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The optimized single-particle wave functions contained in the parameters ofthe Hubbard model (t and U) were determined for an infinite atomic chain. Ineffect, the electronic properties of the chain as a function of interatomicdistance R were obtained and compared for the Lieb - Wu exact solution (LW),the Gutzwiller-Wave-Function approximation (GWF), and the Gutzwiller-ansatzcase (GA). The ground state energy and other characteristics for the infinitechain were also compared with those obtained earlier for a nanoscopic chainwithin the Exact Diagonalization combined with an Ab Initio adjustment of thesingle-particle wave functions in the correlated state (EDABI method). For thesake of completeness, we briefly characterize also each of the solutions. Ourapproach completes the Lieb-Wu solution, as it provides the system electronicproperties evolution as a function of physically controllable parameter - theinteratomic distance.

Lieb-Wu Solution, Gutzwiller-Wave-Function, and Gutzwiller-Ansatz Approximation, with Adjustable Single-Particle Wave Function for the Hubbard Chain