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We propose a general approach for determining the entropy and free energy of complex systems as a function of temperature and pressure. In this method the Fourier transform of the velocity autocorrelation function, obtained from a short (20 ps) molecular dynamics trajectory is used to obtain the vibrational density of states (DoS) which is then used to calculate the thermodynamic properties by applying quantum statistics assuming each mode is a harmonic oscillator. This approach is quite accurate for solids, but leads to significant errors for liquids where the DoS at zero frequency, S(0), remains finite. We show that this problem can be resolved for liquids by using a two phase model consisting of a solid phase for which the DoS goes to zero smoothly at zero frequency, as in a Debye solid; and a gas phase (highly fluidic), described as a gas of hard spheres. The gas phase component has a DoS that decreases monotonically from S(0) and can be characterized with two parameters: S(0) and 3Ng, the total number of gas phase modes 3Ng→0 for a solid and 3Ng→3(N−1) for temperatures and pressures for which the system is a gas. To validate this two phase model for the thermodynamics of liquids, we applied it to pure Lennard-Jones systems for a range of reduced temperatures from 0.9 to 1.8 and reduced densities from 0.05 to 1.10. These conditions cover the gas, liquid, crystal, metastable, and unstable states in the phase diagram. Our results compare quite well with accurate Monte Carlo calculations of the phase diagram for classical Lennard-Jones particles throughout the entire phase diagram. Thus the two-phase thermodynamics approach provides an efficient means for extracting thermodynamic properties of liquids (and gases and solids).
Lin et al. (Sat,) studied this question.