Two-modes approach to the state-to-state vibrational kinetics of CO₂

Two-modes (symmetric–asymmetric) reduction of the CO 2 vibrational kinetics has been introduced systematically for the purpose of state-to-state modeling. The two-modes approach is known from multi-temperature models. Its basic assumption is that vibrational energy of the CO 2 molecule which depends on 4 quantum numbers can be approximated by a function of only 2 numbers. Subsequently, vibrational states of CO 2 with the same quantum numbers of the effective symmetric and asymmetric mode can be grouped into one combined state. The paper presents the calculation of the average probabilities of transitions between combined states based on the Schwartz–Slawsky–Herzfeld theory. Closed analytical formulas are derived for vibrational–translational and vibrational–vibrational transitions.