CLOSED-FORM SOLUTION OF THE ITINERANT OSCILLATOR MODEL OF MOLECULAR LIBRATION

It is shown by using self-consistent (so that action and reaction torq ues are fully accounted for) expressions for the viscous drag and whit e noise terms in the equations of motion of the fixed axis rotator ver sion of the itinerant oscillator model that the characteristic (secula r) equation of the system automatically factorizes. Hence all the corr elation functions of the model (which consists of a ''cage'' of dipola r molecules surrounding a tagged molecule) may be given in closed form . In particular, the orientational correlation functions of the tagged molecule become the products of single particle ones namely those of a free Brownian rotator and a damped harmonic oscillator while the ori entational correlation functions of the cage are simply those of the f ree Brownian rotator, The equations of motion of the system likewise d ecouple when the restrictions of small oscillations and of rotation ab out a fixed axis are removed. Thus, irrespective of the form of the in teraction potential between the cage and the tagged molecule, the rela xation modes of the system separate into those of the tagged molecule and those of its surroundings which behave as an inertia corrected fre e Brownian rotator. (C) 1997 American Institute of Physics.