Lennard-Jones crystal: Complete vibrational spectrum, its local approximation, and thermodynamic functions

Different methods of taking into account the vibrational partition function in Helmholtz free energy for imperfect crystals of inert gases are compared. These methods are based on the complete vibrational spectrum of the fcc lattice or on few local frequencies. Thermodynamic properties of the Lennard- Jones crystal are considered in the framework of the lattice gas model with the potential interaction in the quasi-chemical approximation. In frequency calculations in the quasi-dimeric model, the role of local averaging, which leads to a threefold degeneracy of the vibrational contribution, is compared to the role of the direct diagonalization of the matrix of the second derivatives of potential energy in an imperfect cluster. The effects of different vibrational contributions on internal energy, entropy, and heat capacity at constant volume are considered as a function of temperature. The results of calculating thermal expansion in a vacuum for four inert gas crystals are compared with experimental data.