Dielectric response of molecules in empirical tight-binding theory

In this paper we generalize our previous approach to electromagnetic interactions within empirical tight-binding theory to encompass molecular solids and isolated molecules, In order to guarantee physically meaningful results, we rederive the expressions for relevant observables using commutation relations appropriate to the finite tight-binding Hilbert space. In carrying out this generalization, we examine in detail the consequences of various prescriptions for the position and momentum operators in tight binding. We show that attempting to fit parameters of the momentum matrix directly generally results in a momentum operator which is incompatible with the underlying tight-binding model, while adding extra position parameters results in numerous difficulties, including the loss of gauge invariance. We have applied our scheme, which we term the Peierls-coupling tight-binding method, to the optical dielectric function of the molecular solid PPP, showing that this approach successfully predicts its known optical properties even in the limit of isolated molecules.