  While there are several methods, e.g., anharmonic lattice dynamics and normal
mode decomposition, to compute the modal lattice vibrational information in
perfect crystals, the modal information of vibrations, e.g., vibrational
relaxation time, group velocity and mean free path, in amorphous solids are
still challenge to be captured. By systematically analyzing the normal mode
decomposition and structure factor methods, we conclude that the vibrational
dispersion can be calculated by applying effective wave vectors in the
structure factor method, while the vibrational relaxation time calculated by
the normal mode decomposition method is questionable since the group velocity
cannot be defined on the Gamma point. We also show that the anharmonicity
caused by the system temperature has little effect on the relaxation times of
the propagating modes in amorphous materials, and therefore, the corresponding
modal and total thermal conductivity is temperature independent when all the
vibrations are assumed to be excited. The non-propagating modes, i.e.,
diffusons, conduct heat via thermal coupling between different vibrational
modes, and can be calculated by harmonic lattice dynamics using Allen-Feldman
theory. As a result, the thermal conductivity contributed from diffusons is
also temperature independent when all the vibrational modes are activated which
is the situation in molecular dynamics simulations. The total thermal
conductivity concerning both propagons (50%) and diffusons (50%) agree quite
well with the results computed using Green-Kubo equilibrium molecular dynamics.
By correcting the excitation state of the vibrations in amorphous solids, the
thermal conductivity calculated by the structure factor method and
Allen-Feldman theory can fully capture the experimentally measured
temperature-dependent thermal conductivity.
