A first-principles study of the dissociative adsorption of water on Ge(100)-(2 x 1) is described, on the basis of density functional theory with a cluster model of the surface. Experiments have shown that water incident on the Ge(100)-(2 x 1) surface has a very small probability of dissociative adsorption, indicating the presence of an activation barrier. This is in contrast to the analogous reaction on Si(100)-(2 x 1), which is unactivated. This difference is reproduced in the calculations, demonstrating the predictive capability of the methods used, though some caveats about basis sets are necessary. A frontier orbital analysis is used to identify the interactions that determine the transition state energy and underlie the difference between reactivity on Si and Ge.