We study the influence of germanium atoms upon molecular hydrogen desorption energetics using density functional cluster calculations. A three-dimer cluster is used to model the Si(1-x)Gex(100)-(2X1) surface. The relative stabilities of the various monohydride and clean surface configurations are computed. We also compute the energy barriers for desorption from silicon, germanium, and mixed dimers with various neighboring configurations of silicon and germanium atoms. Our results indicate that there are two desorption channels from mixed dimers, one with an energy barrier close to that for desorption from germanium dimers and one with an energy barrier close to that for desorption from silicon dimers. Coupled with the preferential formation of mixed dimers over silicon or germanium dimers on the surface, our results suggest that the low barrier mixed dimer channel plays an important role in hydrogen desorption from silicon-germanium surfaces. A simple kinetics model is used to show that reasonable thermal desorption spectra result from incorporating this channel into the mechanism for hydrogen desorption. Our results help to resolve the discrepancy between the surface germanium coverage found from thermal desorption spectra analysis, and the results of composition measurements using photoemission experiments. We also find from our cluster calculations that germanium dimers exert little influence upon the hydrogen desorption barriers of neighboring silicon or germanium dimers. However, a relatively larger effect upon the desorption barrier is observed in our calculations when germanium atoms are present in the second layer. (C) 2004 American Institute of Physics.