Molecular Dynamics simulations and discrete perturbation theory for systems interacting via the parabolic-well pair potential

In this work, we performed Molecular Dynamics (MD) simulations to investigate the thermodynamic properties, including vapor pressures, critical points, pressure, excess energy, and vapor-liquid equilibrium, for a continuous version of the parabolic-well (PW) pair potential within the attractive range of 1.5 <= lambda <= 3.0. In addition to conducting extensive MD simulations, we have developed an analytical equation of state for the Helmholtz free energy of particles interacting via the PW pair potential. This development was accomplished within the framework of discrete perturbation theory, involving discrete steps to accurately represent the general shape of the PW potential. Remarkably, our theoretical approach based on discrete perturbation theory demonstrates excellent agreement with MD simulations across a wide range of densities, temperatures, and pressures for the PW pair potential. Our findings demonstrate that PW fluids, characterized by long-range attractive interactions, deviate from the principle of corresponding states. However, for short-range attractive interactions, the fluids moderately follow the Ising universality class. Finally, the integration of discrete perturbation theory with MD simulations proves to be an efficient method for exploring the behavior of molecular fluids and colloidal systems.