Chemical Potential Differences in the Macroscopic Limit from Fluctuations in Small Systems

We present a new method for computing chemical potential differences of macroscopic systems by sampling fluctuations in small systems. The small system method, presented by Schnell et al. [Schnell et al., J. Phys. Chem. B, 2011, 115, 10911], is used to create small embedded systems from molecular dynamics simulations, in which fluctuations of the number of particles are sampled. The sampled fluctuations represent the Boltzmann distributed probability of the number of particles. The overlapping region of two such distributions, sampled from two different systems, is used to compute their chemical potential difference. Since the thermodynamics of small systems is known to deviate from the classical thermodynamic description, the particle distributions will deviate from the macroscopic behavior as well. We show how this can be utilized to calculate the size dependence of chemical potential differences and eventually extract the chemical potential difference in the thermodynamic limit. The macroscopic chemical potential difference is determined with a relative error of 3% in systems containing particles that interact through the truncated and shifted Lennard-Jones potential. In addition to computing chemical potential differences in the macroscopic limit directly from molecular dynamics simulation, the new method provides insights into the size dependency that is introduced to intensive properties in small systems.