Franck-Condon energy

Franck-Condon energy, 21 188, 189 photoemission spectra, 21 186 leghemoglobin reaction, 46 524... 

Fig. 12. Franck-Condon energies of the lowest excited states of the complexes as observed in the absorption/excitation spectra of crystalline samples. The broken lines characterize states of which the assignment or the exact energy have not been confirmed by other experiments yet...

It follows for this specific choice (the TS -e1 5 e+5 with energy E0), that the Franck-Condon energy Efc E+ E equals the orbital difference s. — e1, because the two-electron parts cancel - here, the upper index t refers to quantities connected with the TS. This result is violated, if higher order terms in the expansion A. 1 are taken into account however, calculations using a LDA + GGA functional yield, that the error does usually not exceed 2%. 

AEth is the activation energy for the thermal electron transfer. AEop is the Franck-Condon energy for the photochemical electron transfer... 

Figure 2.2. Scheme of nuclear potentials in the ground electronic state E°(Q) and the excited electronic state E (Q). In the excited state, the frequency changes (i20->S2r) and the equilibrium point is shifted. The classical relaxation energy to the new nuclear configuration in the excited state is the Franck-Condon energy Efc and characterizes the linear exciton-vibration coupling. 

EfC = C2W20 = Franck-Condon energy, an energy stabilization of the localized exciton in the absence of transfer. 

In Section II, we shall collect the relevant data and calculate values of the Franck-Condon energies and we shall attempt to rationalize them qualitatively by making suitable comparisons between related systems. In Section III we shall briefly review the electrostatic theories of solvation and reorganization, and in Section IV we shall make some preliminary comparisons between theory and experiment. 

Calculations of the Franck-Condon energy AGfc for three species are shown in Table II. One complication in the use of the data at this early stage is the variety of solvent systems used another is the fact that, in the case of Fe(CN)64 ion, different salts have been used, and in the less polar media the nature of the cation may be expected to be significant. It is worth noting, however, that, again in the case of Fe(CN)64, the photoemission data of Ballard and Griffith (4),... 

For the former process, Eq. (75) may be applied, and, on comparing this with the Born equation (72), we see that the Franck-Condon energy is expected to be proportional to the solvation energy... 

A similar conclusion follows from the more extensive data on charge transfer to solvent and vice versa. Quantities AG and AG calculated for these systems in Section II,G are not the Franck-Condon energies because they include the unknown interaction energies AGw and AGW which may vary from system to system nevertheless, the main sources of variation are likely to be AGFC and AGFC. ... 

In summary, it appears from this discussion that Franck-Condon energies can now be calculated for a diverse group of inorganic charge-transfer systems and that, although the accuracy of individual values is uncertain, it is possible qualitatively to rationalize the differences between analogous systems. Absolute predictions are much less satisfactory at the present time, and the electrostatic theory based on a dielectric continuum has only very limited applicability to the systems that have so far been studied. When inner-sphere reorganization... 

Table 1. Franck-Condon energies in neutralization of cations ...

Less is known about Franck-Condon effects on collisional electron detachment from anions. For example, the C-N bond in CH2N02 (1.401 A) is 4.5% longer than the same bond in the CH2N02 anion (1.340 A), and vertical neutralization results in 25-30 kj mol-1 vibrational excitation in the radical, as calculated at several levels of theory [18]. Alkoxy radicals and anions also show different C-0 bond lengths, e.g., 1.317 A and 1.371 A in the 1-pentoxy anion and radical, respectively [1], although the Franck-Condon energies associated with... 

The +NR+ spectrum of 8 showed a small survivor ion, but differed substantially from the spectra of other C2H5NO isomers, e.g., 6, 7, AT-methylamino(hy-droxy)carbene (9), and N-methylformamide (10). The low intensity of survivor ions in the NR mass spectra of enol imines is due to Franck-Condon effects in collisional reionization that result in vibrational excitation of the resulting cation radical followed by dissociation. Franck-Condon effects were studied for collisional ionization of acetimidic acid, CH3C(OH)=NH, which was one of the neutral dissociation products of 1 -hydroxy- 1-methylamino-l-ethyl radical, a hydrogen atom adduct to AT-methylacetamide [37]. The cation-radical dissociates extensively upon reionization, and the dissociation is driven by a 74 kj mol-1 Franck-Condon energy acquired by vertical ionization. 

Fig. 2.7. Configuration coordinate diagram of the electronic energies of an impurity centre whose lattice equilibrium configurations in the ground and ionized states are represented by configuration coordinates Qgr and <5free with different values. The thermal ionization energy Eith of such a centre is smaller than the optical ionization energy Ei0 by the Franck-Condon energy Efc...

Figure 2 Franck-Condon energies in vertical neutralization of pyridinium ion. Reprinted with permission of John Wiley and Sons from Turecek F (1998) Modelling nucleobase radicals in the mass spectrometer. Journal of Mass Spectrometry ZZ 779-795.

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