Measurement of chemical potentials of systems with strong excluded volume interactions by computing the density of states

At high densities and low temperatures, the conventional Widom test particle method to compute the chemical potential of a system of particles with excluded volume interactions fails owing to bad statistics. A way to circumvent this problem is the use of expanded ensemble simulation techniques or thermodynamic integration. In this article, we will describe an alternative method to compute the chemical potential which is conceptually much easier, by computing the density of states of systems of N and N + 1 particles directly; and by performing a test particle simulation at very high temperature. The advantage of our technique is that the densities of states of the N and N + 1 particle system are computed in an ensemble in which particles can pass each other, resulting in a more efficient sampling. We will demonstrate our method not only for single particles but also for chain molecules with intramolecular interactions. By using an infinite temperature expansion and an extension of the density of states to very high energies, we will show that it is also possible to compute the chemical potential without having to compute the density of states for the N + 1 particle system.