Rapid determination of entropy and free energy of mixtures from molecular dynamics simulations with the two-phase thermodynamic model

The two-phase thermodynamic (2PT) model is generalized to determine the thermodynamic properties of mixtures. In this method, the vibrational density of states (DoS), obtained from the Fourier transform of the velocity autocorrelation function, and quantum statistics are combined to determine the entropy and free energy from the trajectory of a molecular dynamics simulation. In particular, the calculated DoS is decomposed into a solid-like and a gas-like component through the fluidicity parameter, allowing for treatments for the anharmonic effects in fluids. The 2PT method has been shown to provide reliable thermodynamic properties of pure substances over the whole phase diagram with only about a 20 ps MD trajectory. Here we show how the 2PT method can be used for mixtures with the same degree of accuracy and efficiency. We have examined the 2PT determined excess Gibbs free energies of Lennard-Jones (LJ) mixtures over a wide range of conditions (1 ≤ T* ≤ 3, 0.5 ≤ P* ≤ 2.5, 1 ≤ σBB/σAA ≤ 2, and 1 ≤ εBB/εAA ≤ 2), including the change of the off-diagonal LJ interactions. The 2PT determined values are in good agreement with those from Widom insertion or thermodynamic integration (TI). Our results suggest that the 2PT method can be a powerful method for understanding thermodynamic properties in more complicated multicomponent systems.