Adiabatic Rotations in Unimolecular Rate Theory

The term “adiabatic rotations” describes rotations that are constrained to remain in the same quantum state when the activated complex is formed from the active molecule because of restrictions imposed by angular momentum conservation. It is shown that these rotations decrease the activation energy for dissociation and therefore increase the rate; a priori, the effect is likely to be largest at the high‐pressure limit of a unimolecular decomposition, and least at the low‐pressure limit. The general case is considered of a polyatomic symmetric‐top molecule decomposing unimolecularly. Assuming a Boltzmann distribution of rotational energies of the molecules undergoing decomposition, an expression is derived for the factor $\mathrm{(f)}$ by which the rate constant is increased due to adiabatic rotations. Two approaches are used: one involving the average moment of inertia of complex ${\mathrm{(I}}^{‡})$ , if known from other information, and the second involving the assumption of inverse sixth‐power potential between the two incipient fragments. The former approach is useful in demonstrating the dependence of $f$ on $I^{‡}$ at high and low pressures. The latter approach permits the calculation of $f$ directly from molecular parameters. These calculations are done for four unimolecular decompositions and they show that $I^{‡}$ is larger than has been usually estimated, and also that the pressure dependence of $f$ is substantial enough in the case of complex molecules to contribute appreciably to the falloff with pressure of the unimolecular rate constant. The effect of the assumed power law in the potential is briefly discussed.