SHAPES OF UNIMOLECULAR FALL-OFF CURVES

By using a smoothly varying transition probability model, for which the master equation can be solved analytically for the eigenvalue gamma(0) (the rate constant) and the corresponding eigenvector-psi, some rigorous results concerning the shapes of fall-off curves for thermal unimolecular reactions can be proved. It is shown that, for a fixed set of populations (n(i) approximately) and decay rates (d(i)), the shape of the fall-off curve is determined solely by the collisional relaxation pattern among the reactive states, and the conditions for a multiexponential unimolecular reaction system to yield the usual steady-state "sum of Lindemann forms" expression are demonstrated. Also, the eigenvector corresponding to the low-pressure limiting rate is derived in analytic form for this transition probability model.