Size consistency and size extensivity

In quantum chemistry, size consistency (or strict separability) is a property that guarantees the consistency of the energy behavior when interaction between the involved molecular system is nullified (for example, by distance).

Let A and B be two non-interacting systems. If a given theory for the evaluation of the energy is size consistent, then the energy of the supersystem A-B is equal to the sum of the energy of A plus the energy of B taken by themselves ($E(A-B)=E(A)+E(B)$). This property is of particular importance to obtain correctly behaving dissociation curves.

Of the common quantum mechanical methods Hartree-Fock, coupled cluster, many-body perturbation theory (to any order), and full configuration interaction (CI) are size consistent. A major drawback of truncated CI is that it is not size-consistent and that the quality of the description decreases with increasing size of the system. The error in CISD calculations can be corrected with e.g. quadratic configuration interaction.