Determination of pairwise interactions via the radial distribution function in equilibrium systems interacting with the Mie potential

Particle interactions play a fundamental role in condensed matter physics because they determine both the dynamical behavior and the equilibrium physical properties of a given system at temperature T and density p. However, these interactions are not always precisely known in experiments, or in simulations of coarse-grained systems. A direct determination of the pair interaction potential in a given system could help understand observed behaviors and make further predictions. Given a number of equilibrium configurations of a system, it would be desirable to find a method to directly determine the pair potential by only using these snapshots. We propose two simple methods towards this goal for the specific case of the systems in 3 dimensional space with the Mie potential, which includes two exponents as m and s. Well-equilibrated system configurations are produced by molecular dynamical simulations using the Mie potential with different exponent combinations (m, s). In the first method, we construct a correspondence between the value and location of the first peak of the radial distribution function and the couple (m, s), which allows us to determine the potential with an accuracy of 100% when given a set of equilibrium configurations for an unknown potential. In the second method, we train an artificial neural network to learn this correspondence. We find that all (m, s) combinations are correctly predicted. Both methods support the idea that the pairwise interaction can often easily be inferred by using equilibrium snapshots.