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| In [[quantum chemistry]], '''size consistency''' and '''size extensivity''' are concepts about how the behaviour of a quantum chemistry calculations changes with size. '''Size consistency''' (or '''strict separability''') is a property that guarantees the [[consistency]] 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.<ref>{{cite journal|doi=10.1146/annurev.pc.32.100181.002043|first=R. J.|last= Bartlett|title=Many-Body Perturbation Theory and Coupled Cluster Theory for Electron Correlation in Molecules|journal= Annual Review of Physical Chemistry|volume=32|page=359 |year=1981}}</ref>
| | Andrew Berryhill is what his wife enjoys to call him and he totally digs that name. The preferred pastime for him and his kids is to play lacross and he would by no means give it up. Credit authorising is how she makes a living. Alaska is where he's usually been living.<br><br>Stop by my blog - are psychics real ([http://conniecolin.com/xe/community/24580 http://conniecolin.com/xe/community/24580]) |
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| 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 (<math>E(A-B) = E(A) + E(B)</math>). 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.<ref>{{cite book| first=P. R. |last=Taylor|title= Lecture Notes in Quantum Chemistry: European Summer School|publisher=Springer-Verlag|location= Berlin|year= 1994|pages=125–202}}</ref>
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| Size consistency and size extensivity are sometimes used interchangeably in the literature, However there are very important distinctions to be made between them. <ref>{{cite web|url=http://www.uam.es/docencia/quimcursos/Docs/Knowledge/Fundamental_Theory/cc/node7.html |title=Size-Extensivity and Size-Consistency |publisher=Uam.es |date=1995-01-20 |accessdate=2014-02-01}}</ref> [[Hartree-Fock]], [[coupled cluster]], many-body [[perturbation theory (quantum mechanics)|perturbation theory]] (to any order), and full [[configuration interaction]] (CI) are size extensive but not always size consistent. For example the Restricted [[Hartree-Fock]] model is not able to described correctly the dissociation curves of H2 and therefore all post HF methods will fail in that matter (except FCI). Sometimes numerical errors can cause a method that is formally size-consistent to behave in a non-size-consistent manner.<ref>{{Cite journal|last1=Van Dam|first1=Huub|last2=Van Lenthe|first2=Joop|last3=Pulay|first3=Peter|title=The size consistency of multi-reference Møller-Plesset perturbation theory|journal=Molecular Physics|volume=93|page=431|year=1998|doi=10.1080/002689798169122|issue=3 }}</ref>
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| '''Core-extensivity''' is yet another related property, which extends the requirement to the proper treatment of excited states.<ref>{{cite journal|last1=Mukhopadhyay|first1=S|title=A comparative study of core-extensive and core—valence-extensive coupled-cluster theories for energy differences: Excitation energies|journal=Chemical Physics Letters|volume=173|page=181|year=1990|doi=10.1016/0009-2614(90)80074-N|last2=Chaudhuri|first2=Rajat|last3=Mukhopadhyay|first3=Debasis|last4=Mukherjee|first4=Debashis|issue=2–3}}</ref>
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| ==References==
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| {{Reflist}}
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| [[Category:Quantum chemistry]]
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| {{chem-stub}}
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Revision as of 11:53, 14 February 2014
Andrew Berryhill is what his wife enjoys to call him and he totally digs that name. The preferred pastime for him and his kids is to play lacross and he would by no means give it up. Credit authorising is how she makes a living. Alaska is where he's usually been living.
Stop by my blog - are psychics real (http://conniecolin.com/xe/community/24580)