Exciton Impurity Levels in Molecular Crystals

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Abstract
Impurity levels for excitons in molecular crystals are discussed in terms of the wavefunctions and energy levels of a crystal containing a single substitutional impurity molecule. The problem is formulated in general terms and is found to be soluble in the special case in which the transition dipole moment of the impurity molecule is parallel to those of the host molecules. A simple criterion for the existence of localized bound states is derived, from which it is concluded that such states should be of widespread occurrence. In particular, it is found that bound states can arise even where the impurity molecule has a higher excitation energy than the molecules of the host crystal if its transition moment is sufficiently large. Bound states can also arise where the ``impurity'' is a host molecule at a site of localized strain. The specific case of a one‐dimensional crystal with nearest‐neighbor interactions is treated in some detail as a numerical example.