Linear response phonon model

Here, pv and qv denote the dimensionless momenta and coordinates of the phonon mode with frequency av, and z is the charge number of the ion when the valence orbital is empty. Thus, the first large bracket contains the total charge on the adsorbate. Finally, denotes the coupling between adsorbate and solvent. Instead of using a phonon bath, the solvent can also be modeled as an ensemble of dipoles within the linear response regime, this gives the same result.66 From this Hamiltonian, two important quantities can be defined ... 

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