Fluorescence dipole strength

Carotenoids are characterised by two low lying singlet excited states. The S2( Eu) state has a high absorption dipole strength and is very weakly fluorescent ( F 10 -10 ) [200, 201-204], The state is dipole forbidden... 

The rate constant for fluorescence can be related to the dipole strength for absorption by a line of reasoning that Einstein developed in the period 1914-1917 [1]. Consider a set of atoms with ground-state wavefunction Pa and excited state wavefunction Pf,. Suppose that the atoms are enclosed in a box and are exposed only to the black-body radiation from the walls of the box. According to Eq. (4.8c), the rate at which the radiation causes upward transitions from Pa to Pb is... 

To generalize Eq. (10.81), consider a system with M excited states. If we can evaluate the product of the density matrix and the fluorescence operator for an ensemble of systems, we can use Eq. (10.14) to calculate the fluorescence from any given excited state. Equation (10.74) suggests that the operator F for the dipole strength of fluorescence with polarization if can be written symbolically as... 

The excimer fluorescence (with respect to the excited vdW dimer emission) is red shifted and structureless because the emission is terminated in a repulsive ground-state potential energy surface (Figure 15). For parallel transition moments, emission from the out-of-phase exciton state to the ground state is forbidden and for the in-phase exciton state emission is allowed [28a]. It should be noted, however, that the forbidden emission from the out-of-phase exciton state is expected to have a similar transition dipole moment as the Lb So emission. The actual dynamics of the initially excited vdW dimer depend on the energy gap and the coupling strength between the primary excited (LE) state and the excimer state. 

However, low-temperature spectroscopy, in particular the fluorescence-narrowed emission, can in principle tell one further thing about the influence of proteins on chromophores. There can be a quasi-continuous tail at energies below the ZPL peak, and it represents coupling of the dipole transition to the low-frequency modes (the phonons) of the protein or the solvent. The relative strength of the ZPL to the phonon tail is the Debye-Waller factor and is a measure of the strength of the phonon-chro-mophore coupling. The phonon band is expected to be homogeneously broadened. Unfortunately, at this point no one has been able to use low-temperature spectroscopy to resolve the ZPL and the Debye spectrum in a protein, or observe the Debye factor as a function of temperature. We look forward to these important measurements. 

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