Molecular rototranslation in condensed phases : Single particle theory

Abstract

A multidimensional expansion of the Mori equation in terms of a chain of Markov equations is used to develop a theory of molecular rototranslation in condensed phases. The stochastic equations of motion are solved for transient and equilibrium averages of the relevant dynamical variables. The single particle rototranslational Langevin equations correspond to the first equation of the Markov chain and (with a rotational constraint) are solved using Wiener matrix algebra for a possible sixteen autocorrelation functions. The Einstein result for the mean-square velocity and angular velocity is generalized. The third dimension of the Markov chain corresponds mechanically to the (constrained) rototranslation of a molecule bound to a cage of nearest neighbours by a dissipative matrix γ. The cage is itself undergoing a rototranslational Brownian motion. The problem of evaluating the formal theory with experimental measurements is discussed in terms of the number of parameters associated with each approximant (or dimensionality of the Markov chain). It is possible to avoid using a least-mean-squares fitting procedure by using a broad enough range of data and simulator results.