 Size consistency

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 noninteracting systems. If a given theory for the evaluation of the energy is size consistent, then the energy of the supersystem AB 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. Others have more recently argued that the entire potential energy surface should be welldefined^{[1]}.
Of the common quantum mechanical methods HartreeFock, coupled cluster, manybody perturbation theory (to any order), and full configuration interaction (CI) are size consistent. A major drawback of truncated CI is that it is not sizeconsistent 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 sizeconsistent to behave in a nonsizeconsistent manner^{[3]}.
Sizeextensivity, 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]}.
Coreextensivity is yet another related property, which extends to requirement to the proper treatment of excited states^{[5]}.
References
 ^ Taylor, P. R. (1994). Lecture Notes in Quantum Chemistry: European Summer School. Berlin: SpringerVerlag. pp. 125–202.
 ^ Szabo, Attila; Ostlund, Neil (1982). Modern Quantum Chemistry. Dover. ISBN 0029497108.
 ^ Van Dam, Huub; Van Lenthe, Joop; Pulay, Peter (1998). "The size consistency of multireference MøllerPlesset perturbation theory". Molecular Physics 93: 431. doi:10.1080/002689798169122.
 ^ Bartlett, R. J. (1981). "ManyBody Perturbation Theory and Coupled Cluster Theory for Electron Correlation in Molecules". Ann. Rev. Phys. Chem. 32: 359. doi:10.1146/annurev.pc.32.100181.002043.
 ^ Mukhopadhyay, S (1990). "A comparative study of coreextensive and core—valenceextensive coupledcluster theories for energy differences: Excitation energies". Chemical Physics Letters 173: 181. doi:10.1016/00092614(90)80074N.
Categories: Quantum chemistry
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