Editing Coupled cluster (section)

== General description of the theory ==

The complexity of equations and the corresponding computer codes, as well as the cost of the computation, increases sharply with the highest level of excitation. For many applications CCSD, while relatively inexpensive, does not provide sufficient accuracy except for the smallest systems (approximately 2 to 4 electrons), and often an approximate treatment of triples is needed. The most well known coupled-cluster method that provides an estimate of connected triples is CCSD(T), which provides a good description of closed-shell molecules near the equilibrium geometry, but breaks down in more complicated situations such as bond breaking and diradicals. Another popular method that makes up for the failings of the standard CCSD(T) approach is {{abbr|CR|"completely renormalized"}}-CC(2,3), where the triples contribution to the energy is computed from the difference between the exact solution and the CCSD energy and is not based on perturbation-theory arguments. More complicated coupled-cluster methods such as CCSDT and CCSDTQ are used only for high-accuracy calculations of small molecules. The inclusion of all ''n'' levels of excitation for the ''n''-electron system gives the exact solution of the [[Schrödinger equation]] within the given [[basis set (chemistry)|basis set]], within the [[Born–Oppenheimer approximation]] (although schemes have also been drawn up to work without the BO approximation<ref>{{cite journal | doi = 10.1103/PhysRevA.36.1544 | title = Chemical physics without the Born-Oppenheimer approximation: The molecular coupled-cluster method | year = 1987 | last1 = Monkhorst | first1 = Hendrik J. | journal = Physical Review A | volume = 36 | pages = 1544–1561 | issue = 4 | pmid = 9899035|bibcode = 1987PhRvA..36.1544M }}</ref><ref>{{cite journal | doi = 10.1063/1.1528951 | title = Many-body effects in nonadiabatic molecular theory for simultaneous determination of nuclear and electronic wave functions: Ab initio NOMO/MBPT and CC methods | year = 2003 | last1 = Nakai | first1 = Hiromi | last2 = Sodeyama | first2 = Keitaro | journal = The Journal of Chemical Physics | volume = 118 | pages = 1119 | issue = 3|bibcode = 2003JChPh.118.1119N }}</ref>).

One possible improvement to the standard coupled-cluster approach is to add terms linear in the interelectronic distances through methods such as CCSD-R12. This improves the treatment of dynamical electron correlation by satisfying the [[Kato cusp]] condition and accelerates convergence with respect to the orbital basis set. Unfortunately, R12 methods invoke the [[resolution of the identity]], which requires a relatively large basis set in order to be a good approximation.

The coupled-cluster method described above is also known as the ''[[single-reference]]'' (SR) coupled-cluster method because the exponential ansatz involves only one reference function <math>|\Phi_0\rangle</math>. The standard generalizations of the SR-CC method are the ''[[multi-reference]]'' (MR) approaches: [[state-universal coupled cluster]] (also known as [[Hilbert space]] coupled cluster), [[valence-universal coupled cluster]] (or [[Fock space]] coupled cluster) and [[state-selective coupled cluster]] (or state-specific coupled cluster).