The vibrational spectra of four tetrachlorinated p-dibenzodioxins (the 2,3,7,8-, 1,4,6,9-, 1,3,7,8-, and 1,4,7,8-isomers) have been investigated by the scaled quantum mechanical (SQM) method, using quadratic force fields from density functional theory and scale factors transferred from related molecules. This a priori (though not fully ab initio) method reproduces the experimental infrared spectra, including intensities, very well. It is possible to identify an unknown isomer conclusively by its calculated spectrum, an important point in view of the strong isomer dependence of toxicity. The most toxic 2,3,7,8-isomer shows band doublings for three prominent infrared bands which do not appear in our harmonic calculations, even when the effect of the large-amplitude butterfly vibration (D-2h --> C-2v) and natural-abundance C-13 isotope effects are considered. The extra bands are probably not fundamentals but combination bands in Fermi resonance with strong fundamentals. All fundamentals, including the infrared inactive ones, are predicted and assigned.