Franck-Condon shift

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In the Eu3+ ion emission occurs between two 4/ manifolds that are some 10.000 cm apart. Multiphonon emission is, therefore, highly improbable. If the c.t. state is not accessible, the emission is practically unquenchable by thermal means. The same is true for the Tb + ion (4/ ). In fact the Tb + emission shows only temperature quenching, if the 4/ 5i state is situated at low energy. Struck and Fonger 82) have shown that in La202S-Tb the Z)4-Tb + emission under 5 )4 excitation is temperature-quenched via thermally promoted crossovers to Franck-Condon shifted states. For excitation into the 4pSd state the situation is similar to that of Eu + (79). 

Finally it may be mentioned that other c. t. states can also play a role in the temperature quenching. The absence of Tb + emission in YVO4 has been ascribed to the presence of a low-lying metal-metal c.t. state in which one of the Tb + electrons is transferred to the vanadate group (formally written as Tb4+-1-V4+). (30, 83). Assuming that this c.t. state has a large Franck-Condon shift it is easy to explain the absence of Tb + luminescence. Because one of the 4/ electrons of Pr + is also easily excitable, similar phenomena are expected for Pr +. In fact Pr + in YVO4 luminesces only very weakly. 

It has been proposed (5) that in the case of the Ln + ions an excited state involving a metal d state is responsible for the absence of luminescence. It is then necessary that this state has a large Franck-Condon shift and is situated at energies not very much higher than those of the 4/-c.t. state. Whatever the solution of this problem may be, it is clear that either c.t. or 4f 5d states play an important role in the quenching process of the luminescence. The conclusion of all the material presented in this section is that this is true for all types of lanthanide luminescence. 

A further desirable aspect in the tabulation of levels is the evaluation of correspondence between optical and thermal energies, i.e., values for the Franck-Condon shift (=dF c). We list in Table II such values for several centers (as well as the corresponding thermal energies), where the evaluation... 

Values of Franck-Condon Shift (dD c) for Various Centers... 

Again it should be noted that we have assumed linear temperature variations because the data do not require a more complicated variation. Recent results that are in basic agreement with Eq. (25a) include the absorption measurements of Martinez et al. (1981) (ECr = 0.78 eV at T = 4°K). The fact that the thermal and absorption results are similar suggests that the Franck-Condon shift for the Cr2+ -> Cr+3 transition is small. 

From (240) we obtain the ground state with BfB = 0, and the excited state with B+B = 1, with its new frequency Qe, and with a shift of the fundamental vibration, due in part to the change of the zero-point energy (h 2J2 — ti 20/2) and in part to the Franck-Condon shift giving the energy stabilization — FC. 

For the series of 4m-1-2 carbon rings (m = 2-4), the photoelectron spectra exhibit rather broad bands [6,36]. Since, in the anions, the occupation with an electron of the degenerated LUMO level may lead to the FOJT distortion to lower the molecular symmetry, the electron detachment process should accompany a deformation between the different symmetry structures leading to complex excitations of more than one vibrational mode. The anionic Cio is calculated to have C2V symmetry while 7)51, symmetry for the neutral, thereby C2V —> Fish transition from the anion to the neutral species gives rise to a large Franck-Condon shift consistent with the observed UPS spectra [38c]. 

The optical transition (optical ionization energy /fio) takes place without lattice relaxation while the thermal ionization energy Eith corresponds to an equilibrium configuration. Figure 2.7 shows that in this particular situation, Eith is smaller than E10. The difference is the Franck-Condon shift Epc- This diagram will be used later with some additions in the discussion of the coupling of the electronic transitions of impurities with the phonon modes of crystal. 

The photophysical processes of semiconductor nanoclusters are discussed in this section. The absorption of a photon by a semiconductor cluster creates an electron-hole pair bounded by Coulomb interaction, generally referred to as an exciton. The peak of the exciton emission band should overlap with the peak of the absorption band, that is, the Franck-Condon shift should be small or absent. The exciton can decay either nonradiatively or radiative-ly. The excitation can also be trapped by various impurities states (Figure 10). If the impurity atom replaces one of the constituent atoms of the crystal and provides the crystal with additional electrons, then the impurity is a donor. If the impurity atom provides less electrons than the atom it replaces, it is an acceptor. When the impurity is lodged in an interstitial position, it acts as a donor. A missing atom in the crystal results in a vacancy which deprives the crystal of electrons and makes the vacancy an acceptor. In a nanocluster, there may be intrinsic surface states which can act as either donors or acceptors. Radiative transitions can occur from these impurity states, as shown in Figure 10. The spectral position of the defect-related emission band usually shows significant red-shift from the exciton absorption band. 

Solvatochromic shifts are rationalized with the aid of the Franck-Condon principle, which states that during the electronic transition the nuclei are essentially immobile because of their relatively great masses. The solvation shell about the solute molecule minimizes the total energy of the ground state by means of dipole-dipole, dipole-induced dipole, and dispersion forces. Upon transition to the excited state, the solute has a different electronic configuration, yet it is still surrounded by a solvation shell optimized for the ground state. There are two possibilities to consider ... 

Certain features of light emission processes have been alluded to in Sect. 4.4.1. Fluorescence is light emission between states of the same multiplicity, whereas phosphorescence refers to emission between states of different multiplicities. The Franck-Condon principle governs the emission processes, as it does the absorption process. Vibrational overlap determines the relative intensities of different subbands. In the upper electronic state, one expects a quick relaxation and, therefore, a thermal population distribution, in the liquid phase and in gases at not too low a pressure. Because of the combination of the Franck-Condon principle and fast vibrational relaxation, the emission spectrum is always red-shifted. Therefore, oscillator strengths obtained from absorption are not too useful in determining the emission intensity. The theoretical radiative lifetime in terms of the Einstein coefficient, r = A-1, or (EA,)-1 if several lower states are involved,... 

In contrast, if the medium is too viscous to allow solvent molecules to reorganize, emission arises from a state close to the Franck-Condon state (FC) (as in the case of a nonpolar medium) and no shift of the fluorescence spectrum will be observed (F in Figure 7.2). 

If solvent (or environment) relaxation is complete, equations for the dipole-dipole interaction solvatochromic shifts can be derived within the simple model of spherical-centered dipoles in isotropically polarizable spheres and within the assumption of equal dipole moments in Franck-Condon and relaxed states. The solvatochromic shifts (expressed in wavenumbers) are then given by Eqs (7.3) and (7.4) for absorption and emission, respectively ... 

The goal of theory and computer simulation is to predict S i) and relate it to solvent and solute properties. In order to accomplish this, it is necessary to determine how the presence of the solvent affects the So —> Si electronic transition energy. The usual assmnption is that the chromophore undergoes a Franck-Condon transition, i.e., that the transition occurs essentially instantaneously on the time scale of nuclear motions. The time-evolution of the fluorescence Stokes shift is then due the solvent effects on the vertical energy gap between the So and Si solute states. In most models for SD, the time-evolution of the solute electronic stracture in response to the changes in solvent environment is not taken into accoimt and one focuses on the portion AE of the energy gap due to nuclear coordinates. 

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