Talk:Coupled cluster

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Maybe someone should check the description of CCSD. There was no description so I provided one. But I am just an undergraduate so my words shouldn't be too greatly trusted. 68.179.155.15 06:57, 4 December 2005 (UTC)Nick M:)

Looks good to me. Also, good eye on the annihilation and creation mix-up. Ed Sanville 18:49, 4 December 2005 (UTC)

I think it should be reversed. In the literature, the creation/annihilation operators are typically placed in canonical form where the operators are in normal order. However, there is some ambiguity here, as one can assign the operator with the dagger to either the creation or annihilation operator. --HappyCamper 05:48, 2 January 2006 (UTC)

[edit] What is \psi_0?

\phi_0 is defined, but I don't see a definition of \psi_0.

[edit] Size consistency and size extensivity

The comments about size consistency and size extensivity in coupled cluster theory should be considered with care. Whereas coupled cluster theory is always size-extensive, it need not be size-consistent though. The size-consistency in coupled cluster theory depends on the size-consistency of the reference wavefunction, which is usually a RHF wavfunction that need not necessarily be size-consistent! —The preceding unsigned comment was added by 129.132.232.130 (talk • contribs).

Could you expand on when RHF wave functions are not size-consistent? --Bduke 00:10, 3 June 2007 (UTC)

A method is considered size-consistent if the energy of a system made up of two subsystems A and B at large separation is equal to the sum of the energies of A and B calculated separately using the same method. The original formulation by Pople reffered to a separation in the limit of no interaction. Modern quantum chemistry textbooks, however, normally consider sizCas25 10:16, 4 June 2007 (UTC)e-consistency as the criterion for a correct description of the entire dissociation process AB -> A + B. Obviously, for the case of a closed-shell molecule dissociation into two open-shell fragments, a RHF wavefunction cannot correctly describe the entire dissociation process. —The preceding unsigned comment was added by Cas25 (talk • contribs).

Please sign your posts on talk pages with ~~~~. I do not believe what you are saying in correct. Where in the literature does it say that size-consistency is a correct description of the entire dissociation process? Size consistent is if the energy of AB with A and B at very large distance is the same as the sum of the energies of A and B calculated separately. It does not refer to A and B being at a small distance apart. If A and B are doublet radicals, then, yes, the energy of AB at large distance calculated as a closed shell singlet is not the sum of E(A) and E(B), but if AB is calculated as a diradical by ROHF, I think it is. Can you give an example using couple cluster of what you are saying and is this discussed in the literature anywhere? I would think that MP2 is no different from CC in this respect. I would also add that a lot of sources do not make a clear distinction between size consistency and size extensivity. If you are correct and there is a clear source in the literature, we should certainly add something to the article and the one on MP2. --Bduke 00:09, 4 June 2007 (UTC)

I agree with you that there is considerable confusion over the distinction of these two terms in literature. What you describe is exactly what I stated in the earlier posting: the dissociation of a closed-shell molecule into open-shell systems can only be describet by an UHF or ROHF wave function. Any post-HF correlation method can only be size-consistent if the reference HF-wave function is size-consistent. I think the original definition of size extensivity was by Pople (POPLE JA, BINKLEY JS, SEEGER R, Int. J. Quant. Chem. 11S, 149 (1977)) and refers to the no-interaction limit at large separation. Bartlett pointed out the important distinction between size consistency and size extensivity (Bartlett, R. J. Ann. Rev. Phys. Chem. 32, 359 (1981)). This was more recently reviewed and it was also pointed out that CC-methods are size-extensive, but not necessarily size-consistent (Duch, W. and Diercksen; G. H. F. J. Chem. Phys. 101, 3018 (1994)). And you are right, MP2 is not different from CC in this respect. This issue applies to all post-HF perturbation theory methods. Cas25 10:16, 4 June 2007 (UTC)