Davydov Splitting and Mini-Excitons

The theory of the line shifts and splittings in crystals is due in particular to A. S. Davydov and is known by his name. Here, we shall dispense with a detailed treatment of this theory and refer the reader to the specialised literature (Davydov [11, 12], Craig et al. [13, 14], McClure [15], Knox [16]). Instead, we want to turn our attention to its more important physical consequences and to concentrate on crystals with no more than two molecules in their unit cells. 

In a first step, we consider a physical dimer. This is a pair of equivalent molecules, denoted by 1 and 2, whose distance and relative orientation are the same as in the crystal lattice. In the case of anthracene, let these be the two molecules in a unit cell. Such a configuration gives a mini-exciton [17] in an optically-excited state. This model is explained in Fig. 6.7. Later, we will expand it to include the whole crystal lattice, and will thus obtain the Frenkel excitons. 

We denote the ground-state wavefunctions and energies of the two non-coupled molecules by (pi and 02 and Ei = 2 = Eq. For the wavefunction 4 g and the energy 

Right Monomer and pair emission (mini-exciton). The 0,0-transition of the phosphorescence of C- oHg as a guest molecule in a CioDg host crystal is shown. The spectra from crystals with 0.2, 2, 5, 10 and 20 mole % C- oHg are shifted vertically for 

We now assume that one of the two molecules is excited into a state (pl or (p. Their energy is then E or E = E. In principle, the probability of a molecule being excited is equally great for either of the two molecules. The wavefunctions for the singly-excited system are then the linear combinations 

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