Dynamical theory of molecular crystals in the pseudoharmonic approximation

A theory of a three-dimensional anharmonic molecular crystal formed by rigid particles is constructed using the method of two-time Green's functions in local and fixed coordinates. The theory makes it possible to investigate the lattice dynamics and thermal evolution of the crystalline state to the stability boundary. In the pseudoharmonic approximation of the self-consistent phonon field method, statistical-mechanical formulations are given for the virial theorem and an equipartition theorem for the kinetic energy with respect to the orientational and translational vibrations of the particles. Analysis of them leads to an interpretation of the mechanism of occurrence of structure instability in the system. It is shown that the temperature of dynamic instability is a parametric point corresponding to a conditional extremum of an arbitrary virial of the motion of the particles in the selfconsistent field of the molecular crystal. It is shown that the lattice loses stability simultaneously with respect to all its degrees of freedom. The relation between this conclusion and the concept of gradual melting of organic compounds is considered.