Configurational coordinate diagram transitions

Fig. 12. Configurational coordinate diagram of Prussian blue. Curve g gives the ground state Fe(III)-NC-Fe(II) Curve e gives the MMCT state Fe(II)-NC-Fe(III). The optical transition is indicated by E p, whereas Eo gives the energy difference between the two states. See also text (after data in Ref. [66])...

Figure 5.12 A configurational coordinate diagram with which to analyze transitions between two electronic states. Harmonic oscillators at the same frequency Q are assumed for both states. The absorption and emission band profiles are sketched based on the 0 — m (absorption) and n <— 0 (emission) relative transition probabihties (see the text). For simphcity, the minima of these parabolas, Qo and Qg, are not represented.

Fig. 5.49. Configurational coordinate diagram with emission and excitation transitions in Bi ...

Fig. 8.3. Configurational coordinate diagram representing optical absorption and recombination in a material with a strong phonon coupling. A and B illustrate phonon-assisted non-radiative transitions.

Let us consider the configurational coordinate diagrams of Fig. 5 in order to understand the relevant physical processes. Figure 5a presents essentially the same information as Fig. 3. Absorption and emission transitions are quite possible and are Stokes-shifted relative to each other. The relaxed-excited state may, however, reach the crossing of the... 

A related situation occurs with the transition from the 4fbd to the 4/ configuration of Pr (112). Also this phenomenon is of great technical importance. Figure 29 gives the configurational coordinate diagram of... 

Figure 8.16. Configuration-coordinate diagram for excitation of D" to D. Vertical arrows represent optical transitions non-vertical arrow represents thermal transition.

The potential energy-configurational coordinate diagrams used by Hush to describe IT transitions (32) are presented in Figure 4. Diagrams showing IT transitions for both symmetrical [Reactions 7 (31, 34) and 8 (33)] and unsymmetrical (Reaction 6) mixed-valence ions are... 

Figure 4. Potential energy-configurational coordinate diagrams for symmetrical (A) and unsymmetrical (B) cases, IT transitions are indicated by the arrows.

Fig. 2.5. The optical absorption transition between two parabolas which have an offset relative to each other in the configurational coordinate diagram consists of a broad absorption band, See also text...

Fig. 3.1. Configurational coordinate diagram (see also Fig. 2.3). The absorption transition g- t is for reasons of clarity drawn as one line only (the transition with maximum intensity). After absorption the system reaches high vibrational levels of the excited state. Subsequently it relaxes to the lowest vibrational level v = 0 from where emission e -> g occurs in a broad band. The parabola offset is given by AR...

In general the temperature dependence of the nonradiative processes is reasonably well understood. However, the magnitude of the nonradiative rate is not, and can also not be calculated with any accuracy except for the weak-coupling case. The rea.son for this is that the temperature dependence stems from the phonon statistics which is known. However, the physical processes are not accurately known. Especially the deviation fiom parabolic behaviour in the configurational coordinate diagram (anhar-monicily) may influence the nonradiative rate with many powers of ten. However, it will be clear that the offset between the two parabolas (AR) is a very important parameter for the nonradiative transition rate. This rate will increase dramatically if AR becomes larger. 

Fig. 4.10. Schemaiic configurational coordinate diagram for (4/ ). Drawn parabolas relate to the 4/ configuration the broken parabolas indicate two possible situations for the 4f configuration (1 and II). Excitation into I yields d- /emission from 1 (arrow 1). Excitation into II (with larger offset) yields a nonradiative transition to the 4/ configuration (arrow 2) which may be followed by intraconfigurational 4/ emission...

The excitation of YjOj Eu has already been discussed in Sect. 2.1 the 254 nm radiation is absorbed by the charge-transfer transition of the Eu ion, the 185 nm radiation by the host lattice. Obviously the charge-transfer state is situated in the configurational coordinate diagram in such a Mtay that it feeds the emitting levels exclusively (see Fig. 6.9). The emission spectrum of Eu " was discussed in Sect. 3.3.2. 

FIGURE 22.11 Configuration coordinate diagram of low-energy-excited states in TT-conjugated polymers. Various excitation manifolds are marked by dashed line boxes. Narrow vertical arrows show optical transitions, whereas broad arrows indicate nonradiative relaxation pathways. (From Frolov, S.V., et al., Phys. Rev. B, 65, 205209, 2002. With permission.)... 

Fig. 4.2 a Energetic structure of the luminescence center in the lattice and possible electronic transitions. The CTT and the IT are indicated by red arrows band-to-band and internal transitions in the impurity are indicated by black arrows, b Configurational coordinate diagram representing the ground and excited states of the system from Fig. 4.2a... 

Lattice relaxation Shm = K (K is the elastic constant) accompanies electronic transition in the covalence and ionic crystals. The physical situation is presented by the configurational coordinate diagram in Fig. 4.25. The FT is indicated in Fig. 4.25 by a blue arrow. The IT creates the system in the + e state (solid blue... 

Fig. 4.33 Configurational coordinate diagram representing the structure of Pr in the host, which is represented by the impurity (praseodymium)-trapped exciton PTE a represents the situation at ambient pressure, b at pressure P i (reprinted from Ref. [202], copyright 2013, with permission from Elsevier), and c at pressure P2- The radiative and nonradiative transitions are indicated by solid and dashed arrows, respectively...

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