Isomerization dynamics in viscous liquids: Microscopic investigation of the coupling and decoupling of the rate to and from solvent viscosity and dependence on the intermolecular potential

A detailed investigation of viscosity dependence of the isomerization rate is carried out for continuous potentials by using a fully microscopic, self -consistent mode-coupling theory calculation of both the friction on the re actant and the viscosity of the medium. In this calculation we avoid approx imating the short time response by the Enskog limit, which overestimates th e friction at high frequencies. The isomerization rate is obtained by using the Grote-Hynes formula. The viscosity dependence of the rate has been inv estigated for a large number of thermodynamic state points. Since the activ ated barrier crossing dynamics probes the high-frequency frictional respons e of the liquid, the barrier crossing rate is found to be sensitive to the nature of the reactant-solvent interaction potential. When the solute-solve nt interaction is modeled by a 6-12 Lennard-Jones potential, we find that o ver a large variation of viscosity (eta), the rate (k) can indeed be fitted very well to a fractional viscosity dependence: (k similar to eta(-alpha)) , with the exponent alpha in the range 1 greater than or equal to alpha >0. The calculated values of the exponent appear to be in very good agreement with many experimental results. In particular, the theory, for the first ti me, explains the experimentally observed high value of alpha even at the ba rrier frequency, omega(b). similar or equal to 9 X 10(12) s(-1) for the iso merization reaction of 2-(2'-propenyl)anthracene in liquid eta-alkanes. The present study can also explain the reason for the very low value of vb obs erved in another study for the isomerization reaction of trans-stilbene in liquid n-alkanes. For omega(b) greater than or equal to 2.0 X 10(13) s(-1), we obtain alpha similar or equal to 0, which implies that the barrier cros sing rate becomes identical to the transition-state theory predictions. A c areful analysis of isomerization reaction dynamics involving large amplitud e motion suggests that the barrier crossing dynamics itself may become irre levant in highly viscous liquids and the rate might again be coupled direct ly to the viscosity. This crossover is predicted to be strongly temperature dependent and could be studied by changing the solvent viscosity by the ap plication of pressure. (C) 1999 American Institute of Physics. [S0021-9606( 9950514-X].