Zero-phonon line and Phonon satellite band-Wikipedia

Figure 1. Schematic representation of the profile of an electronic excitement. The narrow part at the Ωˈ frequency is zero-phonon line, the wider part is the phonon satellite strip. The relative positions of the two components during a program are reversed.

The zero-phonon line And Phonon satellite strip In conjunction, the spectral profile of individual molecules absorbing or emitting light (chromophores) included in a solid transparent matrix. When the host matrix contains many chromophores, each of them will contribute to zero-phonon line and the phonon satellite band of the specters. The spectrum from a set of chromophores is said to be enlarged inhomogenic, each chromophore being surrounded by a different environment modifying the required energy for an electronic transition. In an inhomogenic distribution of chromophores, the positions of the individual zero-phonon ray and the phonon satellite band are therefore offset and overlap.

Figure 1 illustrates the typical line profile for electronic transitions from individual chromophores in a solid matrix. The zero-phonon line is located at the frequency ω ’determined by the intrinsic difference in the energy levels between the fundamental and excited states as well as by the local environment. The Phonon satellite line is offset towards a higher frequency in absorption and lower in fluorescence. The frequency gap Δ between zero-phonon line and the pic of the Phonon satellite band is determined by the Franck-Condon principle.

The distribution of the intensity between the zero-phonon line and the Phonon satellite band is strongly dependent on the temperature. At room temperature, there is enough thermal energy to excite many phonons and the probability of zero-phonon transition is almost zero. For organic chromophores in organic matrices, the probability of a zero-phonon electronic transition only becomes possible in below 40 K, but also depends on the intensity of the coupling between the chromophore and the host matrix.

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Figure 2. Energy diagram of an electronic transition with coupling to phonons according to the reaction coordinate q _i , a normal network mode. The rising arrows represent phonon -free absorption and with three phonons. The descending arrows represent the symmetrical emission process.

Figure 3. Representation of three normal network modes ( i , j , k ) and the way in which their intensities combine at zero-phonon frequency, but are distributed in the phonon satellite line due to their different frequencies of characteristic harmonic oscillators Oh .

The transition between fundamental state and excited state is based on the Franck-Condon principle indicating that the electronic transition is very rapid compared to the movement in the network. Energy transitions can be symbolized by vertical arrows between the fundamental state and the excited state, all without displacement along the configuration coordinates during the transition. Figure 2 is an energy diagram for the interpretation of absorption and emission with and without phonons according to the Configurational coordinate Q _i . Energy transitions originate from the lowest phononic energy level in electronic states. As shown in the figure, the largest cover of wave function (and therefore the highest probability of transition) occurs when phonon energy is equal to the difference in energy between the two electronic states ( AND _first – AND ₀ ) plus four quanta of vibrational energy of network mode i (

). This transition to four phonons is reflected in the emission when the excited state is desecrated towards its level of vibration of zero point network by a non -radiative process, and from there, towards its fundamental state by a photon emission. The zero-phonon transition is described as having a less important wave function cover and thus a lower probability of transition.

In addition to the Franck-Condon premise, three other approximations are commonly used and are implicit in the figures. The first is that network vibrational mode is well described by the quantum harmonic oscillator. This approximation is perceptible in the parabolic form of the potential wells in Figure 2, and in the equal spacing between energy levels of the phonons. The second approximation is that only the weakest network vibration (zero point) is excited. This is called low temperature approximation, and this means that electronic transitions do not come from the highest phonon levels. The third approximation is that the interaction between chromophore and the network is the same in the excited state as in the fundamental state. The potential for harmonic oscillator is then the same in both cases. This approximation, called linear coupling, is visible in Figure 2: the potential of the fundamental and excited states have the same parabolic shape, and the levels of phonon energy are spaced equally.

The intensity of a zero-phonon transition comes from the superposition of all network methods. Each network mode m has a vibration frequency Ω _m characteristic which leads to an energy difference between phonons

. When the transitional probabilities of all modes are added, zero-phonon transitions are always added electronic ( AND _first – AND ₀ ), while transitions with phonons contribute to the distribution of energies. Figure 3 illustrates the superposition of the transitional probabilities of several network modes. The contributions of the phonon transitions of all network modes constitutes the Phonon satellite band.

The separation of the frequencies between the maximum of the absorption and fluorescence satellite bands translates the contribution of the phonons to the movement of stokes.

The profile of the line is Lorentzien of width determined by the life of the excited state T _ten According to Heisenberg’s principle of uncertainty. Without the influence of the network, the spectral enlargement (width in half the maximum) of the chromophore is c ₀ = 1/ T _ten . The network reduces the living time of the excited state by induction of non -radiative desexcitation mechanisms. At absolute zero, the excitation time of an excited state influenced by the network is T _first . Above, thermal agitation will introduce random disturbances of the local chromophore environment. These disturbances modify electronic transition energy by introducing an enlargement of the line dependent on temperature. The measured width of the zero-phonon line of a single chromophore, the homogeneous ray width, is then: c _h ( T ) ≥ 1/ T _first .

The shape of the Phonon satellite strip is that of a distribution of fish because translating a discreet number of events, electronic transitions with phonons (see electron-phonon coupling), during a given period of time. At larger temperatures, or when the chromophore interacts strongly with the matrix, the probability of a multiple is high and the Phonon satellite band approaches a Gaussian distribution.

The distribution of the intensity between zero-phonon line and the phonon satellite band is characterized by the Delay-Waller α factor.

Zero-phonon line is an optical analogy with Mössbauer rays, which originates in the emission or absorption without decrease in gamma radiation from the nuclei of the atoms linked in a solid matrix. In the case of an optical zero-phonon line, the coordinates of the chromophore constitute the physical parameter that can be disturbed, while during a gamma transition, the amount of movement of the atoms can be modified. More technically, the key to analogy is the symmetry between position and quantity of movement in the Hamiltonian of the quantum harmonic oscillator. The position and quantity of movement both contribute in the same way (quadratic) to total energy.

• (in) J. Friedrich et D. Haarer (1984). “Photochemical Hole Burning: A Spectroscopic Study of Relaxation Processes in Polymers and Glasses”. Applied Chemistry International Edition in English 23 , 113-140. DOI Link
• (in) Olev Bridge et Kristjan Haller, eds. (1988) Zero-Phonon Lines and Spectral Hole Burning in Spectroscopy and Photochemistry , Springer Verlag, Berlin. ISDN 3-540-19214-X.