4. Characterization of the chemical bond

Quantum theory, which leads to the representation of the electronic state of a system by a wave function, does not allow us to directly recover the intuitive concept of localized bonding between atoms, gradually developed by experimental chemists. Indeed, the Hamiltonian operator cannot be partitioned into local spatial contributions, to which binding energies could be associated. The latter can only be evaluated indirectly (albeit rigorously) by the difference between the total energies of a whole (a molecule, for example) and the sum of those of its reorganized fragments (resulting, for example, from homolytic dissociation).

For example, for crystalline solids composed of several crystallographically non-equivalent elements or atoms, this is the principle behind the so-called "Yin-Yang" method