Ab initio calculations of the 2x1, c(2x8), and 7x7 reconstructions of the diamond, Si, and Ge(111) surfaces are reported. The pi-bonded chain, adatom, and dimer-adatom-stacking fault models are studied to understand the driving forces for a certain reconstruction. The resulting energetics, geometries, and band structures are compared for the elemental semiconductors with different atomic sizes, and chemical trends are derived. We show why the lowest-energy reconstructions are different for the group-IV materials considered.