Electronic energy transitions

Extensive electron delocalization along the chain direction leads to an electronic transition energy for one-photon absorption (E0) of typically 15 000-16 000 cm-l for an unstrained backbone (.7). This value is very close to that of polyacetylene (or... 

FIGURE 4. Observed 0-0 electronic transition energies (cm ) of linear polyenes2,41,42 , 1 ku -... 

We first consider the relative electronic transition energies in cis and trans 1,2-disubstituted ethylenes. From Fig. 28 we can clearly see that the pi HOMO-LUMO energy gap is larger for the case of the cis isomer relative to the trans isomer. Hence, the mr transition is expected to occur at shorter wavelengths in cis 1,2-disubsti-tuted ethylenes. 

Light of definite energy and polarization has a selective power to exclusively excite dye molecules whose electronic transition energy and orientation match these parameters. Thus, if a dye is excited by polarized fight, its emission will also be highly polarized. Depolarization occurs only when the time correlation of these selectively excited species is lost due to their rotation or participation in some... 

Figure 33. Pressure dependence of the electronic transition energies of [Cu(dieten)2](BF4)2 polycrystalline (left panel) and in polyvinyl pyridine matrix (right panel).

As the electron approaches the molecule, an electric field is established that is described in terms of a Coulomb potential, (()(-. It is assumed that when the Coulomb potential reaches the electron transition energy (the ionization potential, Eq) the orbital electron involved in the transition absorbs energy from the field, the efficiency of the ionization depending on the transition probability, F, .. When the electron-induced dipole contribution is neglected, a cross section, which will be an underestimate, can be calculated from the interparticle separation when (()(- = Eq. In order to deduce the maximum ionization cross section, a., the transition probability P,. must be taken into account ... 

Table 11. Observed and calculated electronic transition energies of 7,inev. )...

Here P°jj,)V is a constant (having energy units) characteristic of the bonding interaction between and %v its value is usually determined by forcing the molecular orbital energies obtained from such a qualitative orbital treatment to yield experimentally correct ionization potentials, bond dissociation energies, or electronic transition energies. 

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. 

The parameter (v) is the average thermal velocity of an electron, Nc the density of states in the conduction band, g the degeneracy of the deep level, and A x = EQ — ET the electron transition energy. Equation (9) also relates the capture constant to the emission rate because of the definition... 

Electronic Transition Energies Associated with the 6 - 5 Transition in Metal-Metal Bound Dimers... 

The most important reason for the laige number of technical applications of polymethine dyes is their relatively low electron-transition energies and their highly intense and narrow spectral bands. Indeed, polymethines display strong light absorption and emission, between 300 and 1600 nm. In the 1990s, these dyes are mainly used as photographic sensitizers and desensitizers (11,90), as laser dyes (12,13,91), as probes of membrane potentials (14), and in other applications where the theoretical aspects of polymethines are useful. 

Quite interesting structural features are found for both compounds. The Si—Si bond distance in hepta-f-butylcyclotetrasilane with 254.2 pm is the longest reported so far in cyclotetrasilanes, while the dihedral angles near 16° are relatively small compared with those of other t-butyl-substituted cyclotetrasilanes. The hexa-t-butyl derivative, however, adopts a planar conformation with unexceptional Si—Si bond lengths of 238.7 pm. In the UV spectrum of hepta-f-butylcyclotetrasilane the longest-wavelength absorption maximum appears at 315 nm. This is the lowest electron transition energy of all alkyl-substituted cyclotetrasilanes reported so far. 

Fig. 2.3. Schematic illustration of the transition energies measured by photoelectron spectroscopy of the molecular substance X the dashed lines indicate electronic transition energies of X+.

Excited-state proton transfer relates to a class of molecules with one or more ionizable proton, whose proton-transfer efficiency is different in the ground and excited states. The works of Forster [2-4] and Weller [5-7] laid the foundation for this area on which much of the subsequent work was based. Forster s work led to the understanding of the thermodynamics of ESPT. He constructed a thermodynamic cycle (Forster cycle) which, under certain acceptable approximations, provides the excited-state proton-transfer equilibrium constant (pK f,) from the corresponding ground-state value (pKa) and electronic transition energies of the acid (protonated) and base (deprotonated) forms of the ESPT molecule ... 

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