We have proposed a novel method (EDABI) of approach to nanoscopic correlated systems that combines an exact diagonalization method with an ab initio readjustment of the single-particle orbitals. With the help of this method we study correlated electronic states of atoms and small clusters. In the case of atomic systems with Z < 10 we can perform the analysis of the ground- and excited- states systematically improving the accuracy of the calculation. For the two- and three- dimensional clusters containing up to N=4 atoms the electronic and lattice properties are analyzed as a function of interatomic distance. Three- and four- site interactions are included for simple s-like orbitals. With an increasing interatomic distance the Hubbard gap appears already for the cluster systems.

PACS numbers: 71.10.Fd, 71.27.+a,11.10.Ef