Abstract
The problem of optical absorption by aggregates of molecules whose wavefunctions do not overlap is formulated and it is shown that there are five exact relationships (sum rules) between the absorption spectrum of the aggregate and the spectra of the constituent molecules. An approximation satisfying these sum rules is developed in which aggregate absorption is given explicitly as a function of the spectra of the constituent molecules. This approximation, which makes use of a complete set of vibrational wavefunctions for the aggregate, is a generalization of the weak and strong coupling models in the sense that it contains each as a limiting case. Moreover, it is far superior to either in both the intermediate and strong coupling cases as shown by comparing it to an exact calculation on a model dimer.
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