I'm currently using Clayden's organic chemistry textbook, and when he shows MO diagrams of functional groups of organic molecules, he sometimes treated it as if only orbitals on two atoms are interacting. For example, the carbonyl chemistry is reduced to looking at the interaction between C and O orbitals. (For conjugated systems the MO diagrams he created make more sense to me)
However, as far as I know, MO theory is used to construct wavefunctions that spread over the whole molecule. Hence, how is it justified that we are combining orbitals centered on a pair of atom rather than all atoms in the molecule? What is that powerful assumption that allows us to apply MO theory locally at functional groups?