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Zero-phonon line and phonon sideband


The zero-phonon line and the phonon sideband jointly constitute the line shape of individual light absorbing and emitting molecules (chromophores) embedded into a transparent solid matrix. When the host matrix contains many chromophores, each will contribute a zero-phonon line and a phonon sideband to the absorption and emission spectra. The spectra originating from a collection of identical chromophores in a matrix is said to be inhomogeneously broadened because each chromophore is surrounded by a somewhat different matrix environment which modifies the energy required for an electronic transition. In an inhomogeneous distribution of chromophores, individual zero-phonon line and phonon sideband positions are therefore shifted and overlapping.

Figure 1 shows the typical line shape for electronic transitions of individual chromophores in a solid matrix. The zero-phonon line is located at a frequency ω’ determined by the intrinsic difference in energy levels between ground and excited state as well as by the local environment. The phonon sideband is shifted to a higher frequency in absorption and to a lower frequency in fluorescence. The frequency gap Δ between the zero-phonon line and the peak of the phonon side band is determined by Franck–Condon principles.

The distribution of intensity between the zero-phonon line and the phonon side band is strongly dependent on temperature. At room temperature there is enough thermal energy to excite many phonons and the probability of zero-phonon transition is close to zero. For organic chromophores in organic matrices, the probability of a zero-phonon electronic transition only becomes likely below about 40 kelvins, but depends also on the strength of coupling between the chromophore and the host lattice.

The transition between the ground and the excited state is based on the Franck–Condon principle, that the electronic transition is very fast compared with the motion in the lattice. The energy transitions can then be symbolized by vertical arrows between the ground and excited state, that is, there is no motion along the configurational coordinates during the transition. Figure 2 is an energy diagram for interpreting absorption and emission with and without phonons in terms of the configurational coordinate qi. The energy transitions originate at the lowest phonon energy level of the electronic states. As represented in the figure, the largest wavefunction overlap (and therefore largest transition probability) occurs when the photon energy is equal to the energy difference between the two electronic states (E1E0) plus three quanta of lattice mode i vibrational energy (). This three-phonon transition is mirrored in emission when the excited state quickly decays to its zero-point lattice vibration level by means of a radiationless process, and from there to the ground state via photon emission. The zero-phonon transition is depicted as having a lower wavefunction overlap and therefore a lower transition probability.


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