Editing Coupled cluster (section)

{{Short description|Method for approximating many-body systems}}
{{Electronic structure methods}}

'''Coupled cluster''' ('''CC''') is a numerical technique used for describing [[many-body system]]s. Its most common use is as one of several [[post-Hartree–Fock]] [[ab initio quantum chemistry methods]] in the field of [[computational chemistry]], but it is also used in [[nuclear physics]]. Coupled cluster essentially takes the basic [[Hartree–Fock]] [[molecular orbital]] method and constructs multi-electron wavefunctions using the exponential cluster operator to account for [[electronic correlation|electron correlation]]. Some of the most accurate calculations for small to medium-sized molecules use this method.<ref name="Kümmel">{{cite book | first1 = H. G. |last1 =  Kümmel |chapter = A biography of the coupled cluster method | editor-first=R. F. | editor-last = Bishop  | editor2-first= T.  | editor2-last = Brandes | editor3-first =  K. A. | editor3-last =  Gernoth | editor4-first =  N. R. |editor4-last = Walet |editor5-first = Y. | title = Recent progress in many-body theories Proceedings of the 11th international conference| publisher =  World Scientific Publishing | location =  Singapore | year = 2002 | pages =334–348 | isbn= 978-981-02-4888-8 | editor5-last =Xian }}</ref><ref>{{cite book
  | last = Cramer  | first = Christopher J.
  | title = Essentials of Computational Chemistry
  | publisher = John Wiley & Sons, Ltd.
  | year = 2002
  | location = Chichester
  | pages = 191–232
  | isbn = 0-471-48552-7}}</ref><ref>{{cite book |isbn=978-0-521-81832-2 |publisher=Cambridge University Press |title=Many-Body Methods in Chemistry and Physics: MBPT and Coupled-Cluster Theory |year=2009 |first1=Isaiah |last1=Shavitt |first2=Rodney J. |last2=Bartlett}}</ref>

The method was initially developed by [[Fritz Coester]] and [[Hermann Kümmel]] in the 1950s for studying nuclear-physics phenomena, but became more frequently used when in 1966 [[Jiří Čížek]] (and later together with [[Josef Paldus]]) reformulated the method for electron correlation in [[atoms]] and [[molecules]]. It is now one of the most prevalent methods in [[quantum chemistry]] that includes electronic correlation.

CC theory is simply the perturbative variant of the many-electron theory (MET) of [[Oktay Sinanoğlu]], which is the exact (and variational) solution of the many-electron problem, so it was also called "coupled-pair MET (CPMET)". J.&nbsp;Čížek used the correlation function of MET and used Goldstone-type perturbation theory to get the energy expression, while original MET was completely variational. Čížek first developed the linear CPMET and then generalized it to full CPMET in the same work in 1966. He then also performed an application of it on the benzene molecule with Sinanoğlu in the same year. Because MET is somewhat difficult to perform computationally, CC is simpler and thus, in today's computational chemistry, CC is the best variant of MET and gives highly accurate results in comparison to experiments.<ref>{{cite journal | doi = 10.1063/1.1727484 | title = On the Correlation Problem in Atomic and Molecular Systems. Calculation of Wavefunction Components in Ursell-Type Expansion Using Quantum-Field Theoretical Methods | year = 1966 | last1 = Čížek | first1 = Jiří | journal = The Journal of Chemical Physics | volume = 45 | pages = 4256–4266 |bibcode = 1966JChPh..45.4256C | issue = 11 }}</ref><ref>{{cite book | last1 = Sinanoğlu | first1= O. | last2 = Brueckner | first2 =  K. | title = Three approaches to electron correlation in atoms
| publisher =  Yale Univ. Press | year = 1971| isbn=0-300-01147-4}} See also references therein.</ref><ref>{{cite journal | doi = 10.1063/1.1732596 | title = Many-Electron Theory of Atoms and Molecules. I. Shells, Electron Pairs vs Many-Electron Correlations | year = 1962 | last1 = Si̇nanoğlu | first1 = Oktay | journal = The Journal of Chemical Physics | volume = 36 | pages = 706–717|bibcode = 1962JChPh..36..706S | issue = 3 }}</ref>