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 (). This property 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.[1]
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.[2] The error in CISD calculations can be corrected with e.g. quadratic configuration interaction. Sometimes numerical errors can cause a method that is formally size-consistent to behave in a non-size-consistent manner.[3]
Size-extensivity, on the other hand, is a more mathematically formal characteristic which refers to the correct (linear) scaling of a method with the number of electrons.[4]
Core-extensivity is yet another related property, which extends the requirement to the proper treatment of excited states.[5]
References
- ^ Taylor, P. R. (1994). Lecture Notes in Quantum Chemistry: European Summer School. Berlin: Springer-Verlag. pp. 125–202.
- ^ Szabo, Attila; Ostlund, Neil (1982). Modern Quantum Chemistry. Dover. ISBN 0-02-949710-8.
- ^ Van Dam, Huub; Van Lenthe, Joop; Pulay, Peter (1998). "The size consistency of multi-reference Møller-Plesset perturbation theory". Molecular Physics. 93 (3): 431. doi:10.1080/002689798169122.
- ^ Bartlett, R. J. (1981). "Many-Body Perturbation Theory and Coupled Cluster Theory for Electron Correlation in Molecules". Annual Review of Physical Chemistry. 32: 359. doi:10.1146/annurev.pc.32.100181.002043.
- ^ Mukhopadhyay, S; Chaudhuri, Rajat; Mukhopadhyay, Debasis; Mukherjee, Debashis (1990). "A comparative study of core-extensive and core—valence-extensive coupled-cluster theories for energy differences: Excitation energies". Chemical Physics Letters. 173 (2–3): 181. doi:10.1016/0009-2614(90)80074-N.
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