Chemical potential calculations in non-homogeneous liquids

The numerical computation of chemical potential in dense non-homogeneous fluids is a key problem in the study of confined fluid thermodynamics. To this day, several methods have been proposed; however, there is still need for a robust technique, capable of obtaining accurate estimates at large average densities. A widely established technique is the Widom insertion method, which computes the chemical potential by sampling the energy of insertion of a test particle. Non-homogeneity is accounted for by assigning a density dependent weight to the insertion points. However, in dense systems, the poor sampling of the insertion energy is a source of inefficiency, hampering a reliable convergence. We have recently presented a new technique for the chemical potential calculation in homogeneous fluids. This novel method enhances the sampling of the insertion energy via well-tempered metadynamics, reaching accurate estimates at very large densities. In this paper, we extend the technique to the case of non-homogeneous fluids. The method is successfully tested on a confined Lennard-Jones fluid. In particular, we show that, thanks to the improved sampling, our technique does not suffer from a systematic error that affects the classic Widom method for non-homogeneous fluids, providing a precise and accurate result.