Classical rotational and centrifugal sudden approximations for atom-molecule collisional energy transfer

Thomas Mulloney, George C Schatz

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

The application of centrifugal and rotational sudden approximations to classical trajectory studies of rotational energy transfer in atom-molecule collisions to examined. Two different types of approximations are considered: a centrifugal sudden (CS) approximation, in which the orbital angular momentum is assumed to be constant during collisions, and a classical infinite order sudden (CIOS) approximation, in which the CS treatment is combined with an energy sudden approximation to totally decouple translational and rotational equations of motion. The treatment of both atom plus linear and nonlinear molecule collisions is described, including the use of rotational action-angle variables for the rotor equations of motion. Applications of both CS and CIOS approaches to rotational energy transfer in He + I2 collisions are presented. We find the calculated CS and CIOS rotationally inelastic cross sections are in generally good agreement [errors of (typically) 10-50%] with accurate quasiclassical (QC) ones, with the CS results slightly more accurate than CIOS. Both methods are less accurate for small |Δj| transitions than for large |Δj| transitions. Computational savings for the CS and CIOS applications is about a factor of 3 (per trajectory) compared to QC. We also present applications using the CS method to rotational energy transfer in He, Ar, Xe + O3 collisions, making comparisons with analogous QC results of Stace and Murrell (SM). The agreement between exact and approximate results in these applications is generally excellent, both for the average energy transfer at fixed impact parameters, and for rotationally inelastic cross sections. Results are better for He + O3 and Ar + O3 than for Xe + O3, and better at low temperatures than at high. Since SM's quasiclassical treatment considered only total internal energy transfer without attempting a partitioning between vibration and rotation, while our CS calculation considers only rotational energy transfer, the observed good agreement between our and SM's cross sections indicates that most internal energy transfer in He, Ar, Xe + O3 is rotational. The relation of this result to models of the activation process in thermal unimolecular rate constant determination is discussed.

Original languageEnglish
Pages (from-to)213-223
Number of pages11
JournalChemical Physics
Volume45
Issue number2
DOIs
Publication statusPublished - Jan 15 1980

Fingerprint

Energy transfer
energy transfer
Atoms
Molecules
approximation
atoms
molecules
collisions
internal energy
Equations of motion
cross sections
equations of motion
Trajectories
trajectories
Angular momentum
rotors
Rate constants
angular momentum
Rotors
Chemical activation

ASJC Scopus subject areas

  • Physical and Theoretical Chemistry
  • Spectroscopy
  • Atomic and Molecular Physics, and Optics

Cite this

Classical rotational and centrifugal sudden approximations for atom-molecule collisional energy transfer. / Mulloney, Thomas; Schatz, George C.

In: Chemical Physics, Vol. 45, No. 2, 15.01.1980, p. 213-223.

Research output: Contribution to journalArticle

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abstract = "The application of centrifugal and rotational sudden approximations to classical trajectory studies of rotational energy transfer in atom-molecule collisions to examined. Two different types of approximations are considered: a centrifugal sudden (CS) approximation, in which the orbital angular momentum is assumed to be constant during collisions, and a classical infinite order sudden (CIOS) approximation, in which the CS treatment is combined with an energy sudden approximation to totally decouple translational and rotational equations of motion. The treatment of both atom plus linear and nonlinear molecule collisions is described, including the use of rotational action-angle variables for the rotor equations of motion. Applications of both CS and CIOS approaches to rotational energy transfer in He + I2 collisions are presented. We find the calculated CS and CIOS rotationally inelastic cross sections are in generally good agreement [errors of (typically) 10-50{\%}] with accurate quasiclassical (QC) ones, with the CS results slightly more accurate than CIOS. Both methods are less accurate for small |Δj| transitions than for large |Δj| transitions. Computational savings for the CS and CIOS applications is about a factor of 3 (per trajectory) compared to QC. We also present applications using the CS method to rotational energy transfer in He, Ar, Xe + O3 collisions, making comparisons with analogous QC results of Stace and Murrell (SM). The agreement between exact and approximate results in these applications is generally excellent, both for the average energy transfer at fixed impact parameters, and for rotationally inelastic cross sections. Results are better for He + O3 and Ar + O3 than for Xe + O3, and better at low temperatures than at high. Since SM's quasiclassical treatment considered only total internal energy transfer without attempting a partitioning between vibration and rotation, while our CS calculation considers only rotational energy transfer, the observed good agreement between our and SM's cross sections indicates that most internal energy transfer in He, Ar, Xe + O3 is rotational. The relation of this result to models of the activation process in thermal unimolecular rate constant determination is discussed.",
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