Theory of the Vibrational Structure of Molecular Excitons. Soluble Onehyphen;ldquo;Phononrdquo; Models

摘要

Solutions of several models of vibronic coupling in molecular crystals are presented using the techniques of second quantization. In the first, theVEPmodel, vibronic excitonVtransmutes into another vibronic excitonEby emitting a vibrational excitonP(the phonon). StableVexcitons are regarded as bound states ofEandP. If Pauli commutators are replaced by Bose ones, theVEPHamiltonian admits two constants of motion, and the Hilbert space breaks into sectors belonging to distinct eigenvalues of the constants. Weak and strong coupling correspond to stable and unstableVexcitons, respectively. For the latter case, decay ofVintoEsngbnd;Pscattering states is briefly considered. Explicit formulas are given for theEsngbnd;Pscattering states for stable and unstableV. In the second model, interactions neglected in the first are crudely approximated by a separable pairing interaction. A new bound state ofEandPresults, illustrating the influence of the previously ignored terms in creating bound states. The third model is based on the Hamiltonian of Rashba in which electronic and vibrational excitation are treated separately. In this model, exciton and phonon numbers are constants and a solution exists if terms comparable to those neglected in theVEPmodel are ignored. When simplified the secular equation is found to have the same form as an earlier solution of theVEPmodel. Other avenues of investigation opened by the present work are discussed.