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

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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 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.

Original languageEnglish
Pages (from-to)3929-3938
Number of pages10
JournalJournal of Chemical Physics
Volume72
Issue number7
Publication statusPublished - 1980

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Trajectories
trajectories
Angular distribution
cross sections
excitation
vibrational states
Molecular beams
Carbon Monoxide
angular distribution
approximation
Hamilton-Jacobi equation
Anisotropy
collisions
Experiments
Ions
angular velocity
molecular beams
eigenvectors
perturbation theory
interactions

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

A quasiclassical trajectory study of collisional excitation in Li ++CO2. / Schatz, George C.

In: Journal of Chemical Physics, Vol. 72, No. 7, 1980, p. 3929-3938.

Research output: Contribution to journalArticle

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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 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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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.

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