Theoretical investigations of the bonding properties of 34 elemental and compound semiconductors are reported. From self-consistent band-structure calculations (within the local-density approximation) valence charge densities are calculated. The densities are obtained by transforming muffin-tin orbitals to a localized basis. Using another representation, an orthogonal basis, we construct ${\mathrm{sp}}^{3}$ hybrids and project out the bond and antibond characters, i.e., we derive first-principles values for ${\mathrm{sp}}^{3}$ bond orders. These, together with the first-principles tight-binding parameters, are used to study chemical trends. Relations to Phillips ionicity (${f}_{i}$) scale are established and it is demonstrated, for example, that the critical ionicity value ${f}_{i}$=0.786 found empirically separating the fourfold- from the sixfold-coordinated crystal structures also follows from total-energy calculations.