quantum chemistry Quantum chemistry, also called molecular quantum mechanics, is a branch of physical chemistry focused on the application of quantum mechanics to chemical systems, particularly towards the quantum-mechanical calculation of electronic contributions ...

, size consistency and size extensivity are concepts relating to how the behaviour of quantum chemistry calculations changes with size. Size consistency (or strict separability) is a property that guarantees the

consistency In classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent ...

of the energy behaviour when interaction between the involved molecular system is nullified (for example, by distance). Size-extensivity, introduced by Bartlett, is a more mathematically formal characteristic which refers to the correct (linear) scaling of a method with the number of electrons. 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, separated by a sufficiently large distance so there is essentially no shared electron density, 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 of size consistency is of particular importance to obtain correctly behaving dissociation curves. Others have more recently argued that the entire potential energy surface should be well-defined. Size consistency and size extensivity are sometimes used interchangeably in the literature, However, there are very important distinctions to be made between them. Hartree–Fock,

coupled cluster Coupled cluster (CC) is a numerical technique used for describing many-body systems. Its most common use is as one of several post-Hartree–Fock ab initio quantum chemistry methods in the field of computational chemistry, but it is also used in ...

, many-body

perturbation theory In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle ...

(to any order), and full

configuration interaction Configuration interaction (CI) is a post-Hartree–Fock linear variational method for solving the nonrelativistic Schrödinger equation within the Born–Oppenheimer approximation for a quantum chemical multi-electron system. Mathematical ...

(CI) are size extensive but not always size consistent. For example, the Restricted Hartree–Fock model is not able to correctly describe the dissociation curves of H₂ and therefore all post HF methods that employ HF as a starting point will fail in that matter (so-called single-reference methods). Sometimes numerical errors can cause a method that is formally size-consistent to behave in a non-size-consistent manner. Core-extensivity is yet another related property, which extends the requirement to the proper treatment of excited states.

References

Quantum chemistry {{quantum-chemistry-stub