Experimentally determined directional Compton profiles and the X-ray scattering factors f(2,2,2) of crystalline diamond, silicon and germanium are fitted by using a model for the one-electron density matrix containing only interactions between nearest neighbours. It is concluded that such a model is only capable of reproducing the anisotropic properties of the electronic ground state, whereas isotropic ground-state properties require the consideration of intraatomic hybrid-hybrid interactions as well as interatomic interactions between higher-order neighbours.