Talk:Coupled cluster

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Comment[edit]

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:)[reply]

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

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)[reply]

Some of the statements were incorrect. (i) if the Hbar is projected to psi_0, it will give the correlation energy; (ii) Hbar is always non-Hermitian unless all t's are zero (iii) Hbar itself is not quadratic in T_2 -- what makes quadratic in T_2 is the fact that the projection manifolds are limited to those with up to doubly-excited configurations from the reference; (iv) this is the non-linear equations. Therefore, you cannot solve using Ax=0 with A being the Jacobian. Instead, all the packages solve it iteratively with some tricks. 209.251.139.60 (talk) 00:41, 15 November 2008 (UTC)[reply]

    could you please make it more clear in paragraph 1.what exactly is the relation between size   
  consistency and size extensivity? what makes the CC method to be size consistent which doesn't 
  work for CI since both have RHF reference method?
     If it is the exponential ansatz for CC then what does it exactly do to make it size 
  consistent?[[Special:Contributions/221.133.36.14|221.133.36.14]lili

Cluster operator[edit]

In this section there is mistake with the order of creation and annihilation operators, they should be in reverse order in T_1 and: a+_b a+_a a_i a_j in T_2. But I'm not expert. —Preceding unsigned comment added by 79.191.52.86 (talk) 02:07, 10 February 2009 (UTC)[reply]

Either is fine, since in fact a_a^dagger and a_i are both "creation" operators to the HF vacuum (it is not the case for the operator with general indexes including both virtual and occupied). Usually, people working on CC prefer a_a^dagger a_i notation in literature, but I leave the article unchanged...--209.251.138.154 (talk) 16:53, 10 May 2009 (UTC)[reply]

difference with CI[edit]

what makes this method to be different from the configuration interaction? As I have understood, both consider electron correlation with exciting them to virtual orbitals.please correct me. thanks lili —Preceding unsigned comment added by Lililola (talk • contribs) 14:03, 9 March 2009 (UTC)[reply]

It does a better job and it is size consistent, which CI with limited excitations such as CISD is not. --Bduke (Discussion) 02:42, 10 March 2009 (UTC)[reply]

It does a better job because it is size-extensive which is different than being size consistent, though it is that as well. It means that coupled-cluster methods, at least for ground state coupled-cluster approaches, have only linked diagrams that contribute to the resulting equations whereas truncated CI approaches have unlinked terms that contribute to their expressions. This can be phrased another way as well: if you look at the equations in the symmetry adapted cluster subsection of the coupled-cluster article you'll notice they are energy dependent. These are the unlinked terms. The coupled-cluster equations for the ground state on the other hand are energy independent because the energy dependent terms and the unlinked terms cancel each other out. It's important to note that size extensivity and size consistency are not the same thing, though one could argue that they are related albeit in a not-necessarily-trivial way, and should not be confused. Size consistency has to do with how non-interacting fragments and their energies are related when computed in a single calculation versus when they are computed individually (e.g., in isolation from the other non-interacting pieces). Size extensivity, as discussed above, has to do with whether unlinked diagrams are included in the resulting expressions or not (CEPA and other approximate many-body methods have had issues with this as well). Jahansen (talk) 19:43, 11 August 2015 (UTC)Jahansen[reply]