By Ilya Prigogine, Stuart A. Rice
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Extra resources for Advances in Chemical Physics, Vol. 74
Scheme, in the various types of coupling, of the dispersion of the excitonvibration system as a function of the total wave vector. The energy origin is the lower excitonic state. For weak coupling, the free-exciton scattering on the vibrations provides a good picture (a, b). For strong coupling the localized exciton provides the most appropriate picture: molecular vibronic states (c) or self-trapped exciton (d). The hatched areas represent continua of states where the excitonic wave vector is arbitrary.
The Raman-active modes at k = O(r) are marked R , and have symmetry A@) or B,(A). Note the weak dispersion of the lower R mode along c*. K SPECTROSCOPY OF A MOLECULAR CRYSTAL 39 2. Coupling t o the Electronic Excitutions In the Born-Oppenheimer approximation" the electronic energy E'(R) and the wave function e ( R ) at the nuclear configuration of the isolated molecule allow one to calculate the potential in which the nuclei move, the electrons following adabatically in the state e(R). In the crystal, the presence of a vibration coupled to the electronicexciton will modify the motion of the latter; thus the electronic state e ( R ) and the Born-Oppenheimer approximation must be abandoned for the description of the crystal states.
More, it diverges over distances smaller than the molecular diameter. Furthermore, the calculation of the multipole coefficients requires that of the wave functions of the molecule, which is not a simplification of the problem. The coulombic interactions between transitions f and g of molecules no and mp are written for short distances as ; : I . 86)allow us to consider only singly excited states of the crystal. They will simply be dropped; that corresponds to the quasi-boson approximation (low excitation densities) implicit in all our calculations.