A Stochastic Model for Crankshaft Transitions

The model of three coupled rotors is analyzed by solving the corresponding Fokker-Plank equation of Smoluchowski type. From the numerical eigenvalues of the Fokker-Planck operator, the kinetic coefficients for conformational transitions are derived in the presence of bistable potentials for the torsional angles. Besides single-bond transitions through a saddle point of the internal potential, this procedure allows the identification of an anomalous type of kinetic processes, described as transitions of the inner rotor when the outer ones remain almost immobile (or rotate together). Their anomalous character derives from the absence of a saddle point crossing. Because of the localization within the chain, they can be assigned to transitions of crankshaft type. As expected on a qualitative ground, the increase of the friction of the outer rotors favors crankshaft transitions with respect to single-bond transitions. The implications of the model for the observation of crankshaft transitions in molecular systems are discussed in the conclusion.