Resolving vibrational and structural contributions to isothermal compressibility

The well-known and general "compressibility theorem" for pure substances relates κT=−(∂lnV/∂p)N,T to a spatial integral involving the pair correlation function g(2). The isochoric inherent structure formalism for condensed phases separates g(2) into two fundamentally distinct contributions: a generally anharmonic vibrational part, and a structural relaxation part. Only the former determines κT for low-temperature crystals, but both operate in the liquid phase. As a supercooled liquid passes downward in temperature through a glass transition, the structural contribution to κT switches off to produce the experimentally familiar drop in this quantity. The Kirkwood-Buff solution theory forms the starting point for extension to mixtures, with electroneutrality conditions creating simplifications in the case of ionic systems