Molecular phonons and their absorption/emission spectra from the far IR to microwaves

Abstract

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.