Exact Treatment of Electron Correlations

The determination of electron correlation effects, cluster geometry and their interplay is a difficult problem. Most theoretical studies performed so far have attempted to deal with one of these aspects at a time [4-11, 43-46]. For example, in Refs [4-7, 10, 11] the electron interactions were treated in mean-field approximations (X a, local spin density, unrestricted Hartree-Fock) and only a few, mostly highly symmetric structures were considered. Optimizations of the cluster geometry were performed in Ref. [8] for 

The Hubbard model for small clusters is solved by expanding the eigenfunctions 1 /) into the complete basis given by the states 4 which have definite occupation numbers for all orbitals ia (/i/al m) = = 0, 1). The eigenstate i) 

The values of nsatisfy the usual conservation of the number of electrons v = v - -vi and of the z component of the total spin 5 = (v - v )/2, where Taking 

In the following we present results obtained using the theoretical methods described in the previous section and which are characteristic of the state of the art of various problems. 

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