  In order to get insight into the connection between the vibrational dynamics
and the atomic level Green-Kubo stress correlation function in liquids we
consider this connection in a model crystal instead. Of course, vibrational
dynamics in liquids and crystals are quite different and it is not expected
that the results obtained on a model crystal should be valid for liquids.
However, these considerations provide a benchmark to which the results of the
previous molecular dynamics simulations can be compared. Thus, assuming that
vibrations are plane waves, we derive analytical expressions for the atomic
level stress correlation functions in the classical limit and analyze them.
These results provide, in particular, a recipe for analysis of the atomic level
stress correlation functions in Fourier space and extraction of the wavevector
and frequency dependent information. We also evaluate the energies of the
atomic level stresses. Obtained energies are significantly smaller than the
energies that were obtained in MD simulations of liquids previously. This
result suggests that the average energies of the atomic level stresses in
liquids and glasses are largely determined by the structural disorder. We
discuss this result in the context of equipartition of the atomic level stress
energies. Analysis of the previously published data suggests that it is
possible to speak about configurational and vibrational contributions to the
average energies of the atomic level stresses in a glass state. However, this
separation in a liquid state is problematic. We also consider peak broadening
in the pair distribution function with increase of distance. We find that peak
broadening (by ~40%) occurs due to the transverse vibrational modes, while
contribution from the longitudinal modes does not change with distance.
Finally, we introduce and consider atomic level transverse current correlation
function.
