Three-level excitonic interaction

Partial Diagonalization of the Three-Level Excitonic Interaction... 

We model the amide band as a system of N interacting localized vibrations. For the sake of third-order spectroscopies, we only need to consider the lowest three levels of each peptide group with energies 0, Gm, Gnl(m = 1,..., N). The matrix elements of the dipole operator corresponding to the 0-1 and 1-2 transitions are denoted /j.m and //ra, respectively, and their ratio is Km = To introduce the vibrational Frenkel exciton model,... 

The binding of 9-aminoacridine to calf thymus DNA has been studied at low ratios of dye/polymer [87]. Once the dye concentration levels were increased to the point where bound dye molecules could interact with each other, the spectra could be interpreted in terms of exciton coupling. In another system involving the same intercalation system [88], the observed spectra were deconvoluted into contributions from three n- w transitions and the dipole and rotatory strengths of one long-axis and one short-axis polarized transition were determined for each intercalating species. Through comparison of the experimental results with those of theoretical calculations on the induced CD, it proved to be possible to draw several conclusions about the nature of the intercalated species ... 

If the part of the interaction which depends on electronic spins is not taken into account, the molecule energy level in a triplet state is three-fold degenerate with respect to the molecular spin orientation (M = 0, 1). In this case there are a excitonic bands corresponding to each value of M (a being the number of molecules in unit cell), and the respective wavefunctions have the form... 

We now wish to extend the dimer model to encompass an infinitely large three-dimensional crystal lattice this is very similar to the transition from the covalent bonding of two atoms to the band structure of a metal or a semiconductor with delocalised states. Starting from the more or less sharp energy levels in the two-body system, we arrive at a band of energy states whose width depends on the interactions of the individual molecules or the overlap of the molecular orbitals in the lattice. We must then take the interaction of an excited molecule with aU the other molecules in the crystal and with the periodic lattice potential into account The levels and E in the dimer model of Fig. 6.7 are transformed into a more or less broad band of energy levels. These are the excitonic bands of the crystal, which we shall treat in this section. 

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