Bonding levels, antibonding orbitals

The fuzzy frontier between the molecular and the nanometric level can be elucidated from an electronic point of view. Molecules and small clusters can be described as systems in which the metal atoms form well-defined bonding and antibonding orbitals. Large clusters or small nanoparticles (quantum dots) with dimensions of a few nanometers are intermediate between the size of molecules and bulk material, presenting discrete energy levels with a small band gap owing to quantum-mechanical rules. Finally, larger particles tend to lose this trend and display a typical band structure similar to that of the bulk material. 

These diagrams of molecular energy levels combining to form new bonding and antibonding orbitals are almost identical to those we used in Chapter 4 to make molecular orbitals from atomic orbitals. 

In the case of weak interactions with the electronic levels of the electrode (wide band approximation) Eq. (27) has the form of two Lorentz distributions centred at the energies of the bonding and antibonding states (see Fig. 12). The integral of Eq. (27) up to the Fermi level gives the occupation of both, bonding and antibonding orbitals and in the case of the wide band approximation it is an analytical expression ... 

Example Formation of MOs by LCAO method and MO energy-level diagram for the fomiation of Li2 from Li atoms. Formation of bonding and antibonding orbitals ... 

---