Quantum study of vibrational excitation in the three-dimensional collisions of CO2 with rare gas atoms

Abstract

A combined vibrational close‐coupling and rotational infinite order sudden technique is described for calculating vibrational excitation cross sections σ_vv′ for the three‐dimensional collisions of atoms with linear triatomic molecules. The method treats anharmonic, Coriolis, and vibrational angular momentum terms in the molecular Hamiltonian accurately, and is applicable to any realistic potential energy surface expressed in numerical or functional form. Application of the method to X–CO₂(v₁v₂^λv₃) collisions, where X = He, Ne, or Ar, is described. An accurate anharmonic CO₂ potential, expressed in terms of bond and angle displacements, is employed. The X–CO₂ interaction potentials are more approximate and are expanded in terms of atom–atom pair potentials. Calculations of σ_vv′, over a grid of energies sufficient to give rate coefficients k_vv′ for transitions between the low‐lying states of CO₂ for temperatures up to 300 K, have been performed. Propensities for particular collisional excitations involving the symmetric stretch, bending, and asymmetric stretch vibrational modes of CO₂ are examined. It is found that the magnitudes of the σ_vv′ are largely determined by the energy differences between the v and v′ levels. For example, excitation of the ground (00 ⁰0) state to the first excited bending state (01¹0) is found to be favored. σ_vv′ for near resonant transitions such as (02 ⁰0)→(02 ²0) are found to increase with increasing mass of X. Deactivation of the (00 ⁰1) state to the (11 ¹0) state is favored over other transitions. The ratios of the deactivation cross section for the level (00 ⁰1) to the deactivation cross sections for lower levels such as (01 ¹0) are small, although these ratios do increase with increasing mass of X, in agreement with experimental findings. Comparison of calculated k_vv′, for deactivation of the (01 ¹0) level, with those obtained in recent photoacoustic experiments is quite encouraging, considering the approximate nature of the X–CO₂ interaction potentials used. For X = He and Ne these calculated k_vv′ are within a factor of 5 of the experimental results and have the correct temperature dependence, while for X = Ar the calculations are much larger than the experimental results, and the temperature dependence is too shallow. The computer program used in the calculations is automatic and general, and should be applicable to many other atom–linear triatomic molecule collisions.