A theoretical model for amorphous silicon-fluorine alloys proposed earlier by one of the authors in the study of vibrational excitations using a cluster-Bethe lattice method has been investigated in detail. The vibrational frequencies have now been obtained for isolated SiFn (n=1,3) configurations for the two adjacent interacting monofluorides (SiF)2 and the polymer-like (SiF2)n chain configurations in a rotationally invariant valence force-field model (VFFM). Extra structure in the bulk phonon density originates from the two interacting T20 defects lying on the nearest-neighbour sites. The bond-stretching vibrational frequencies associated with the Si-F bonds in SiFn complexes in isolation are retained when embedded in the silicon matrix. A very successful assignment of the peaks observed in the infrared data, both within and outside the bulk phonon region, has been made in terms of the vibrational mode frequencies of the various simple units and the interacting ones for the first time. In particular, the location and the relative strengths of the three peaks at 212, 300 and 515 observed in the bulk phonon region of the infrared data are very well explained by the presence of the simple SiF and SiF2/SiF3 units in a-Si:F alloys. The other high-frequency peaks observed at 650, 827, 870, 920 and 965 cm-1 originate from the interaction of the two adjacent SiF2 units, a result also supported by the analysis of the photoemission spectra of these alloys made elsewhere.