Like the atomic orbitals of the preceding chapter, these molecular orbitals will have different shapes, sizes, and energies. The next step is to feed all of the electrons available from the atoms into these molecular orbitals one at a time with a maximum of two per orbital, starting with the lowest-energy orbital and progressing upward. This buildup of the molecule by the filling of molecular orbitals is exactly analogous to the buildup of atoms in the preceding chapter, by the filling of atomic orbitals. The main practical problem in this theory is one of deciding how the MO's are to be constructed from the available AO's, and what their energies are. The principal difficulty of MO theory is that orbitals for molecules with more than a small number of atoms become too complicated to calculate, even with the help of highspeed digital computers. Fortunately, instead of considering the entire molecule at once, one often can drop back to the easier approach of looking at bonds between pairs of atoms. This is called localized MO theory, and it has the advantages of being mathematically simpler, very pictorial even without mathematics (which will be our approach), inherently sensible, and fairly accurate. We shall use complete MO theory for some simple two-atom molecules such as H, 0, and HF, and then show how a localized MO theory can work with larger molecules, and how it fails for molecules with delocalized electrons.