Density dependence of attractive forces for hydrogen stretching vibrations of molecules in compressed liquids

An empirical analysis of pressure-induced shifts for quasidiatomic C–H or O–H stretching vibrations in solution shows that the portion attributable to attractive forces exhibits an approximately quadratic dependence on the solvent density, with exponents in the range sA=2.1±0.3 for ten systems. This is much stronger than the linear density dependence (sA=1) postulated for attractive forces by Schweizer and Chandler. Theoretical estimates of the attractive part of the frequency shifts are derived by averaging attractive R−n potentials (n≥6) using the hard-sphere radial distribution function. This yields a simple, explicit formula with an exponential dependence on density. We find attractive exponents of sA∼2.0±0.1 for the experimental density regime, whereas sA→1 for the zero-density limit. The sA values at high density are insensitive to the potential exponent n and comparable to the repulsive exponents sR∼3.5 obtained from the hard-sphere model. The density dependence for attractive as well as repulsive contributions thus is governed chiefly by packing effects and is only mildly affected by the form of the intermolecular potential. This situation permits attractive potential parameters to be evaluated by inverting experimental data on pressure-induced vibrational frequency shifts.