Reorientational dynamics of molecules in liquid methane: A molecular dynamics simulation study

Abstract

Rotational motion of molecules in liquids plays an important role in determining the liquids' Nuclear Magnetic Resonance (NMR) spin-relaxation properties. The traditional theory of NMR spin relaxation assumes that the reorientational dynamics of molecules in liquids can be described by a continuous-time rotational-diffusion random walk with a single rotational-diffusion coefficient. However, recent experimental and theoretical studies have demonstrated that the simple rotational-diffusion model does not fully capture the rotational dynamics of molecules in liquids: for example, the reorientation of molecules in liquid water occurs through a combination of continuous-time rotational diffusion and discrete, large angular jumps resulting from collective rearrangements of the hydrogen-bond network of water.

In order to obtain further insights into the origin of large angular jumps in the rotational motion of liquid water, we studied the rotational dynamics of methane - an apolar, non‑hydrogen-bonding liquid with a spherically symmetric molecule. The reorientational propagator and the ensemble-averaged Legendre polynomial reorientational functions of liquid methane were analysed using molecular dynamics simulations. On the femtosecond timescale, the reorientational motion of methane molecules was found to be characterised by free-rotation gas-like Gaussian decay of the reorientational Legendre polynomials, a result consistent with the available experimental data for liquid methane. On the long timescale (picoseconds) the decay of the reorientational Legendre polynomials was exponential, suggestive of a Debye-like continuous-time rotational diffusion behaviour. However, the ratios of the exponential time constants for different orders of the Legendre polynomials failed to match the rotational-diffusion model. We discuss the implications of these findings for the understanding of rotational motion of molecules in hydrogen-bonding and non‑hydrogen-bonding liquids.