Rate constants excited state decay

We now discuss the lifetime of an excited electronic state of a molecule. To simplify the discussion we will consider a molecule in a high-pressure gas or in solution where vibrational relaxation occurs rapidly, we will assume that the molecule is in the lowest vibrational level of the upper electronic state, level uO, and we will fiirther assume that we need only consider the zero-order tenn of equation (BE 1.7). A number of radiative transitions are possible, ending on the various vibrational levels a of the lower state, usually the ground state. The total rate constant for radiative decay, which we will call, is the sum of the rate constants,... 

Rate constants" for the excited state decay of 7-azaindole in H/D solvent mixtures... 

FIG. 12 Simulation of fluorescent decays for dye species located in the aqueous phase following laser pulses in TIR from the water-DCE interface according to Eq. (38). A fast rate constant of excited state decay (10 s ) was assumed in (a). The results showed no difference between infinitely fast or slow kinetics of quenching. On the other hand, a much slower rate of decay can be observed for other sensitizers like Eu and porphyrin species. Under these conditions, heterogeneous quenching associated with the species Q can be readily observed as depicted in (b). (Reprinted with permission from Ref 127. Copyright 1997 American Chemical Society.)... 

In 1963, E. J. Bowen published his classic review The Photochemistry of Aromatic Hydrocarbon Solutions, in which he described two major reaction pathways for PAHs irradiated in organic solvents photodimerization and photooxidation mediated by the addition of singlet molecular oxygen, 02 ) (or simply 102), to a PAH (e.g., anthracene). For details on the spectroscopy and photochemistry of this lowest electronically excited singlet state of molecular oxygen, see Chapter 4.A, the monograph by Wayne (1988), and his review article (1994). For compilations of quantum yields of formation and of rate constants for the decay and reactions of 02( A), see Wilkinson et al., 1993 and 1995, respectively. 

Wilkinson, F., W. P. Helman, and A. B. Ross, Rate Constants for the Decay and Reactions of the Lowest Electronically Excited Singlet State of Molecular Oxygen in Solution. An Expanded and Revised Compilation, J. Phys. Chem. Ref. Data, 24, 663-1021 (1995). 

Wilkinson F, Helman WP, Ross AB (1995) Rate constants for the decay and reactions of the lowest electronically excited singlet state of molecular oxygen in solution. An expanded and revised compilation. J Phys Chem Ref Data 24 663-1021... 

The excited triplet state of 3,4-dimethoxyacetophenone is quenched by both phenolic hydroxyl and methoxyl functionalities. The rate constant for decay of the 3,4-dimethoxyacetophenone triplet state k, in the presence of a quencher Q is related to the rate of triplet state decay in the absence of quencher k, the quenching rate constant kq and the quencher concentration according to Equation 2. 

In contrast to the reference compounds 4a-c, the singlet excited state deactivates in the dyads and triads much faster than in the oFL references with rate constants typically on the order of 1012 s-1 (Fig. 8.13). These values match the quantitative quenching of the oFL fluorescence in 5 and 6. A comparison between the decay rates of the conjugates carrying one C60 or two C60 moieties, reveals a 2-fold acceleration of the o/igo(fluorene) deactivation in the latter. Conclusively, placing two Ceos instead of one onto the oFL backbone significantly accelerates the excited state decay. 

In contrast to the references, 23a,b, the singlet-excited state deactivation in the Fc-oFL -C60 conjugates, 24a,b, occurs with rate constants of around 1010 s-1 (Fig. 9.64). The values are in good agreement with the observed quantitative quenching of the oFL fluorescence (Fig. 9.62a). At the conclusion of the singlet-excited state decay, two important transient maxima resemble the successful formation of the radical ion pair state, namely a weak shoulder of the transient... 

The line width Av of a rotational transition accompanying an electronic or vibronic transition is related to the lifetime r of the excited state and the first-order rate constant k for decay by... 

Figure 3 Recombination of oppositely charged, statistically independent carriers (e, h) can lead to the creation of an emitting excited state through a Coulombically correlated charge pair (e—h). The charge pair formation time (diffusion motion time) and its capture time are indicated in the figure as im and tc, respectively. The excited states decay radiatively (hi/) with the rate constant k and non-radiatively with an overall rate constant kn. After Ref. 21a.

With the advent of convenient techniques in recent years, it has become popular to measure "lifetimes" of excited states. Decay characteristics are useful adjuncts to quantum yields as they provide further knowledge about the mechanism of reaction, particularly with regard to evaluation of rate constants for excited molecule reactions. Only when the decay is exponential can a unique lifetime be defined. 

The experimental ilc computed from Eq. (21) can be related to the mechanistic rate constants. In general, the relationship is very complex, but in some limiting cases the correspondance of the experimental and mechanistic rate constants can be made by inspection. For example, in the dissociative mechanism when CrL is formed but is negligible, k computed from Eq. (21) is ka- In an associative mechanism when CrLJ is not reformed by geminate recombination, = k while in a concerted mechanism Kx = rp + rp- However when geminate recombination reforms CrLJ, the excited state decay is nonexponential. At long times is reduced by the recombination and k is a more complicated function of the several rate constants that appear in the mechanistic description. 

It should be mentioned that direct recombination from the excited molecule to the ground state, and also the ground state recovery due to recombination and transfer of electrons via surface states (compare with Fig. 10.21), have been neglected in this derivation. According to Eq. (10.17), the exponential decay is determined by k. Since in heavily doped electrodes, ki includes the tunneling rate constant kj, the decay should... 

Excited-State Kinetics. A principal emphasis of this chapter is concerned with how the application of hydrostatic pressures influences rates of ES processes such as those illustrated in Figure 9. In this simple model, it is assumed that electronic excitation leads efficiently to the formation of a single, bound state, which can decay by unimolecular radiative decay (rate constant kr), nonradiative decay (fc ), or chemical reaction to give products (kp). Alternatively, there may be bimolecular quenching of the ES dependent on the nature and concentration of some quencher Q (fcq [Q]). Each of these processes may be pressure dependent. 

Let us first consider the situation where initial excitation is followed by relaxation to a bound LEES, which is then responsible for the ligand substitution chemistry. In accord with the above discussion, the quantum yield <1>S for ligand substitution from that state would be fl>lscfcst, where intersystem crossing from the state(s) initially formed, ks is the rate constant for ligand substitution from the LEES, and r = kd1 (kd being the sum of the rate constants for the decay of the LEES). The apparent activation volume for the photoreaction quantum yields is therefore defined as... 

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