Riemann tensor theory of liquid state chain dynamics

The Riemann–Kirkwood–Fixman diffusion equation is applied to the analysis of rotational and torsional dynamics of alkane chains in liquids. It is found that the covariant metric can be calculated for chains of arbitrary length. For the three bond chain, butane, the covariant metric can be easily inverted and a diffusion equation for overall as well as internal rotation is derived. The internal torsional and overall rotational degrees of freedom are coupled by an internal angular momentum, originally proposed by Eckart. The time dependent torsion angle distribution function satisfies a diffusion equation with a nonlocal diffusion coefficient that is found to be in accord with our earlier work [J. Chem. Phys. 70, 2362 (1979)] and that of Pear and Weiner [J. Chem. Phys. 71, 212 (1979)].