Master equation approach to vibrational energy transfer between two diatomic molecules

In this paper a semiclassical non-markovian master equation is derived. We begin by using the well-known tetradic form of the Liouville equation for a reduced density operator. By projecting the diagonal matrix elements of the operator, we obtain an infinite-order master equation. This equation is then applied in the lowest-order approximation to collinear collisions between the diatomic molecules: H₂H₂, N₂N₂ and Cl₂Cl₂. With an assumed form of the interaction potential for such a problem we have also derived an analytical expression for the V—V transition probabilities. They are then calculated over a wide range of velocities of the colliding molecules and compared with exact semiclassical ones. An excellent agreement of the results is found for small velocities (i.e. υ ≈ 10⁴ cm/s). For larger values of υ (≈ 10⁵ cm/s) the results obtained from the master equation approach agree with the exact ones only in the low-velocity range for light molecules and low oscillatory states.