Coupled cluster is a non-variational method, meaning that it can give energies that are below the true FCI energy (the "variational limit" for variational methods).

Often coupled cluster still gives energies far above the true FCI energy, and sometimes it gives energies that dip below the variational limit.

Is there some guidelines on when this will happen and when we are safe to assume it will not? I'm aware that coupled cluster generally works best when there is one dominant determinant (single-reference cases), so I am asking about within the single-references cases, when we might expect to get energies that violate the variational principle.

  • $\begingroup$ This doesn't exactly address your question, which is a very good one. But, Sherrill and colleagues wrote a 2005 paper on diatomic carbon as a benchmark to compare the validity of CCSD(T) and MR-CI. Reviewing the abstract reveals that coupled clusters provided good agreement with MR-CI between 1.0 and 2.0 angstroms: doi.org/10.1063/1.1867379 This older presentation of Meissner has an excellent graph of deviation of CCSD and MR-CI from FCI, which could be considered as an exact solution to the equation: academia.edu/download/42658253/Meissner1.pdf $\endgroup$ – Bertram Dec 14 '19 at 4:05
  • $\begingroup$ @Bertram, the second link leads (for me) to the message "Oops! It looks like you're in the wrong aisle". As for the Sherrill paper, I really don't see any connection between that paper and my question, at all. $\endgroup$ – user1271772 Dec 16 '19 at 3:10

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