Choosing a Model and Appropriate Transition Dipole Moments for Time-Dependent Calculations of Intervalence Electronic Transitions

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Intervalence electron transfer spectra in mixed-valence molecules are frequently modeled by an interacting pair of adiabatic potential energy surfaces. The presence or absence of a double minimum in the lower surface is correlated with trapped or delocalized charges, respectively. In the time-dependent picture of the spectroscopy, calculations are conveniently carried out in a diabatic basis. The choice of a diabatic basis for a given adiabatic potential surface is not unique. The appropriateness of a given representation depends on the physical model that is chosen to represent the system. We present three diabatic models that give the same adiabatic potential surface. The first model represents charge transfer between two sites, the second represents a transition between bonding and antibonding molecular orbitals, and the third represents a nonbonding to nonbonding transition. Each of these models gives rise to a different calculated absorption spectrum even though they arise from the same adiabatic picture. A very important consideration after a model is chosen is the selection of the transition dipole moment. We derive and discuss the symmetry of the transition dipole moment for each of the models for the different polarization directions of the incident light and show how the symmetry depends on the choice of the model. Surprisingly, the Condon approximation corresponds to different polarization directions in the different models. We derive the explicit relationships and interconnections between the three models and the adiabatic model.



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