The master equation approach for single-well systems

4 The master equation approach for single-well systems 

The review of pressure-dependent reactions, which so far was based on the strong collision assumption, is readily adapted to more sophisticated collision models. Here, we discuss the description of unimolec-ular reactions in form of the ME. Our initial scheme 

Written as eigenvalue problem (see equation (64)) we can identify the matrix elements 

The eigenvalues of this eigenvalue problem are found by diagonalizing the matrix M. The situation is more complicated if collisional relaxation is not fast compared to chemical reaction. In that case, the solution will yield more than one small negative eigenvalues and the overall reaction will proceed on a non-exponential time scale. In other words, if collisional relaxation interferes with unimolecular reaction, the reaction process cannot be described by a time-independent rate constant A uni-We now take a look at the corresponding chemically activated reaction, 

Several features of this equation make the solution more challenging compared to the dissociation (1) The last term on the right-hand side makes equation (69) non-linear, because [A] and [B] are both time dependent. (2) Often, the association or recombination rate is only known as high-pressure rate k 2 j T). (3) The deactivation of energized AB is reversible so that stabilized AB can be reactivated. Starting with the second problem, it can be resolved by introducing a new function h E) to convert k 2,co(T) to an energy-dependent rate constant. This function 

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