Electron localization from the combined exact diagonalization—ab initio approach in one dimension

Exact ground state properties are presented by combining the exact diagonalization of the Hamiltonian (including all hopping integrals and all two-site interactions) with ab initio optimization of the single-particle (Wannier) functions. Such a procedure is carried out for linear systems up to N=12 atoms. We study the system evolution as a function of lattice parameters. Electrons are essentially localized for the interatomic distance R > 2.2 Å. The statistical distribution evolves from the Fermi-liquid limit (at R $\sim$ 1 – 2 Å) to continuous momentum distribution for R > 2.2 Å. The single-particle correlation functions are also discussed.