The combined exact diagonalization– ab initio approach and its application to correlated electronic states and Mott–Hubbard localization in nanoscopic systems

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 localization–delocalization 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 Luttinger-liquid-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.