The two-phase thermodynamic (2PT) model is used to determine the absolute entropy and energy of carbon dioxide over a wide range of conditions from molecular dynamics trajectories. The 2PT method determines the thermodynamic properties by applying the proper statistical mechanical partition function to the normal modes of a fluid. The vibrational density of state (DoS), obtained from the Fourier transform of the velocity autocorrelation function, converges quickly, allowing the free energy, entropy, and other thermodynamic properties to be determined from short 20-ps MD trajectories. The anharmonic effects in the vibrations are accounted for by the broadening of the normal modes into bands from sampling the velocities over the trajectory. The low frequency diffusive modes, which lead to finite DoS at zero frequency, are accounted for by considering the DoS as a superposition of gas-phase and solid-phase components (two phases). The analytical decomposition of the DoS allows for an evaluation of properties contributed by different types of molecular motions. We show that this 2PT analysis leads to accurate predictions of entropy and energy of CO2 over a wide range of conditions (from the triple point to the critical point of both the vapor and the liquid phases along the saturation line). This allows the equation of state of CO2 to be determined, which is limited only by the accuracy of the force field. We also validated that the 2PT entropy agrees with that determined from thermodynamic integration, but 2PT requires only a fraction of the time. A complication for CO2 is that its equilibrium configuration is linear, which would have only two rotational modes, but during the dynamics it is never exactly linear, so that there is a third mode from rotational about the axis. In this work, we show how to treat such linear molecules in the 2PT framework.

The enthalpy, entropy, and free energy of water are important physical quantities for understanding many interesting phenomena in biological systems. However, conventional approaches require different treatments to incorporate quantum and diffusive effects of water in different states of matter. In this work, we demonstrate the use of the two-phase thermodynamic (2PT) model as a unified approach to obtain the properties of water over the whole phase region of water from short (∼20 ps) classical molecular dynamics trajectories. The 2PT model provides an effective way to separate the diffusive modes (gas-like component) from the harmonic vibrational modes (solid-like component) in the vibrational density of states (DoS). Therefore, both diffusive and quantum effect can be properly accounted for water by applying suitable statistical mechanical weighting functions to the DoS components. We applied the 2PT model to systematically examine the enthalpy, entropy, and their temperature dependence of five commonly used rigid water models. The 2PT results are found to be consistent with those obtained from more sophisticated calculations. While the thermodynamic properties determined from different water models are largely similar, the phase boundary determined from the equality of free energy is very sensitive to the small inaccuracy in the values of enthalpy and absolute entropy. The enthalpy, entropy, and diffusivity of water are strongly interrelated, which challenge further improvement of rigid water model via parameter fitting. Our results show that the 2PT is an efficient method for studying the properties of water under various chemical and biological environments.