Rotational Motion in Solution: Hydrogen Halides in Cyclohexane

The dipole correlation function and the average kinetic rotational energy of hydrogen fluoride, hydrogen chloride, and deuterium chloride have been computed from the published far-infrared absorption bands [P. Datta and G. M. Barrow, J. Chem. Phys. 43, 2137 (1965)]. The computations show that the dissolved hydrogen halide molecules undergo fast, large-angle rotational diffusional jumps: for instance, the dissolved HF molecules which are in their most populous state have regained their original orientation after a time interval of 0.2 × 10−12 sec following the disturbance of their equilibrium state. The coherence of their rotational motion has completely decayed after about 0.4 × 10−12 sec. A comparison with the dipole correlation function of the classical ensembles of freely rotating molecules shows that the intermolecular forces between HF and cyclohexane become observable only after a time interval of 0.08 × 10−12 sec; the corresponding value for dissolved DCl is 0.14 × 10−12 sec. These time intervals seem to correlate with some “average free volume” in liquid cyclohexane. This was shown by an estimate of the translational and rotational motion of the hydrocarbon from proton spin–lattice relaxation measurements, evaluation of the band shape of its a2u fundamental (522 cm−1), and some simple gas–kinetic considerations. Quantitative estimates of collision-induced absorption between the HF and cyclohexane molecules indicate that dipole–induced-dipole and quadrupole–induced-dipole absorption is appreciable. It is shown that the quadrupole–induced-dipole absorption must be subtracted out in order to obtain good values for the average rotational kinetic energy of the dissolved hydrogen halide molecules.