One-electron energies and bond energy trends

The following analysis follows that of Hammer and Nprskov [4,8]. 

Consider an adsorbate a outside a metal surface m. We want to estimate the change in adsorption energy of the adsorbate when the metal is modified slightly to m. The modification could for instance be that another atom or molecule was adsorbed on m close to a, or that m was exchanged for another metal close to m in the Periodic Table. 

With the frozen density ansatz all terms in parenthesis in the last equation will be zero. The only contribution from F to the adsorption energy difference is therefore the non-local electrostatic energy, 

In the same way, the frozen potential and density ansatz renders the net contribution from the nv integrals in the kinetic energy difference zero, and only the difference in the one-electron energies calculated with the frozen potentials outlined above will contribute to the kinetic energy contribution  

The difference in adsorption energy is therefore given by the one-electron energy difference plus the difference in electrostatic interaction between the surface and the adsorbate in the two situations  

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