Theory of the Vibrational Structure of Molecular Exciton States

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Abstract
The interaction of excitons with molecular vibrations is formulated in the second quantization formalism. The Hamiltonian which describes interacting excitons and molecular phonons is derived. The exciton creation and destruction operators can be eliminated resulting in a reduced Hamiltonian which contains phonon operators only. A natural variational function for the lowest state of the reduced Hamiltonian is suggested by the forms of the eigenstates for the two exactly soluble limiting cases of vanishing exciton—phonon coupling and vanishing exciton bandwidth. Numerical calculations of the properties of the exciton in the lowest state are carried out for a simple one-dimensional nearest-neighbor interaction model.

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