Full Cluster Expansion Theories in Hilbert Space

FULL CLUSTER EXPANSION THEORIES IN HILBERT SPACE 

As explained in Sec.2, the full cluster—expansion theories in Hilbert space are designed to compute wave-functions for the open-shell states that are explicitly size-extensive with respect to the total number of electrons N. The underlying cluster structure of all these developments is what was envisaged by Silverstone and Sinanoglu/48/s 

As discussed in Sec 2., the most commonly used strategy is to take a set of model space functions. that is complete with respect.to valence occupancies. The cluster operators T in that case generate from the model space determinants., the virtual determinants X by exciting core orbitals to valence/particle orbitals and, in addition, some valence orbitals to particle orbitals. Since it is possible to produce a particular determinant from several. s by.the action of the appropriate components of the T1 operators, the overall amplitude of a particular X. comes out as a combination of several T amplitudes. If we explicitly indicate by an additional label 1 the determinant X that is generated by a T, then we may write 

Another way to circumvent the linear dependency of the T amplitudes is suggested by the more recent Multireference Cl (MR-CI) developments/111,112/. In an 

MBPT framework. It should be noted that Brandow s 

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