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Can you explain the difference between these two computational methods ?

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In short, (T) means a perturbative (non-iterative) correction to a CCSD calculation. From a talk demonstrating the derivation of the CCSD(T) method:

The CCSD(T) method consists of a perturbative (noniterative) correction to the CCSD energy.

• Utilizing the expressions from perturbation theory, approximate second order triples amplitudes & T(2) 3 are generated from the CCSD T2 amplitudes (rather than from first order amplitudes).

• The second order corrected wave function is then used to compute the fourth and fifth order energy corrections, which are added to the CCSD energy.

  • Wikipedia has a decent page about CC in general.
  • A very good review by T. Daniel Crawford and Henry F. Schaefer III is available online, but if the link ever dies, it's been published Reviews in Computational Chemistry, Volume 14, ISBN: 978-0-471-35495-6. Here's a quick link to the section discussing the (T) correction.
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  • $\begingroup$ Yann: Your links to UGA are broken now. $\endgroup$ – Jeff Apr 13 '13 at 20:17
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There are many ways to answer this, but CCSD is only complete through third-order in many-body perturbation theoretic terms, while CCSD(T) is complete through fourth-order. It was the desire to have a fourth-order complete method that led Bartlett and coworkers to develop CCSD[T]. The CCSD(T) method includes a fifth-order term (at least in the RHF case), which was later shown to be fourth-order in the ROHF case by Stanton, which helps to explain why the inclusion of that term has such an impact on the accuracy of CCSD(T) relative to CCSD[T].

The CFOUR Bibliography page has a list of most (all?) the seminal papers on coupled-cluster theory, which might be of interest.

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