We overview the EDABI method developed recently combining the exact diagonalization and ab initio aspects of electron states in correlated systems and apply it to nanoscopic systems. In particular, we discuss the localizationdelocalization transition for the electrons that corresponds to the Mott-Hubbard transition in bulk systems. We show that the statistical distribution function for electrons in a nanochain evolves from Fermi-Dirac-like to Luttingerliquid-like with the increasing interatomic distance. The concept of Hubbard subbands is introduced to nanoclusters, and corresponds to the HOMO-LUMO splitting in the molecular and organic solid states. Also, the nanochains exhibit magnetic splitting (Slater-like), even without the symmetry breaking, since the spin-spin correlations extend over the whole system. Thus, the correlated nanoscopic systems exhibit unique and universal features, which differ from those of molecular and infinite systems. These features define unique properties reflecting 'the Mott physics' on the nanoscale. We also employ the EDABI method for the transport properties in nanoscopic systems. For example, we show that the particle-hole symmetry is broken when the tunnelling conduction through the H 2 molecule is calculated.

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We summarize briefly the main results obtained within the proposed EDABI method combining Exact Diagonalization of (parametrized) many-particle Hamiltonian with Ab Initio self-adjustment of the singleparticle wave function in the correlated state of interacting electrons. The properties of nanoscopic chains and rings are discussed as a function of their interatomic distance R and compared with those obtained by Bethe ansatz for infinite Hubbard chain. The concepts of renormalized orbitals, distribution function in momentum space, and of Hubbard splitting as applied to nanoscopic systems are emphasized.