Size consistency

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 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(AB) = 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 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 to requirement to the proper treatment of excited states[5].


  1. ^ Taylor, P. R. (1994). Lecture Notes in Quantum Chemistry: European Summer School. Berlin: Springer-Verlag. pp. 125–202. 
  2. ^ Szabo, Attila; Ostlund, Neil (1982). Modern Quantum Chemistry. Dover. ISBN 0029497108. 
  3. ^ Van Dam, Huub; Van Lenthe, Joop; Pulay, Peter (1998). "The size consistency of multi-reference Møller-Plesset perturbation theory". Molecular Physics 93: 431. doi:10.1080/002689798169122. 
  4. ^ Bartlett, R. J. (1981). "Many-Body 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. 
  5. ^ Mukhopadhyay, S (1990). "A comparative study of core-extensive and core—valence-extensive coupled-cluster theories for energy differences: Excitation energies". Chemical Physics Letters 173: 181. doi:10.1016/0009-2614(90)80074-N. 

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