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The method used earlier for analysis of correlated nanoscopic systems isextended to infinite (periodic) s-band like systems described by the Hubbardmodel and its extensions. The optimized single-particle wave functionscontained in the parameters of the Hubbard model (the hopping \textit{t} andthe magnitude of the intraatomic interaction \textit{U}) are determinedexplicitly in the correlated state for the electronic systems of varioussymmetries and dimensions: Hubbard chain, square and triangular planarlattices, and the three cubic lattices (SC, BCC, FCC). In effect, the evolutionof the electronic properties as a function of interatomic distance $R$ isobtained. The model parameters in most cases do not scale linearly with thelattice spacing and hence, their solution as a function of microscopicparameters reflects only qualitatively the system evolution. Also, the atomicenergy changes with $R$ and therefore should be included in the model analysis.The solutions in one dimension (\textit{D} = 1) can be analyzed both rigorously(by making use of the Lieb--Wu solution) and compared with the approximateGutzwiller treatment. In higher dimensions (\textit{D} = 2, 3) only the latterapproach is possible to implement within the scheme. The renormalized singleparticle wave functions are almost independent of the choice of the schemeselected to diagonalize the Hamiltonian in the Fock space in D=1 case. Themethod can be extended to other approximation schemes as stressed at the end.

Extended Hubbard model with renormalized Wannier wave functions in the correlated state: beyond the parametrized models