The Buchdahl dispersion model provides a rapidly converging polynomial form for describing the dispersion of refractive materials. Via this model, the dispersion of a material over the waveband of concern can be accurately characterized by a simple polynomial form, often out to only the second order. In this paper, the Buchdahl model is applied to hybrid refractive-diffractive achromats for both 3-5<i>μm</i> (MWIR) band and 8-12<i>μm</i> (LWIR) band. For each waveband, Buchdahl dispersion coefficients of IR materials and the diffractive optical element (DOE) are defined by optimally choosing the Buchdahl chromatic coordinate and best-fitting the Buchdahl model to the dispersion of materials and the DOE. The principles for selecting 1 to 2 IR materials combined with a DOE to produce hybrids achromatized at 3 and 4 wavelengths are discussed. A series of thin lens predesign examples are presented.