Moment Theorems for Vibronic Exciton Spectra of Molecular Crystals

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Abstract
The mean energy and second moment of an absorption band can be calculated exactly without a knowledge of the energies and eigenstates of the upper levels of the transition. Application of this theorem to exciton spectra of molecular crystals having two molecules per unit cell shows that the purely electronic part of the factor-group splitting is given by the difference of the mean energies of absorption in the two relevant polarizations and that the second moment of the absorption band is independent of the intermolecular coupling strength. These results are independent of the vibronic coupling strength and of whether or not the vibrations are harmonic. The finite-temperature form of the mean energy theorem is derived and is employed to discuss the broadening of exciton spectra resulting from interaction with lattice vibrations.

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