First-principles prediction and interpretation of propagation and transfer rate coefficients

Propagation and transfer rate coefficients in free-radical polymerizations are calculated from first principles, using quantum calculations (both ab initio and semi-empirical) to determine geometries, frequencies, torsional potentials and energies of reactants and transition state, after which transition state theory yields the Arrhenius parameters. While activation energies can only be calculated for small species and with large computational resources, acceptable frequency factors (A) are obtained with relative ease provided that lower frequencies corresponding to torsions are treated as hindered rotors, not harmonic oscillators; this entails finding the torsional potential and exact evaluation of the corresponding partition function. Simple theory can be used to find A because this involves a ratio of partition functions of reactant and transition state, and because torsions (which are dominated by geometrical considerations) dominate A. A is determined by three modes in the transition state: rotation of the monomer about the forming bond, rotation of a “propylene”-group about the terminal C–C bond in the radical, and simultaneous bending of the two angles associated with the forming bond. Calculations on ethylene and acrolein give agreement with experiment. These studies explain some experimental observations. (i) Changing the penultimate unit gives a small but significant change in the torsion of two of the three modes dominating A, leading to a penultimate-unit effect of ca. a factor of 1–10. (ii) Deuteration affects the moments of inertia of the torsions, leading to changes in A in accord with experiment. (iii) A, but not the activation energy, changes predictably along a homologous series (e.g., methyl, butyl methacrylate). (iv) For a given monomer, A's for transfer to monomer and propagation are similar.