Sodium binding energy curve

We can understand the behaviour of the binding energy curves of monovalent sodium and other polyvalent metals by considering the metallic bond as arising from the immersion of an ionic lattice of empty core pseudopotentials into a free-electron gas as illustrated schematically in Fig. 5.15. We have seen that the pseudopotentials will only perturb the free-electron gas weakly so that, as a first approximation, we may assume that the free-electron gas remains uniformly distributed throughout the metal. Thus, the total binding energy per atom may be written as... 

Fig. 5.14 The binding energy U as a function of the Wigner-Seitz radius fiws for sodium. The bottom of the conduction band, 1 is given by the lower curve to which is added the average kinetic energy per electron (the shaded region). (After Wigner and Seitz (1933).)...

The intensities of peaks B and C decrease as the intensities of the two new peaks increase. This behavior is consistent with the removal of states from the band edge of the neutral molecular material to form the new states within the energy gap. In the bottom curve in Fig. 3, peaks B and C have coalesced into a weak-intensity feature. From the XPS C(ls) and Na(ls) spectra, the doping level at which the two new peaks can first be detected in the UPS spectrum, second curve from the top, is estimated to be about 0.4 Na-atoms per DP7 molecule. The highest doping level (bottom curve) is estimated to be about 2 sodium atoms per DP7 molecule. Since the binding energy of the Na(ls) indicates that the Na-species is ionic, each molecule is expected to accommodate two excess electrons. 

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