Properties of molecules and nanoscopic systems from a combined exact diagonalization - ab initio approach

Józef Spałek, Adam Rycerz, Robert Podsiadły

Adam Rycerz, Józef Spałek, Robert Podsiadły

Józef Spałek, Edward M. Görlich, Adam Rycerz +1 more

We overview the EDABI method developed recently and 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 the Fermi-Dirac-like to the 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 to the transport properties in nanoscopic systems. For example, we show that the particle-hole symmetry is broken when the tunneling conduction through H2 molecule is calculated.

Swapan K. Ghosh

Edward M. Görlich, Adam Rycerz, Józef Spałek

Abstract We provide a brief overview of the results for correlated nanoscopic systems obtained from the Exact‐Diagonalization Ab Initio (EDABI) method. Explicitly, after a brief summary of the method and its testing for the atomic and crystal‐field states, we summarize the fundamental properties of nanochains modeling a simple‐metal quantum nanowire. All the results are analyzed as a function of interatomic distance and characterize an evolution of electronic states from the Fermi‐liquid‐like state to a localized state via an intermediate Luttinger‐liquid‐like regime. The renormalized electronic (band) structure and the concept of statistical distribution function are shown to be applicable for N = 8 ÷ 16 atoms arranged in chain or ring configurations. The role of boundary conditions involving a ficticious flux representing the Berry phase is also briefly discussed. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Adam Rycerz

We present our new method of approach to the interacting electron systems combining the exact diagonalization of the Hamiltonian in the Fock space (including all hopping integrals and all two‐site interactions) with an ab initio optimization of the single particle (Wannier) functions in the resultant ground state. Such a procedure is applied to the analysis of the electron localization in nanoscopic chains containing up to N = 12 atoms. Electrons are essentially localized for the interatomic distance R > 2.2 Å. The statistical distribution evolves from the Fermi‐liquid limit (at R ∼ 1 − 2 Å) to continuous momentum distribution for R > 2.2 Å. The Mott and the Hubbard criteria of localization are explicitly evaluated and the importance of the former is stressed. Futher applications of our method are listed at the end.