Editing Coupled cluster (section)

=== Configuration interaction ===
The ''C<sub>j</sub>'' excitation operators defining the CI expansion of an ''N''-electron system for the wave function <math>|\Psi_0\rangle</math>,

: <math>|\Psi_0\rangle = (1 + C) |\Phi_0\rangle,</math>

: <math>C = \sum_{j=1}^N C_j,</math>

are related to the cluster operators <math>T</math>, since in the limit of including up to <math>T_N</math> in the cluster operator the CC theory must be equal to full CI, we obtain the following relationships<ref>{{cite book | last1 = Paldus | first1 = J. | title = Diagrammatic Methods for Many-Fermion Systems | year = 1981 | edition = Lecture Notes | location = University of Nijmegen, Njimegen, The Netherlands}}</ref><ref>{{cite book | last1 = Bartlett | first1 = R. J. | last2 = Dykstra | first2 = C. E. | last3 = Paldus | first3 = J. | title = Advanced Theories and Computational Approaches to the Electronic Structure of Molecules | editor-last = Dykstra | editor-first = C. E. | year = 1984 | pages = 127}}</ref>

: <math>C_1 = T_1,</math>

: <math>C_2 = T_2 + \frac{1}{2} (T_1)^2,</math>

: <math>C_3 = T_3 + T_1 T_2 + \frac{1}{6} (T_1)^3,</math>

: <math>C_4 = T_4 + \frac{1}{2} (T_2)^2 + T_1 T_3 + \frac{1}{2} (T_1)^2 T_2 + \frac{1}{24} (T_1)^4,</math>

etc. For general relationships see J. Paldus, in ''Methods in Computational Molecular Physics'', Vol. 293 of ''Nato Advanced Study Institute Series B: Physics'', edited by S. Wilson and G. H. F. Diercksen (Plenum, New York, 1992), pp.&nbsp;99–194.