Transition-Monopole Treatments of Interaction Matrix Elements and Mixing with Charge-Transfer Transitions

3 Transition-Monopole Treatments of Interaction Matrix Elements and Mixing with Charge-Transfer Transitions 

If the interacting molecules are in direct contact, descriptions of the system in terms of molecular orbitals for the individual molecules become problematic. One possibility is to treat the entire complex as a supermolecule with molecular orbitals that extend over all of the constituents. An intermediate approach is to augment Eq. (8.17) with charge-transfer transitions in which an electron moves from one molecule to the other [12, 15, 16]. 

If we consider only the HOMO and LUMO of the two molecules, a dimer will have two charge-transfer (CT) states in addition to the two exciton states that we have considered above. An electron can move from the HOMO of molecule 1 to the LUMO of molecule 2, as shown schematically in Fig. 8.6, or from the HOMO of 2 to the LUMO of 1. The two CT states can lie either above or below the corresponding exciton states of the dimer, depending mainly on the electrostatic interactions of the species with each other and with the surroundng medium. 

We discussed CT transitions of transition-metal complexes in Chap. 4. Charge-transfer transitions between more widely separated molecules usually have very little intrinsic dipole strength because, to a first approximation, the initial and final molecular orbitals have no atoms in common at the level of Eq. (4.26), the transition dipole is zero. However, CT states can mix with exciton states to give hybrid eigenstates that are shifted up or down in energy and have varying amounts of CT character. 

The strength of the mixing of CT and intramolecular transitions depends on the extent of orbital overlap between the interacting molecules [12]. The coefficients 

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