Anharmonic lattice dynamics and computer simulation for simple model systems

We have made anharmonic-lattice-dynamics calculations of phonon frequencies and bandwidths up to order ${\lambda }^4$ for simple model systems consisting of linear chains of diatomic and triatomic molecules, bound by van der Waals intermolecular forces. For each model we discuss the relevant relaxation mechanisms of the optical modes at the Γ point in terms of the anharmonic phonon-phonon coupling coefficients and of the phonon density of states. Calculated bandwidths and anharmonic shifts are compared to the results of computer simulations for the same models at various temperatures. The comparison shows that bandwidths calculated by the perturbative lattice-dynamics treatment to order ${\lambda }^4$ agree with those calculated in the computer simulation, thus showing that the imaginary part of the self-energy expansion converges already to this order. The convergence of the imaginary part of the self-energy is further investigated by a calculation of the contribution of some relevant diagrams of order ${\lambda }^6$ and ${\lambda }^8$ to the bandwidth of the internal modes. On the contrary, the real part of the self-energy converges much slower and therefore anharmonic shifts calculated by lattice dynamics are different from those obtained by computer simulation.