most of the vibrational energy is locked up in antisymmetric stretch motion. Molecules in this region of phase space relax much more slowly than in chaotic and resonant regions. In addition, molecules starting initially in a chaotic region can be kicked into this hyperspherical mode region, leading to an additional slowing of the relaxation as the molecule drops down the well. This additional slowing plays an important role in determining the dependence of 〈ΔE〉 on the molecular vibrational energy E. In particular, we find that 〈ΔE〉 varies linearly with E if phase space undergoes forced randomization after each collision, but it shows a stronger than linear dependence when redistribution is not forced. This implies that deviations from linearity in the dependence of 〈ΔE〉 on E provide a measure of the division of phase space into regions that have very different relaxation characteristics.

AB - This paper presents a detailed theoretical analysis of the vibrational relaxation of highly excited CS2 (initially 32 640 cm-1) in collinear collisions with a thermal bath of He atoms. The relaxation is simulated by a classical molecular dynamics method in which CS2 undergoes successive collisions with thousands of He atoms. In most of our studies the CS2 coordinates and momenta at the end of one collision are used as input to the next collision, so it is possible to examine the detailed evolution of the CS2 vibrational phase space during the relaxation process. By restricting motion to being collinear, it is possible to characterize this evolution using surfaces of section and other methods. Comparisons of our collinear results with corresponding three-dimensional simulations indicates that the collinear restriction does not alter the relaxation process significantly. Our phase space analysis indicates that individual relaxation sequences can evolve in a variety of different ways depending on the initial location in phase space and on the details of subsequent collisions. Much of the initial phase space is chaotic, and if a sequence starts in such a region then after usually less than 30 collisions, the CS2 has moved into a nonlinear resonance zone where the antisymmetric and symmetric stretch modes have frequency ratios of 5:2, 7:3, or 9:4. These nonlinear resonances do not greatly change the ensemble averaged energy transfer per collision 〈ΔE〉 compared to the chaotic regions, but they are collisionally stable relative to these regions. As a result, it takes an energetic collision to kick the molecule out of a nonlinear resonance. If kicked out, then usually within a few more collisions another nonlinear resonance (or perhaps the same) has been entered. As relaxation progresses molecules caught in nonlinear resonances eventually drop down to simple quasiperiodic regions where the frequency ratio is not constrained to be a ratio of integers. We do find a region of phase space that is quasiperiodic even at 32 640 cm-1, corresponding to a "hyperspherical mode" in which most of the vibrational energy is locked up in antisymmetric stretch motion. Molecules in this region of phase space relax much more slowly than in chaotic and resonant regions. In addition, molecules starting initially in a chaotic region can be kicked into this hyperspherical mode region, leading to an additional slowing of the relaxation as the molecule drops down the well. This additional slowing plays an important role in determining the dependence of 〈ΔE〉 on the molecular vibrational energy E. In particular, we find that 〈ΔE〉 varies linearly with E if phase space undergoes forced randomization after each collision, but it shows a stronger than linear dependence when redistribution is not forced. This implies that deviations from linearity in the dependence of 〈ΔE〉 on E provide a measure of the division of phase space into regions that have very different relaxation characteristics.

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UR - http://www.scopus.com/inward/citedby.url?scp=0005704865&partnerID=8YFLogxK

M3 - Article

VL - 92

SP - 6561

EP - 6573

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 11

ER -