Coupling of the overall molecular motion with the conformational transitions. I. The model sysstem of two coupled rotors

Models based on the neglect of the coupling of the overall molecular rotations with the conformational transitions are normally used to interpret spectroscopic data, like NMR relaxation times or dielectric relaxation spectra of flexible molecules. However, when the mobile parts of the molecule have a comparable size, the effects of such coupling cannot be ignored. A theoretical analysis of the problem is presented for the model system of two coupled rotors whose time evolution is given by a diffusion equation under the influence of the intramolecular potential. When the potential is steep enough to determine stable conformers, an approximate description of the system is obtained in terms of a time evolution operator of mixed type: diffusion motion for the rotation of the overall system and generalized random walk among sites for the internal degree of freedom. The localized functions formalism allows one to generate the approximate time evolution operator without neglect of the coupling, so recovering two important effects: the dependence of the diffusion coefficient for the overall motion on the conformational state, and the recoil rotations of the rods during a conformational transition. The results of the approximate model have been compared with the numerical solutions of the complete diffusion equation, and small deviations on the spectral densities have been found with potential barriers typical of alkyl chains at room temperature.