Combining rules, such as the Lorentz-Berthelot rules, are routinely used to calculate the thermodynamic properties of mixtures using molecular simulations. Here we extend the expanded Wang-Landau simulation approach to determine the impact of the combining rules on the value of the partition function of binary systems, and, in turn, on the phase coexistence and thermodynamics of these mixtures. We study various types of mixtures, ranging from systems of rare gases to biologically and technologically relevant mixtures, such as water-urea and water-carbon dioxide. Comparing the simulation results to the experimental data on mixtures of rare gases allows us to rank the performance of combining rules. We find that the widely used Lorentz-Berthelot rules exhibit the largest deviations from the experimental data, both for the bulk and at coexistence, while the Kong and Waldman-Hagler provide much better alternatives. In particular, in the case of aqueous solutions of urea, we show that the use of the Lorentz-Berthelot rules has a strong impact on the Gibbs free energy of the solute, overshooting the value predicted by the Waldman-Hagler rules by 7%. This result emphasizes the importance of the combining rule for the determination of hydration free energies using molecular simulations.
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