Molecular Vibrations in the Exciton Theory for Molecular Aggregates. I. General Theory

A molecular aggregate is defined as an ordered array of identical molecules. This definition includes molecular crystals, dimers, and certain polymeric aggregates of dye molecules. The vibronic states of an electronically excited molecular aggregate are studied theoretically. The aggregate is treated as an array of non-rigid molecules in a rigid lattice. The simplest form of the exciton theory is assumed to be correct except with regard to intramolecular vibrations. The molecules in the aggregate are considered as harmonic oscillators with one vibrational degree of freedom, whose individual wave functions are Born-Oppenheimer separable. The molecules are assumed to interact by a purely electronic mechanism. Born-Oppenheimer separable wave functions for the whole aggregate, here called E-V functions, are defined. It is shown that the interaction integrals between E-V functions may be expressed in terms of integrals which depend only on the properties of individual molecules. Explicit expressions are given for the latter integrals. The resonance interactions between E-V functions are described. On this basis, the limiting conditions under which the E-V functions steadily approach exact vibronic state functions of the aggregate are specified. The vibrational overlap integrals between E-V and electronic ground-state wave functions are studied. These integrals may be expressed as sums of products of vibrational overlap integrals for individual molecules. Explicit expressions for the latter integrals are obtained through an approximation to Hutchisson's theory.