Memory Effects Explain the Fractional Viscosity Dependence of Rates associated with Internal Friction: Simple Models and Applications to Butane Dihedral Rotation

Barrier-crossing rates of biophysical processes, ranging from simple conformational changes to protein folding, often deviate from the Kramers prediction of an inverse viscosity dependence. In many recent studies, this has been attributed to the presence of internal friction within the system. In our previous work, we showed that memory-dependent friction arising from the non- equilibrium solvation of a single particle can also cause such a deviation and be misinterpreted as internal friction. Here, we show that, even in the absence of an explicit solvent, memory effects can arise from within the molecule due to the coupling of the reaction coordinate motion with frictionally orthogonal degrees of freedom. Further, we find that the strength of the coupling determines the extent of the deviation from Kramers Theory. We show this for not only a simple diatom model but also cis-trans isomerization rates of butane, establishing the generality of our results.