Double well isomerization in solution: a new comparison of theory and experiment

The first-excited-singlet state of each of the compounds 2-vinylanthracene (2VA) and 2-(2′-propenyl) anthracene (22PA) undergoes an electronically adiabatic torsional double-well isomerization which interconverts a s-cis conformation and a s-trans conformation. The forward rate constant kf for the isomerization was measured by picosecond fluorescence spectroscopy as a function of temperature and solvent viscosity η in the range 0.23–3.25 cP, i.e., in the C5–C16 normal alkanes. For 2VA, kf is independent of η within experimental uncertainty (∼5%), while for 22PA kf≂cη−0.23. An effective torsional isomerization potential of the form V(φ)=(V1/2)(1−cos φ)+(V2/2)(1−cos 2φ) was determined from thermochemical data on the isomerization. Torsional well (ω0) and barrier (ωb) frequencies were calculated from the effective potential and the appropriate moments of inertia. With an estimate in hand for ωb, it was possible to directly evaluate theoretical predications from the (i) theory of Kramers and alternatively from the (ii) theory of Grote and Hynes [employing the Zwanzig–Bixon–Metiu–Oxtoby–Freed (ZBMOF) expression for the frequency dependent friction ζ̂(λ)]. Kramers’ theory incorrectly predicts a large η dependence of kf for both 2VA and 22PA. In contrast, Grote–Hynes, with the ZBMOF ζ̂(λ), correctly predicts the absence of a significant η dependence of kf for 2VA, but underestimates the η dependence of kf for 22PA.