Collisional energy transfer in unimolecular systems is often described using a master equation. The lack of detailed knowledge of energy transfer events combined with the computationally intensive nature of this approach makes approximate methods attractive, especially for parametrizing experimental results. One such approximation is based on the diffusion equation. In this paper a number of diffusion equation approximations is examined. Troe and Nikitin have derived such approximations by truncation of the Kramersndash;Moyal expansion of the master equation. A new approximation, using a similar approach is presented here. The diffusion equation can also be obtained as the limit of a sequence of master equations as the collision energy transfer becomes infinitely small and frequent. The derivation of such a limiting diffusion equation is presented. A further set of approximations in which the energy transfer process is imbedded in a diffusion process is also examined. The accuracy of all approximations is assessed by comparison with full solutions of the corresponding master equations for energy transfer in azulene and ethane, and for the kinetics of methane dissociation.
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