Among the three general phases of matter, the liquid phase (considered broadly) is understood to be the most difficult to understand and model. Gases are made easy because they do not have many intermolecular interactions, and solids are simplified by their long-range order, and minimal excursions from it. There are good, solvable reference systems that can be used as a starting point for the characterization of these phases. Liquids, on the other hand, present us with no such starting point for their description. This, coupled with the richness of their behavior, is part of what makes them intellectually challenging. They are moreover of great relevance to chemical engineering, particularly in the growth areas of nano- and bio-technology.

There nevertheless remain some interesting questions to examine and problems to solve for the “easy” phases.

The virial equation of state provides the standard treatment for the gas phase, yet because of the difficulty involved in computing the virial coefficients its mathematical behavior and general utility are largely unexplored. Can it, for example, be used to provide a general location for the critical point? What is its convergence behavior when applied to realistic systems? Mixture properties are treated exactly in the virial equation (given a model for the cross-interactions), so what can we learn about mixture behavior from it? Calculation of virial coefficients can be computationally expensive, but it is highly parallelizable. The present trends in computing technology favors such types of calculation, so it may be worthwhile to see what can be accomplished in this direction.

The solid phase is described reasonably well with harmonic analysis, but the treatment required to build from this starting point is complex and largely ineffective. Molecular simulation consequently is a key tool for the study of crystalline phases. In the materials community solid-phase simulations typically focus on mechanical, optical, and electronic properties, as well as some transport and kinetic phenomena. Many fewer studies attempt to capture the full thermodynamics, and in particular the phase behavior, in part because of the difficulty in evaluating solid-phase free energies by simulation. But the prediction of stable solid phases is an unsolved problem of great practical importance, particularly in application to molecular crystals. We discuss some of the challenges and opportunities arising in this area.