General expression for rates of solution reactions influenced by slow solvent fluctuations, and its experimental evidence

Abstract

Dynamics in solution reactions is determined by solvent fluctuations: In second-order reactions, two species of molecules approach sufficiently closely before reaction, by diffusion, which becomes possible due to thermal fluctuations of solvents. First-order reactions take place within a solute molecule, but in general when its solvation structure takes specific molecular arrangements most favorable for reactions. These specific conformations can be taken as a result of solvent fluctuations. Also intramolecular vibrational fluctuations in solute molecules play important roles in general, as understood from the fact that atomic arrangements reorganize in solute molecules after reaction. The former fluctuations are much slower than the latter ones. In this situation the rate constant takes a general form of 1 (k TST −1 + k f −1) with k f > 0, where k TST represents the rate constant expected from the transition state theory. k f represents the rate constant with which the molecular arrangements most favorable for reactions are attained in the solute-solvent system as a result of solvent fluctuations. k Tst does not depend on the speed of solvent fluctuations measured by the inverse of their relaxation time τ, but k f is proportional to τ − α with 0 < α ⩽ 1. Usually τ is proportional to the solvent viscosity η. This general expression was confirmed with the rate constant k obs observed for the thermally-recovering Z/E isomerization of substituted azobenzenes as N-benzylidene anilines in various solvents. Here a variation range of η as wide as 10 8 times under pressure covered both the TST-valid regime at low η, where obs ≈ k TST since k TST⪡ k f , and the TST-invalid fluctuation-controlled regime at high η, where k obs ≈ k f since k f ⪡ k TST. These data cannot be rationalized in the framework of frequency-dependent friction.