Multicomponent Cluster States in Dilute Mixed Molecular Crystals, with Application to 1B2u Naphthalene Excitons

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Abstract
We develop the theory of Frenkel excitons for multicomponent cluster states in medium‐dilute mixed molecular crystals. This theory can be applied to both secondary host traps induced by a single impurity and to multicompositional, chemical, or isotopic clusters. A Green's function technique, which is a generalization of the Koster‐Slater method, is developed and utilized. Symmetry properties of such clusters are discussed, with emphasis on interchange equivalent sites in nonsymmorphic crystals. The optical spectra of naphthalene‐h8 in naphthalene‐d8 can now be further analyzed, with the help of some numerical calculations on multicomponent cluster states. Using our recently acquired dispersion relation for the 1B2u naphthalene exciton state we fit satisfactorily both the fine structure and the ``hyperfine'' structure, without any additional parameters, except for the experimentally known trap‐depths of a few isotopic impurities. This corroborates both the importance of the exciton superexchange effect and the validity of the exciton dispersion formula