Reversible biphasic model for isomerizations

Isomerizations proceed from reactants R to products P, and back. Our reversible biphasic model assumes that the reaction is from R via the transition state species ‡ to P, and back. We derive the analytical solution of the rate equations. It allows simple applications to special cases. For example, for strongly exothermic reactions with negligible back reactions it brings about the same rate constant k as for transition state theory (TST). In contrast, for nearly or perfectly thermoneutral reactions, k is just half the TST reference. The results are exemplified for the nearly thermoneutral Cope rearrangement of mono deuterio-1,5-dimethylsemibullvalene. Reversible biphasic model of isomerization from the reactant (R, red) via the transition state species (‡, blue) to the product (P, green), and back, exemplified for the Cope rearrangement of mono deuterio-1,5-dimethylsemibullvalene ( d 1 -DMSBV, top panel). Deuteration of the parent DMSBV breaks its symmetry, with energy levels of ‡ above slightly lower energy levels of P compared to R (bottom panel, schematic, with wavy lines for the nuclear densities of R, ‡, P). Consequently, the nearly thermoneutral isomerization proceeds with rate constants k −1 ≈ k 2 but k 1 > k −2 . • From reactant (R) via transition state species (‡) to product (P), and back. • Extension from thermoneutral to exothermic unimolecular reactions. • Uses comprehensive quantum definition of observable species R, ‡, P. • Modifies result of transition state theory by transmission factor 1/2 < κ < 1. • Exemplified for Cope rearrangement of mono deuterio-1,5-dimethylsemibullvalene.