When Linus Pauling was faced with the task of rationalizing molecular geometries with atomic orbitals his solution was to consider the characteristics of the original orbitals and compare them to the electron distributions that must exist in the valence levels of molecules in order to explain their shapes.
The result fits nicely within Valence Bond Theory, an early model for describing how electron sharing occurs in the valence level of atoms connected to one another by a covalent bond.
It is important to remember that this is only a model. Whether the electrons actually do the things we describe in the model is sort of beside the point. The utility of the model is judged on the basis of whether it has predictive power and whether it makes some kind of theoretical sense.
Pauling (and others) faced two significant problems.