Strictly, anything that changes the Hamiltonian of a system, changes the excitation spectrum of that system. Considering the band structure as calculated in the framework of the Kohn-Sham equations of the density-functional theory where the effective potential is a functional of the total number density n(r) (or partial number densities n↑(r) and n↓(r) in performing spin-polarised calculations), clearly n(r) changes through the process of physisorption. In this connection, even though the interaction corresponding to absorption may be weak (this is what distinguishes physisorption from chemisorption) so that one may to a good approximation express n(r) as the sum of the number densities corresponding to the unperturbed host system and that corresponding to the unperturbed adsorbed atoms, respectively nh(r) and na(r), since the exchange-correlation potential is a non-linear functional (function, in the case of the local-density approximation), it cannot be written as the sum of the exchange-correlation potential associated with nh(r) and that associated with na(r). If it could, then on account of the localised nature of na(r) one could at least within the framework of the local-density approximation, LDA, argue that since the exchange-correlation potential associated with na(r) amounts to a nearly constant potential in the k space, it led, barring a rigid shift, to a small change in the electronic structure.
In general, adsorbates can bend the bands by forming dipoles with the surface (or changing existing dipoles), and can form gap states (among others). These would induce new electrostatic boundary conditions which could result in changes in the potential distribution / fields / band bending
The interaction between the adsorbent and adsorbate particles, even weak, will modify the energy of electrons in the valence and/or conduction bands.
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