A multi-scale approach to characterize pure CH₄, CF₄, and CH₄/CF₄ mixtures

In this study, we develop three intermolecular potentials for methane (CH₄), tetrafluoromethane (CF₄), and CH₄/CF₄ dimers using a novel ab initio method. The ultimate goal is to understand microscopically the phase-separation in CH₄/CF₄ systems, which takes place in the liquid states near their freezing points. Monte-Carlo (MC) simulations of the pure CH₄ system are performed using the ab initio energies to verify the potential. The simulations reproduce quite well the experimentally known liquid densities, the internal energies, the second virial coefficients, and the radial distribution function. The essentially six-dimensional (6D) ab initio potential is then reduced to a one-dimensional (1D) effective potential using the inverse Monte-Carlo technique. This potential, too, successfully reproduces the experimental results. Interestingly, the MC study cannot be extended to the pure CF₄ system and the CH₄/CF₄ mixed system because the two respective ab initio potentials present very rough potential landscapes. This renders the interpolation of energies for the MC simulations and thus the multi-scale approach unreliable. It suggests, however, a possible driving force for the experimentally observed phase separation of the CH₄/CF₄ system at low temperatures. Furthermore, we carefully study the determination of 1D effective potentials via inverse MC techniques. We argue that to a good approximation the temperature dependence of the 1D potentials can be estimated via reweighting techniques for a fixed temperature.