Molecular phonons and their absorption/emission spectra from the far IR
  to microwaves
  Together with their fingerprint modes, molecules carry coherent vibrations of
all their atoms (phonons). Phonon spectra extend from $\sim$20 to more than
$10^{4}\,\mu$m, depending on molecular size. These spectra are discrete but
large assemblies of molecules of the same family, differing only by minor
structural details, will produce continua. As such assemblies are expected to
exist in regions where dust accumulates, they are bound to contribute to the
observed continua underlying the Unidentified Infrared Bands and the 21-mum
band of planetary nebulae as well as to the diffuse galactic emission surveyed
by the Planck astronomical satellite and other means. The purpose of this work
is to determine, for carbon-rich molecules, the intensity of such continua and
their extent into the millimetric range, and to evaluate their detectability in
this range. The rules governing the spectral distributions of phonons are
derived and shown to differ from those which obtain in the solid state. Their
application allow the extinction cross-section per H atom, and its maximum
wavelength, to be determined as a function of molecular size and
dimensionality. Chemical modeling of more than 15 large molecules illustrate
these results. It is found that the maximum phonon wavelength of a 2D structure
increases roughly as the square of its larger dimension. Spectral energy
distributions were computed as far as 4000 mum, for molecules up to 50 A{\deg}
in length.
