Hybrid orbitals geometrical constructions

In the case of a molecule such as BeF, we know from experimental evidence that the molecule is linear and therefore the electron density surrounding the central atom is no longer spherical, but must be concentrated along two directions 180° apart, and we need to construct a function t2 having these geometrical properties. There are any number of ways of doing this, but the simplest is to use a new set of functions v / (which we call hybrid orbitals) that are constructed by combining the atomic s,p,d, f functions that are already familiar to us. 

Theoretical determination methods of hybrid orbitals 2.1 Geometrical constructions... 

More generally, hybrids pointing in any direction around an atomic site A can be obtained by straightforward geometrical constructions [41] provided the form of the molecule is already known (i.e., by another theoretical or experimental way). The vectorial character of the px, py, pz orbitals transforming as the axes of a cartesian coordinate system ensures the success... 

The actual values of the atomic multipole moments depend on the coefficients of the hybrid orbitals in the individual bond orbitals (bond polarities), on the orientation of the hybrids and on the degree of hybridization. Since these latter two parameters depend significantly on the geometrical arrangement of the atoms [47], the bond increment method may be an adequate tool for constructing the zeroth order wave function, which nevertheless describes the main trends in the conformational and geometrical dependence of the atomic charge distributions and consequently of the electrostatic potential. 

---