Importance of hindered rotations in the thermal dissociation of small unsaturated molecules: Classical formulation and application to HCN and HCCH

A standard low-pressure limit Rice–Ramsperber–Kassel–Marcus rate constant is shown to significantly underestimate, by factors of three or more, the measured thermal dissociation rates for HCCH and HCN if the correct value of the bond-dissociation energy is used. An explanation for this discrepancy is sought by examining anharmonic effects due to isomerization. Classical expressions for the density of states and partition function are developed which include isomerization anharmonicity and can be substituted in the standard rate constant expression for corresponding harmonic terms. These expressions are then applied to HCN and HCCH. For HCN, the resulting expression can be compared both to experiment and to a previous quantum mechanical study using the same Hamiltonian form and potential for isomerization. The classical and quantum mechanical agreement is excellent. Good agreement with experiment is obtained with the consensus dissociation energy. For HCCH, electronic structure calculations are performed to produce the required potential for isomerization. With this potential, comparison between measured rate constants and those calculated with the consensus dissociation energy is also good. In both of these applications, adiabatic influences from the two stretching frequencies are argued to reduce the effective isomerization barrier and increase the effective mass of the rotation. Based on these detailed applications, an approximate, closed-form multiplicative factor for the rate constant expression is derived. This expression can be regarded as a generalization of one-dimensional hindered rotor formulas for the inherently multidimensional hindered rotors of isomerization. The expression is parametrized by the height of the hindered-rotor barrier. With the correct barrier height, this expression reproduces the more detailed calculations on HCN and HCCH. Its application to other systems indicates that the kinetic importance of isomerization in olefins is a rather general effect, not relegated only to small molecules.