Single particle dynamics in an anharmonic potential with translation-rotation coupling: crossover from weak localisation via chaos to free rotation

Abstract

The single particle dynamics of a rigid NH₃-molecule in an anharmonic mean crystal potential is analysed. The potential parameters used have been derived earlier from experimental neutron diffraction data on single crystals of Ni(NH₃)₆X₂ (X = I, NO ₃, PF ₆): in all these compounds the ammonia molecules show dynamical orientational disorder. The mean crystal potential which is experienced by the three protons of one ammonia molecule is given by a two-dimensional anharmonic four-well potential, which leads to a coupling of the rotation of the molecule around its threefold axis to the translational motion of the molecular center of mass. Thus the dynamical problem is restricted to three degrees of freedom. The corresponding Hamiltonian equations of motion are solved numerically. Fourier analysis, reconstruction of trajectories in the six dimensional phase space and next-amplitude-maps from the simulated time series reveal either multiple periodic or chaotic solutions, depending on the potential parameters and the energy of the system. The anharmonic potential produces, as a generic property, three different kinds of proton orbits. At low energy, i. e. low temperatures, closed orbits related to hypocycloid functions occur. At intermediate temperatures the orbits are chaotic. High temperature simulations show circular orbits with a week high frequency jitter superimposed. Thus a crossover from weak localization via chaos to nearly free rotation is obtained by a variation of the energy in the simulation.