Size and shape effects on electronic energy levels:: From infinite to nanoscopic systems in three-dimensional space

The size and shape effects on the electronic energy levels of a system are studied in the light of a recently proposed solvable model for the non-relativistic quantum scattering in three-dimensional space of a particle off several interactions centred at N arbitrary points. The: transition from infinite to finite size is studied numerically for perfect systems, such as a massive solid, a layer and a linear chain. In particular, the case of systems with lithium atomic centres is tackled. Finally, with the more stable geometries of small lithium clusters found in the literature, the vertical ionization potential is also discussed qualitatively within the present model.