A simple model for an adsorbate

Though the partial charge on an adsorbate cannot be measured, it is a meaningful concept within quantum-chemical calculations. Here we will present a simplified version of the Anderson-Newns model applied 

As discussed in Chapter 4.3, the interaction with the metal broadens the electronic energy levels of an adsorbate. If r is the average lifetime of an electron before it is transferred to the metal, the associated energy broadening is A = h/r. In a simple approximation the density of states of the adsorbate has a Lorenz shape [6]  

The width A is typically of the order of 1 eV and hence is much broader than kT. It is therefore permissible to replace /(a ) by a step function  

2This is true for a class of models such as the Born model, in which the interaction energy in the Hamiltonian is proportional to the charge see Problem 1. 

The first term is the intrinsic electronic energy of the adsorbate eo is the energy required to take away an electron from the atom. The second term is the potential energy part of the ensemble of harmonic oscillators we do not need the kinetic part since we are interested in static properties only. The last term denotes the interaction of the adsorbate with the solvent the are the coupling constants. By a transformation of coordinates the last two terms can be combined into the same form that was used in Chapter 6 in the theory of electron-transfer reactions. 

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