Hindered Molecular Rotation in Liquids

Abstract

Expressions for the angular velocity autocorrelation function of a classical spherical top rigid rotator and the NMR correlation time τ₂ are derived. A general relationship of the product of the spin—rotational correlation time (τ₁) and τ₂ is presented which is proportional to the mean square angular displacement in a diffusive rotational step. The present expression for τ₂ is compared with that based on the quasilattice random flight (QLRF) model. The most characteristic difference between the two expressions for τ₂ is that present expression depends on the square root of the moment of inertia while the QLRF relationship depends on the square root of molecular mass. In favorable situations this difference can be used to ascertain the mechanism of molecular reorientation such as for NH₃ and ND₃. Root mean square angular displacement in a diffusive step are computed from observed values of τ₂ and compared with the results of infrared measurements. A value for the time τ₁ for liquid water at 34°C is calculated from the results of recent computer experiments of Rahman and Stillinger and the product τ₁τ₂ is evaluated. This result indicates that the molecular rotation in liquid water is not small step rotational diffusion.