Energy Transfer in Near-Resonant Molecular Collisions due to Long-Range Forces with Application to Transfer of Vibrational Energy from ν3 Mode of CO2 to N2

The cross section for the near‐resonant transfer of vibrational energy from CO₂(001) to N₂(0), CO₂(001) + N₂(0)→CO₂(000) + N₂(1) + ΔE, is calculated for the isotopes ${}^{14}{\mathrm{N}}_2\text{(ΔE\hspace{0.17em}=\hspace{0.17em}18}{\mathrm{cm}}^{\text{−1}})$ and ${}^{15}{N}_2\text{(ΔE\hspace{0.17em}=\hspace{0.17em}97}{\mathrm{cm}}^{\text{−1}})$ . The impact parameter (semi‐classical) approximation is used, and it is assumed that the vibrational‐energy transfer is caused by the interaction of the instantaneous CO₂ dipole moment with the N₂ quadrupole moment. When proper account is taken of the rotational motions of the molecules it is found that in collisions of CO₂ with ¹⁴N₂ only the low rotational levels of the CO₂ and N₂ molecules contribute to Reaction (1). In collisions of CO₂ with ¹⁵N₂, only those rotational levels contribute which undergo transitions cancelling most of the relatively large (97 cm⁻¹) vibrational‐resonance defect. For ¹⁴N₂ below about 1000°K, where the cross section displays a negative temperature dependence, the results are in excellent qualitative and quantitative agreement with available experimental data, with no adjustable parameters in the theory. Above about 1000°K the experimental cross‐section data display a positive temperature dependence indicating that some other mechanism becomes important there. For ¹⁵N₂ the calculations are in good agreement with an experimental measurement at 300°K. Data at other temperatures are not presently available. The theoretical results indicate that the cross section for the vibrational‐energy transfer should have maximum around 200°K. Below this temperature the higher rotational levels which dominate the energy‐transfer process are unfavorably weighted in the Boltzmann distribution.