Excitation transfer rate constants

Single molecule data measured at room temperature indicated that a distri bution of excitation transfer rate constants could be observed [18], while Basche and co-workers [19] showed, studying linewidths at low temperature, that the observed rates are larger than expected from classical Forster excitation transfer theory and suggested that in these systems through-bond interaction might play a role. 

Fortunately, other experimental parameters are sensitive to olefin triplet geometry and assist in the evaluation of the They include (1) the triplet lifetime, which (see Table 4) is long for nearly planar triplets (ms-p,s) and short for nearly perpendicular triplets (ns), (2) the magnitude of triplet-triplet excitation-transfer rate constants, e.g. which is large for planar and small for perpendicular triplets, (3) the shape of the triplet-triplet absorption spectrum and its dependence on structural or medium constraints to torsion about the olefinic double bond, (4) the fraction of quenching interactions which give 02( Ag), and (5) where applicable, the trans/cis decay ratio, 87(1 — 8 ), associated with the O2 quenching interaction. 

TABLE 7. EXCITATION TRANSFER RATE CONSTANTS (k-,) for THIOXANTHONES and PHOTOINITIATORS" ... 

Eor a bimolecular quenching reaction, the k t corresponds to k [Q]. However, for a covalently linked E/Q dyad or E/Q assembly, the k t is the intramolecular or intra-assembly first-order excitation transfer rate constant. 

The first type of interaction, associated with the overlap of wavefunctions localized at different centers in the initial and final states, determines the electron-transfer rate constant. The other two are crucial for vibronic relaxation of excited electronic states. The rate constant in the first order of the perturbation theory in the unaccounted interaction is described by the statistically averaged Fermi golden-rule formula... 

Time-resolved method 1 decay of the donor fluorescence If the fluorescence decay of the donor following pulse excitation is a single exponential, the measurement of the decay time in the presence (td) and absence (t ) of transfer is a straightforward method of determining the transfer rate constant, the transfer efficiency and the donor-acceptor distance, by using the following relations ... 

Time-resolved method 2 increase in the acceptor fluorescence The transfer rate constant can also be determined from the increase in the acceptor fluorescence following pulse excitation of the donor. The concentration of excited acceptors following (5-pulse excitation of the donor obeys the following differential equation ... 

In phase-modulation fluorometry, it is worth noting that the transfer rate constant can be determined from the phase shift between the fluorescence of the acceptor excited directly and via donor excitation. 

More subtle factors that might affect k will be the sites structures, their relative orientation and the nature of the intervening medium. That these are important is obvious if one examines the data for the two copper proteins plastocyanin and azurin. Despite very similar separation of the redox sites and the driving force (Table 5.12), the electron transfer rate constant within plastocyanin is very much the lesser (it may be zero). See Prob. 16. In striking contrast, small oxidants are able to attach to surface patches on plastocyanin which are more favorably disposed with respect to electron transfer to and from the Cu, which is about 14 A distant. It can be assessed that internal electron transfer rate constants are =30s for Co(phen)3+, >5 x 10 s for Ru(NH3)jimid and 3.0 x 10 s for Ru(bpy)3 , Refs. 119 and 129. In the last case the excited state Ru(bpy)3 is believed to bind about 10-12 A from the Cu center. Electron transfer occurs both from this remote site as well as by attack of Ru(bpy)j+ adjacent to the Cu site. At high protein concentration, electron transfer occurs solely through the remote pathway. 

Since the values of i/ depend on several factors noted above, in the absence of additional data such as the temperature dependence of the electron transfer rate constants for i-2 it is difficult to analyze the apparent difference between i/ for the charge separation reaction and that of the radical ion pair recombination reaction. However, the difference between these two values of u is not unreasonable given that the charge separation involves oxidation of an excited state of the donor, while radical ion pair recombination involves two ground state radicals. Small changes in the nuclear coordinates of the donor and acceptor for these two reactions should be sufficient to produce the observed difference in i/. The electronic coupling factor between ZnTPP and AQ should be different than that between ZnTPP " and AQ". 

The inverted region was initially predicted by Marcus and the decrease in the electron transfer rate constant with —AG° has been observed experimentally many times.18 This is an important and remarkable result both for natural and artificial photosynthesis and energy conversion it predicts that, following electron transfer quenching of the excited A -B, the back electron transfer in the inverted region for the charge-separated state A + -B becomes slower as the energy stored increases. 

We now consider hydrogen transfer reactions between the excited impurity molecules and the neighboring host molecules in crystals. Prass et al. [1988, 1989] and Steidl et al. [1988] studied the abstraction of an hydrogen atom from fluorene by an impurity acridine molecule in its lowest triplet state. The fluorene molecule is oriented in a favorable position for the transfer (Figure 6.18). The radical pair thus formed is deactivated by the reverse transition. H atom abstraction by acridine molecules competes with the radiative deactivation (phosphorescence) of the 3T state, and the temperature dependence of transfer rate constant is inferred from the kinetic measurements in the range 33-143 K. Below 72 K, k(T) is described by Eq. (2.30) with n = 1, while at T>70K the Arrhenius law holds with the apparent activation energy of 0.33 kcal/mol (120 cm-1). The value of a corresponds to the thermal excitation of the symmetric vibration that is observed in the Raman spectrum of the host crystal. The shift in its frequency after deuteration shows that this is a libration i.e., the tunneling is enhanced by hindered molecular rotation in crystal. 

Hydrogen atom transfer from anthracene, excited into its lowest excited singlet state, to anthraquinone impurity molecules creates a radical pair that strongly quenches the fluorescence from anthracene crystals. The reverse transfer rate constant, found from measurements of fluorescence intensity and its characteristic lifetime at different moments after the creation of the radical pair, varies from 106 to 10s s 1 in the range 110-65 K, kc = 4 x 104 s 1, TC = 60K. The kc values drops to 102 s 1 in the deuteroanthracene crystal [Lavrushko and Benderskii, 1978]. 

In several cases, dependent on the donor, the electron transfer triplet energy transfer from the triplet state of the fullerenes to the donor was observed. For example, excitation of C6o/perylene (Pe) mixtures leads to 3Pe and C6o in a fast reaction ((1.4 0.1) X 109 M 1 s-1). The electron transfer from Pe to 3C o occurs with a rate one-third of triplet energy transfer [127]. Ito et al. investigated the photoexcitation of mixed system of C6o and (3-carotene [141], They observed triplet energy transfer from 3C o to (3-carotene in polar as well as in nonpolar solvents besides electron transfer from (3-carotene to 3C o However, the electron transfer rate constant increases with solvent polarity while the energy transfer is only less effected by the change of solvent polarity (Table 5). 

The effect of the FC term on ICT and MLCT-based chemosensors appears when the electron transfer rate constant is generalized within the context of nonradiative decay theory [191-193], MLCT excited states are produced directly upon excitation whereas ICT states are produced by a surface crossing from an initially prepared localized excited state (see Fig. 9). Return of the system from the charge transfer excited state to ground state has the overall form of an electron transfer recombination problem that is described by the inverted Marcus curve of Fig. 13. As described by the FC term of Eq. (5), the rate constant for... 

A question that arises in consideration of the annihilation pathways is why the reactions between radical ions lead preferentially to the formation of excited state species rather than directly forming products in the ground state. The phenomenon can be explained in the context of electron transfer theory [34-38], Since electron transfer occurs on the Franck-Condon time scale, the reactants have to achieve a structural configuration that is along the path to product formation. The transition state of the electron transfer corresponds to the area of intersection of the reactant and product potential energy surfaces in a multidimensional configuration space. Electron transfer rates are then proportional to the nuclear frequency and probability that a pair of reactants reaches the energy in which they have a common conformation with the products and electron transfer can occur. The electron transfer rate constant can then be expressed as... 

Fig. 1 A schematic view of the donor-acceptor photophysics. D/A and D /A correspond to the ground and excited donor/acceptor, respectively. It is assumed that only the donor is photoexcited at the rate of k X. Icet is the donor-to-acceptor energy transfer rate constant, and ko/kA are the free donor/acceptor fluorescence rate constants.

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