Vibrational relaxation of carbon dioxide in the three-temperature kinetic-theory
approach is studied. The focus is on the evaluation of the vibrational energy production terms in the coupled symmetric-bending and asymmetric modes. Using the generalized Chapman–Enskog method, the energy production terms are expressed as functions of the gas temperature, vibrational temperatures of CO2 modes and probabilities of corresponding transitions. It is shown that a modification of the Landau–Teller formula can be obtained from the rigorous theoretical expressions using several limiting assumptions. Whereas VT relaxation in the bending mode can be described by the Landau–Teller approximation with a satisfactory accuracy, its application to the inter-mode exchange requires introducing relaxation times depending on the vibrational temperatures of the modes involved to the transitions.