Do Inverse Monte Carlo Algorithms Yield Thermodynamically Consistent Interaction Potentials?

We numerically verify a statistical mechanics theorem which shows that there is a one-to-one equivalence between the structure of a liquid (i.e., the pair correlation function) and its pairwise additive intermolecular potential. Specifically, we show for three systems interacting with simple spherically symmetric pairwise additive potentials that inverse Monte Carlo (IMC) simulations can obtain the underlying potentials by only using the target pair correlation functions. The convergence of potentials obtained by the standard IMC procedure is, however, extremely slow. Interestingly, we find that the repulsive part of the potential converges rapidly, consistent with the well-accepted notion that it essentially determines the structure of condensed liquids. We show that additional information about the system, such as thermodynamic properties (e.g., average energy and or pressure) can be included in a modified IMC procedure. Because internal energy and pressure are primarily sensitive to the attractive part of the potential, the convergence to the true potential is improved by an order of magnitude. Although the improved convergence is a technical advance, no new information is obtained on the final converged potential by this approach, as expected by the Henderson theorem.