Near-Resonant Vibrational Energy Transfer Among Isotopes of CO2

Quantitative calculations are presented which show that large (approximately gas kinetic) cross sections observed for vibrational-vibrational energy transfer between isotopes of C${\mathrm{O}}_2$ are due to long-range forces. The mechanism involved in the transfer of a quantum of asymmetric stretch vibration from ${\mathrm{C}}^{12}$ ${\mathrm{O}}_2^{16}$ to ${\mathrm{C}}^{12}$ ${\mathrm{O}}_2^{16}$ and ${\mathrm{O}}^{16}$ ${\mathrm{C}}^{12}$ ${\mathrm{O}}^{18}$ can be described in terms of dipole-dipole coupling. However, dipole-dipole coupling is too weak to describe the energy transfer to ${\mathrm{C}}^{13}$ ${\mathrm{O}}_2^{16}$. It is shown that in this case dipole-octupole coupling is expected to be stronger than dipole-dipole coupling. The room-temperature results are reproduced by assuming a value of 1 × ${10}^{-67\mathrm{}}$ stat ${\mathrm{C}}^2$ ${\mathrm{cm}}^6$ for the square of matrix element for the vibrational transition. Temperature dependence of the rate constant is calculated to put this hypothesis to test.