Three-Dimensional Hard Dumbbell Solid Free Energy Calculation Via the Fluctuating Cell Model

Abstract

Determination of the solid–liquid phase transition point of a molecular substance requires calculation of the free energy in both phases. Progress has been made on this problem by modeling molecules as fused hard spheres and adding attraction and electric multipole moments perturbatively. The solid free energy of hard heteronuclear dumbbells of bond length L*, used to model diatomic molecules, can in principle be calculated exactly via the Frenkel–Ladd method, but this is computationally intensive. Use of Lennard Jones–Devonshire fixed cells to calculate free energy is much simpler computationally but is an approximation. The fluctuating cell model is investigated as an alternative intermediate method which is still computationally simpler than the Frenkel–Ladd method. As was found earlier in two dimensions, for small L* the simple cell model is in better agreement with Frenkel–Ladd than the fluctuating cell model, but for larger L* the fluctuating cell model is in better agreement. The probability distributions of free volumes are also analyzed and show different functional behavior for near-zero bond length and appreciable bond length.