The photo-excited molecules, which was shown as an example of microcanonical ensemble, are intuitive example, but are rarely the target of the microcanonical calculations. The reason is that, for the photolysis processes, the microcanonical ensemble may be a zero-th order approximation, but the lifetime of the excited molecules are usually too short to accomplish the complete statistical distribution.

One of the most important application of the microcanonical statistics is the theory of unimolecular reactions. The fact that the rate constants for unimolecular reactions start to decrease as pressure decreases below the certain range, is explained by the deviation of the internal energy distribution from the Boltzmann distribution. In other words, the unimolecular rate constants in fall-off region can be quantitatively calculated by averagingk(k), microscopic (= microcanonical) rate constant, with respect to a distribution different from the Boltzmann distribution.

## Keywords

Microscopic rate constant, Unimolecular reactions, RRKM theory,
High-pressure limit, Low-pressure limit, Fall-off region