Quantum chemical calculations using density functional theory are reported for the diatomic molecules LiF, BeO, and BN. The nature of the interatomic interactions is analyzed with the Energy Decomposition Analysis-Natural Orbitals of Chemical Valence (EDA-NOCV) method, and the results are critically discussed and compared with data from Quantum Theory of Atoms in Molecules, Natural Bond Orbital, and Mayer approaches. Polar bonds, like nonpolar bonds, are caused by the interference of wave functions, which lead to an accumulation of electronic charge in the bonding region. Polar bonds generally have a larger percentage of electrostatic bonding to the total attraction, but nonpolar bonds may also possess large contributions from Coulombic interaction. The term "ionic contribution" refers to valence bond structures and is misleading because it refers to separate fragments with negligible overlap that occur only in the solid state and in solution, not in a molecule. The EDA-NOCV method gives detailed information about the individual orbital contributions, which can be identified by visual inspection of the associated deformation densities. It is very important, particularly for polar bonds to distinguish between the interatomic interactions of the final dissociation products after bond rupture and the interactions between the fragments in the eventually formed bond. The bond formation in LiF is dominated by orbital interactions (90%) between Li and F yielding a single bond, but the eventually formed bond comes mainly from the electrostatic attraction between Li+ and F-, where the minor orbital interactions (10%) have equally strong σ and π components. The symmetry allowed bond formation of BeO between Be in the 1S ground state and O in the excited 1D state is dominated (90%) by a strong dative Be → O σ bond with negligible π interactions. The final bond situation in BeO is best described by the interaction between Be+ and O-, where the Coulombic forces provide 60% of the attraction and the orbital interactions give equally strong σ and π bonds. The chemical bond in BN is analyzed in the X3Π ground state and the a1Σ+ excited state. Both states have triple bonds with strong π bonds, which are in the a1Σ+ state even stronger than the σ bond.