### Abstract

We present quasiclassical trajectory calculations of the state-to-state differential cross sections for vibrational excitation in Li^{+}+CO _{2} collisions and compare our results with analogous results of molecular beam experiments. In the trajectory calculations, the initial and final semiclassical eigenstates of CO_{2} are numerically determined before and after each collision by using a classical perturbation theory calculation of the good action-angle variables associated with molecular vibrational motion. Two approximations are used to simplify this action-angle analysis. First, an angular motion sudden approximation is introduced into the dynamics to separate angular from vibrational motion in solving the molecular Hamilton-Jacobi equation. Second, the off-diagonal parts of the intramolecular potential are neglected to eliminate Fermi resonant coupling between the bending and symmetric stretch modes. This latter approximation precludes the accurate determination of state-to-state cross sections to certain nearly degenerate states such as (020) and (100), but should still enable the accurate determination of the sums of the cross sections to those states (which is all that is available from experiment). The intramolecular potential is approximated in two different ways, both using pairwise additive potentials. In Surface I, the usual ion-induced dipole long range interaction is added to a sum of He-Ne pair potentials which simulate the short range Li^{+}-C and Li ^{+}-O potentials. In Surface II, the sizes of the radius parameters in the short range part of Surface I are changed to correctly reproduce the anisotropy present in the experimentally derived He-CO_{2} interaction potential. The resulting ratios of inelastic to elastic differential cross sections (for the states (010), (020)+(100) and (030)+(110)) are in reasonable quantitative agreement with the experimental measurements, with errors typically smaller than a factor of two using Surface II at 4.72 eV translational energy and a factor of three at 6.87 eV. Some qualitative features of the angular distributions are actually quite accurately described, including the crossing of the (010) and (020)+(100) ratios near 24° at 4.72 eV and 18° at 6.87 eV, and the similar angular dependence of the (020)+(100) and (030)+(110) cross sections. In addition, a detailed interpretation of many features of the distributions of final vibrational states is developed, including relative propensities for certain types of overtone and combination mode excitation, and the variation in angular distributions as a function of final vibrational state.

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

Pages (from-to) | 3929-3938 |

Number of pages | 10 |

Journal | Journal of Chemical Physics |

Volume | 72 |

Issue number | 7 |

Publication status | Published - 1980 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

^{+}+CO

_{2}.

*Journal of Chemical Physics*,

*72*(7), 3929-3938.

**A quasiclassical trajectory study of collisional excitation in Li ^{+}+CO_{2}.** / Schatz, George C.

Research output: Contribution to journal › Article

^{+}+CO

_{2}',

*Journal of Chemical Physics*, vol. 72, no. 7, pp. 3929-3938.

}

TY - JOUR

T1 - A quasiclassical trajectory study of collisional excitation in Li ++CO2

AU - Schatz, George C

PY - 1980

Y1 - 1980

N2 - We present quasiclassical trajectory calculations of the state-to-state differential cross sections for vibrational excitation in Li++CO 2 collisions and compare our results with analogous results of molecular beam experiments. In the trajectory calculations, the initial and final semiclassical eigenstates of CO2 are numerically determined before and after each collision by using a classical perturbation theory calculation of the good action-angle variables associated with molecular vibrational motion. Two approximations are used to simplify this action-angle analysis. First, an angular motion sudden approximation is introduced into the dynamics to separate angular from vibrational motion in solving the molecular Hamilton-Jacobi equation. Second, the off-diagonal parts of the intramolecular potential are neglected to eliminate Fermi resonant coupling between the bending and symmetric stretch modes. This latter approximation precludes the accurate determination of state-to-state cross sections to certain nearly degenerate states such as (020) and (100), but should still enable the accurate determination of the sums of the cross sections to those states (which is all that is available from experiment). The intramolecular potential is approximated in two different ways, both using pairwise additive potentials. In Surface I, the usual ion-induced dipole long range interaction is added to a sum of He-Ne pair potentials which simulate the short range Li+-C and Li +-O potentials. In Surface II, the sizes of the radius parameters in the short range part of Surface I are changed to correctly reproduce the anisotropy present in the experimentally derived He-CO2 interaction potential. The resulting ratios of inelastic to elastic differential cross sections (for the states (010), (020)+(100) and (030)+(110)) are in reasonable quantitative agreement with the experimental measurements, with errors typically smaller than a factor of two using Surface II at 4.72 eV translational energy and a factor of three at 6.87 eV. Some qualitative features of the angular distributions are actually quite accurately described, including the crossing of the (010) and (020)+(100) ratios near 24° at 4.72 eV and 18° at 6.87 eV, and the similar angular dependence of the (020)+(100) and (030)+(110) cross sections. In addition, a detailed interpretation of many features of the distributions of final vibrational states is developed, including relative propensities for certain types of overtone and combination mode excitation, and the variation in angular distributions as a function of final vibrational state.

AB - We present quasiclassical trajectory calculations of the state-to-state differential cross sections for vibrational excitation in Li++CO 2 collisions and compare our results with analogous results of molecular beam experiments. In the trajectory calculations, the initial and final semiclassical eigenstates of CO2 are numerically determined before and after each collision by using a classical perturbation theory calculation of the good action-angle variables associated with molecular vibrational motion. Two approximations are used to simplify this action-angle analysis. First, an angular motion sudden approximation is introduced into the dynamics to separate angular from vibrational motion in solving the molecular Hamilton-Jacobi equation. Second, the off-diagonal parts of the intramolecular potential are neglected to eliminate Fermi resonant coupling between the bending and symmetric stretch modes. This latter approximation precludes the accurate determination of state-to-state cross sections to certain nearly degenerate states such as (020) and (100), but should still enable the accurate determination of the sums of the cross sections to those states (which is all that is available from experiment). The intramolecular potential is approximated in two different ways, both using pairwise additive potentials. In Surface I, the usual ion-induced dipole long range interaction is added to a sum of He-Ne pair potentials which simulate the short range Li+-C and Li +-O potentials. In Surface II, the sizes of the radius parameters in the short range part of Surface I are changed to correctly reproduce the anisotropy present in the experimentally derived He-CO2 interaction potential. The resulting ratios of inelastic to elastic differential cross sections (for the states (010), (020)+(100) and (030)+(110)) are in reasonable quantitative agreement with the experimental measurements, with errors typically smaller than a factor of two using Surface II at 4.72 eV translational energy and a factor of three at 6.87 eV. Some qualitative features of the angular distributions are actually quite accurately described, including the crossing of the (010) and (020)+(100) ratios near 24° at 4.72 eV and 18° at 6.87 eV, and the similar angular dependence of the (020)+(100) and (030)+(110) cross sections. In addition, a detailed interpretation of many features of the distributions of final vibrational states is developed, including relative propensities for certain types of overtone and combination mode excitation, and the variation in angular distributions as a function of final vibrational state.

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M3 - Article

VL - 72

SP - 3929

EP - 3938

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 7

ER -