We performed density-functional calculations using cluster models of the C(100), Si(100), and Ge(100) surfaces in order to address two issues. First, we resolve the differences in the results from slab calculations and from cluster calculations. Second, we want to contribute to an understanding of the nature and energetics of dimer buckling on these surfaces. We performed calculations using a number of different geometry constraints and three different cluster sizes. The results show that for, at least for density-functional cluster calculations, the geometry, and the buckling energetics are both significantly dependent upon both the choice of geometry constraints and the size of the cluster. Our calculations show that the ground state has a symmetric dimer geometry for the carbon surface and an asymmetric dimer geometry for the silicon and germanium surfaces. This is in agreement with the latest first-principles slab calculations and also consistent with experimental results. Some previous cluster calculations favor a symmetric dimer on the silicon surface. Our density-functional results suggest that the use of either inadequate cluster sizes or inappropriate geometry constraints or a combination of both could have affected these previous calculations. The change in energy of the cluster as a function of the dimer buckling angle is also investigated for all three surfaces. We observed that dimer-buckling is driven by a lowering of the kinetic energy of the electrons. We also find that the nature of the dimer bond is qualitatively different between the carbon surface on the one hand and the silicon and germanium surfaces on the other. We rationalize this in terms of the small core size of the carbon atom and relate it to the different ground-state dimer symmetry found for the C(100) surface as opposed to Si(100) and Ge(100) surfaces.