Polariton Modes of Molecular Crystals and Helical Polymers

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Abstract
The exciton modes of a molecular crystal are expressed in a second-quantized form by a model Hamiltonian which may be exactly diagonalized by the Bogoljubov canonical transformation. The formal connection between theories based upon one-electron functions and theories based upon one-molecule functions is demonstrated. The exciton-photon interaction is formulated, and the exponential term in the interaction coefficient is retained. The polariton modes of the molecular crystal are found by a Bogoljubov canonical transformation of the total exciton-photon Hamiltonian. The secular equation for those polariton modes which represent electromagnetic waves propagating in a dispersive medium is solved, and a general refractive index is defined. The general refractive index is used for the formulation of the optical dispersion and optical activity of the molecular crystal entirely in terms of molecular moments, molecular energies, and intermolecular interactions. Since the intermolecular interaction is not treated as a perturbation, this theory correctly represents the intensities of crystal transitions which arise from even the weakest molecular transitions. The helical polymer is considered as a special case of the molecular crystal. A major term in the optical rotation of the helical polymer follows directly from the correct dipole selection rules. Use of periodic boundary conditions for the formulation of the optical rotation of the helical polymer is shown to be valid.