Case 1 Atom on a Metal of Constant Electron Density

1 Case 1 Atom on a Metal of Constant Electron Density 

Let us describe the solid as having a constant electron density for all energies. Of course, such metals do not exist, but the situation gives us the simplest case. The matrix element Vat has also been assumed to be constant, meaning that A(e) is proportional only to the electron density of the metal. 

From the Kronig-Kramer relation it immediately follows that A(e) = 0, as the function to be integrated is odd, and hence the resulting projected density of states becomes 

Lorentzian shape centered at the original energy of the adsorbate. The choice of the energy zero is the same as in the subsequent two figures, but is irrelevant in this case. 

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