Rotational correlation times for small molecules in liquids

Abstract

I w i l l focus on the ro ta t iona l motion of small molecules in l iqu ids . This mot ion is often "slow" compared to a l l other relevant molecular motions, which is equivalent to saying that rotat ions are Markovian or d i f fus iona l . In this case the correla t ion function for a normalized spherical harmonic, Y Lm(COS@), relaxes exponent ia l ly with a decay time m~. In broad terms we can iden t i f y two classes of exponential rotat ional re laxat ion in l iqu ids : one which is d i f fus ional in that the motion takes place via small random angular jumps, and the other in which the molecule rotates quite rapid ly but not frequently because most of the time i t is held in an osc i l l a to ry well which i t s e l f loosens up only in f requent ly [ I ] . This l a t t e r motion corresponds to random large angular jumps; although for this motion the slow decay mode does indeed appear to be exponential, the l i b ra t i ona l modes are important and give r ise to an appreciable high frequency rotat ional spectrum. I t is l i k e l y that the large angular jumps become increasingly important at high v iscosi ty . Whether or not the motion is exponent ia l , we can always define a corre la t ion time [2]