  We discuss the van der Waals (Casimir) free energies and pressures of thin
metallic films, consisting from one to fifteen atomic layers, with regard to
the anisotropy in their dielectric properties. Both free-standing films and
films deposited on a dielectric substrate are considered. The computations are
performed for a Au film and a sapphire substrate. According to our results, for
free-standing Au films consisting of one and three atomic layers the respective
relative error arising from the use of an isotropic (bulk) dielectric
permittivity is equal to 73% and 37% for the van der Waals energy, and 70% and
35% for the pressure. We tabulate the energy and pressure van der Waals
coefficients of thin Au films computed with account of their anisotropy. It is
shown that the bulk permittivity of Au can be used for the films consisting of
more than 30 atomic layers, i.e., more than approximately 7 nm thickness. The
role of relativistic effects is also investigated and shown to be important
even for the films consisting of two or three layers. The obtained results can
find applications in the investigation of stability of thin films and
development of novel nanoscale devices.
