Optical Absorption by Charge-Transfer Molecules.

An analytical formalism is developed for the calculation of absorption of radiation by charge-transfer molecules with electronic density delocalized between the donor and acceptor parts. The theory consistently incorporates both the vibronic coupling to quantum intramolecular vibrations and electrostatic interactions with a classical polarizable medium. The formulation operates in terms of basis-invariant parameters and can be used for calculations based on both the localized diabatic states and delocalized adiabatic wave function produced by standard quantum-chemistry algorithms. The basis-invariant reorganization energy is particularly important, since it determines observable spectroscopic parameters, in contrast to the adiabatic reorganization energy based on the molecular charge distributions in the adiabatic vacuum states. Analytical formulas are derived for the charge-transfer absorption band and first two spectral moments connecting spectroscopy to properties of charge-transfer molecules. Electronic delocalization requires a new definition of the Huang-Rhys factor traditionally used to construct vibronic band shapes. Theory's performance is illustrated by application to experimental data for self-exchange charge-transfer optical absorption and for metal-to-ligand emission transitions.