Stationary States of Systems with Interacting Molecules

1 Stationary States of Systems with Interacting Molecules 

Our discussion will concern mainly what are called Frenkel excitons, in which an electron that has been excited to a normally empty molecular orbital remains associated with a vacancy or hole in a normally filled orbital as they migrate from 

As long as the two molecules are not so close together as to become covalently bonded, it still makes sense to describe the wavefunctions of a dimer with combinations of the individual molecular wavefunctions, as we did in Eqs. (7.2), (7.4), and (7.6)  

As before, the basis states tpi and 2 for Pb represent states in which the excitation is localized on molecule 1 or 2, respectively. These are not stationary states because excitations hop back and forth between the two molecules. Setting one of the coefficients Ci or C2 to 1 and the other to zero cannot, therefore, describe the system well on time scales comparable to, or longer than the oscillation period. But we will see that it is possible to find values of the coefficients that make Ps into a stationary state. As we might expect, the values of Ci and C2 that are required depend strongly on the interaction term in the Hamiltonian, H, which is the term that mixes the two basis states (Sects. 2.3.6 and 7.2). 

Let s consider how the energies of the ground and excited states described by Eqs. (8.1) and (8.2) depend on H. The electronic energy of the ground state is  

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