  We discuss physical properties of strongly correlated electron states for a
linear chain obtained with the help of the recently proposed new method
combining the exact diagonalization in the Fock space with an ab initio
readjustment of the single-particle orbitals in the correlated state. The
method extends the current discussion of the correlated states since the
properties are obtained with varying lattice spacing. The finite system of N
atoms evolves with the increasing interatomic distance from a Fermi-liquid-like
state into the Mott insulator. The criteria of the localization are discussed
in detail since the results are already convergent for N>=8. During this
process the Fermi-Dirac distribution gets smeared out, the effective band mass
increases by ~50%, and the spin-spin correlation functions reduce to those for
the Heisenberg antiferromagnet. Values of the microscopic parameters such as
the hopping and the kinetic-exchange integrals, as well as the magnitude of
both intra- and inter-atomic Coulomb and exchange interactions are calculated.
We also determine the values of various local electron-lattice couplings and
show that they are comparable to the kinetic exchange contribution in the
strong-correlation limit. The magnitudes of the dimerization and the zero-point
motion are also discussed. Our results provide a canonical example of a
tractable strongly correlated system with a precise, first-principle
description as a function of interatomic distance of a model system involving
all hopping integrals, all pair-site interactions, and the exact one-band
Wannier functions.
