Multidimensional stochastic models for the study of molecular motions in liquids and liquid crystals

Multidimensional stochastic equations are set up to interpret rotational molecular dynamics in isotropic solutions and liquid crystalline phases. The description of the dynamics is based on standard or augmented Fokker-Planck type equations, containing a classical Liouville term acid dissipation terms including fluctuating interactions with the local environment. Numerically exact solutions of the equations are obtained by using orthogonal functions of the phase space coordinates (Euler angles, conjugated momenta, and solvent collective variables) and special algorithms for handling large and sparse non-Hermitian matrices. Under regimes of particular dynamics, Born-Oppenheimer separation is employed. Solutions of the dynamic problem are provided in the time-correlation function language, suitable for direct interpretation of spectroscopic observables. As an example, the interpretation of quasi-elastic neutron scattering experiments for molecules with a single scattering centre in a nematic liquid crystalline phase is presented.