Perturbation Theory of Liquids: Weeks Chandler Anderson Model To put simply, what is the big deal about the WCA model of describing solutes in liquid theory?
I understand that the WCA model splits the potential into a repulsive force component, and an attractive force perturbation. This simplifies the mathematics of the way intermolecular interactions can be handled when we move step by step from describing ideal gases to interacting systems and then to liquids. What makes this perturbation model so prevalent across liquid theory research, aside from simplifying calculations? Also, why does this model not hold when describing liquid-vapor interfaces?
For context, I'm working with biological solutes in water.
 A: Welcome to Physics StackExchange! I'll try and give an answer, but I'm not sure if it is exactly what you are looking for.
Firstly, the WCA approach is popular because it is quite accurate, for simple liquids, not just because it simplifies the mathematics. It is very difficult to construct a proper theory of liquids, i.e. one which takes the interactions between atoms as input, and predicts the structure and thermodynamics. It is not just a question of moving step by step from the ideal (and non-ideal) gas as a starting point. If you want to look into the details, the book by J-P Hansen and IR McDonald, Theory of Simple Liquids gives them, but you may have done that already.
The division of the potential by WCA separates the problem in a physically useful way. The repulsive forces dictate the structure of the liquid, and this is related back to the hard sphere model system, for which some fairly accurate analytical and numerical results are available. The thermodynamics of the hard sphere system is also fairly well understood: it is completely dictated by entropy effects, as there are no interaction energies at all. The attractive forces do not have much effect on the structure, so they are suitable to treat in a perturbative way: to a large extent this handles the energetics. The method generalizes in a straightforward way to liquid mixtures, and hence is applicable to discuss the structure and energetics of solvent around solute. I have to say, though, that the proper treatment of solutes in water, including the tetrahedral hydrogen-bond network, hydrophobic effects and so on, is not trivial. David Chandler made contributions in all these areas, and you might be interested in his autobiographical review which was published around the time of his death last year in Ann Rev Phys Chem, 68, 19 (2017).
The WCA approach was formulated for homogeneous liquids, and not intended to directly address the liquid-vapour interface. For that you need something extra. Probably the most successful approach is density functional theory in which the free energy of the system is minimized with respect to variations in the local density. The simplest version of this requires information regarding the homogeneous system as a function of bulk density: a local free energy density, and an estimate of the direct correlation function, which underpins the liquid structure. In principle, the WCA approach could provide these quantities, but it doesn't work out well enough: as pointed out by Lutsko, also published in J Chem Phys, 127, 054701 (2007), WCA is not accurate enough at low densities and fails to reproduce the second virial coefficient of the gas, or the low-density limit of the direct correlation function. So, typically, different approximations are used to describe the liquid-vapour interface by density functional theory.
