Electron clusters disjoint

T introduces true n-particle correlation, and products like T T etc., arising out of the expansion eq.(3.2 ), generate simultaneous presence of k-particle amd m-particle correlations in a (k+m)-fold excited determinants etc. The truncation of T == T then corresponds to the pair—correlation model of Sinanoglu, while incorporating higher excited states with several disjoint pair excitations induced through the powers T - The amplitudes for T may be called linked or connected clusters for n electrons. The difficulty of a linear variation method such as Cl lies in its inability to realize the cluster expansion structure eq.(3.2),in a simple and practicable manner. 

The coupled-cluster (CC) method (Cizek and Paldus, 1971 Harris, 1977a,b Bartlett and Purvis, 1978) is an attempt to introduce interactions among electrons within clusters (predominantly pairs) as well as coupling among these clusters of electrons and to permit the wavefunction to contain all possible disjoint clusters. For example, we know, from the early work of Sinanoglu (1962) and others, that electron pair interactions are of utmost importance and that contributions of quadruply excited configurations to... 

These equations show which excitation processes contribute at each excitation level. Thus, the quadruply excited configurations are generated by five distinct mechanisms, where, for instance, the disconnected term represents the independent interactions within two distinct pairs of electrons and the connected f4 terra describes the simultaneous interaction of four electrons. The disconnected terms represent interactions of product clusters within disjoint sets of electrons and vanish whenever two or more spin-orbital indices are identical. 

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