Decay of excited states

The value of k so determined could then be compared with the theoretical value of 4ttN aD. However, when viscosity is considerable and/or for short lifetimes, the transient effect in diffusion is not negligible and -30% of the transfer may be attributable to the transient phase. In such a case, the luminescence decay is not simply exponential (Sveshnikov, 1935). For a brief pulse excitation, a complicated decay ensures on the other hand, for so prolonged an excitation as to generate a steady state, the resultant decay curve in many cases is indistinguishable from an exponential (Yguerabide et ah, 1964). 

The rate of energy transfer at a very short donor-acceptor separation R by the exchange mechanism has been given by Dexter (1953) as follows  

5) the donor emission spectrum/ and the acceptor absorption spectrum eA are separately normalized to unity, so that the transfer rate is independent of the oscillator strength of either transition. Unfortunately, the constants W and L are not easily determined by experiment. Nevertheless, an exponential dependence on the distance is expected. It should be noted that this type of transfer involves extensive orbital overlap and is guided by Wigner s (1927) spin rule. 

If the coupling is zero, the bound states will live forever. However, immediately after we have switched on the coupling they start to decay as a consequence of transitions to the continuum states until they are completely depopulated. Our goal is to derive explicit expressions for the depletion of the bound states l iz) and the filling of the continuum states 2(E,0)). The method we use is time-dependent perturbation theory in the same spirit as outlined in Section 2.1, with one important extension. In Section 2.1 we explicitly assumed that the perturbation is sufficiently weak and also sufficiently short to ensure that the population of the initial state remains practically unity for all times (first-order perturbation theory). In this section we want to describe the decay process until the initial state is completely depleted and therefore we must necessarily go beyond the first-order treatment. The subsequent derivation closely follows the detailed presentation of Cohen-Tannoudji, Diu, and Laloe (1977 ch.XIII). 

As in Section 2.5 we expand the total time-dependent wavefunction as 

To simplify the notation we have assumed that the light pulse has prepared the system in a single bound state. The probabilities for finding the system in states I J/ n) and 1 2(E,0)) at time t are aij(i) 2 and a2(t) E,/3) 2, respectively. Inserting (7.3) into the time-dependent Schrodinger equation with the full Hamiltonian which also includes the coupling W and utilizing (7.1) and (7.2) yields the coupled equations 

dau t)/dt depends on the entire history of the system from the beginning at t = 0 until the actual time t. Equation (7.7) is still exact within the limiting assumptions discussed above. 

As a consequence of the oscillatory phase factor in (7.7), contributions to the integral over t stem mainly from the region around t t so that an t ) on the right-hand side may be approximated by its value at time t. With this substitution Equation (7.7) becomes an ordinary differential equation,t 

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Matsika S (2004) Radiationless decay of excited states of uracil through conical intersections. J Phys Chem A 108 7584... 

The ko. A, and Fa parameters obtained for a few alkanes are collected in Table 3. kg is around 10 sec A 10 to 10 sec and Fa 10 to 20 kJ mol h In principle, the decay of excited states may involve Si- Sx-type internal conversion transitions [IC, where Sx is some singlet state that gives the product(s) of chemical decomposition] and Si T -type intersystem crossing processes (ISC). The temperature-independent decay was attributed, on the basis of the size of the rate parameter (ko 10 sec ), to Si T -type intersystem crossing. At the same time the temperature-activated decay with a frequency factor of 10 to 10 sec was attributed to an internal conversion process that takes place by overcoming a barrier of Fa 10-20 kJ mol and leads finally to some... 

Picosecond-resolved thermochemical information can be extracted from the evolution of a transient grating produced by the crossing of two laser pulses and interrogated with a third short pulse of light. Several groups have applied this method to thermodynamic questions about the decay of excited states and the evolution of excited states into reactive intermediates. 

Such a system is then as ergodic as, for example, a classical gas, only the mechanisms of ergodicity are different (in one case elastic collisions, in the other decay of excited states through induced and spontaneous emission). 

Let us assume the availability of a useful body of quantitative data for rates of decay of excited states to give new species. How do we generalize this information in terms of chemical structure so as to gain some predictive insight For reasons explained earlier, I prefer to look to the theory of radiationless transitions, rather than to the theory of thermal rate processes, for inspiration. Radiationless decay has been discussed recently by a number of authors.16-22 In this volume, Jortner, Rice, and Hochstrasser 23 have presented a detailed theoretical analysis of the problem, with special attention to the consequences of the failure of the Born-Oppenheimer approximation. They arrive at a number of conclusions with which I concur. Perhaps the most important is, "... the theory of photochemical processes outlined is at a preliminary stage of development. Extension of that theory should be of both conceptual and practical value. The term electronic relaxation has been applied to the process of radiationless decay. 

If the time period for creation of excited states and relaxation of electronic shells is much less than the lifetime of an excited state and if interference effects between various processes binding the same initial and final states may be neglected, then the creation and decay of excited states may be treated separately as a two-step process. Such an approach is widely used in X-ray and electron spectroscopy. 

Equal Times. This is a border case, xB = xA= x, when the decay of excited states and the redistribution between them proceed independently. 

This type of laser produces output pulses which are typically between 1 and 10 ns duration and are well suited to provide initial excitation in the study of the decay of excited states and other transient effects in small molecules. Many fundamental processes, however, occur on a time scale much shorter than the 1—10 ns resolution available with dye lasers of the type discussed above. These processes, such as the relaxation of large biological molecules and dyes in solution, exciton decay and migration in solids, charge-transfer and other non-radiative transfer processes between molecules, and many more, take place on a picosecond time scale. 

In the case of 7-diethylamino-4-(trifluoromethyl)coumarin ( coumarin-35 ), which has an amino group that is free to rotate, another competitive solvent-dependent decay path has been proposed rotation of the amino group of the planar ICT excited-state molecule can lead to a twisted intramolecular charge-iransfer (TICT) excited-state molecule, from which a radiationless decay to the ground-state molecule occurs [341], Solvent-dependent rate constants for both the radiative and nonradiative decay of excited-state coumarin dyes have been determined [341]. For critical discussions concerning the electronic structure of the excited states of 7-(dialkylamino)coumarins and 7-aminocoumarin ( coumarin-151 ), see references [341d, 341e]. 

The source of the problem lies in the requirement that photoinduced electron transfer be very rapid in order to compete with decay of excited states by the usual photophysical processes. Rapid transfer requires significant electronic coupling between the initial and final states (Eq. 1), and such coupling nearly always results in... 

Figure 14. Transient 480-nm absorption of Cr(CO) following 310-nm excitation into excited state that is unstable with respect to CO ligand loss. Nonexponential decay of excited-state absorption at short times is believed to reflect the process of bond breakage. This is followed by solvent complexation at longer times (see inset).

Time-resolved luminescence spectroscopy complements the steady-state method and can provide essential kinetic information about the decay of excited states. Application of time-resolved fluorescence spectroscopy for analytical chemistry, where low concentrations might require the use of long... 

Accordingly, there is always a competition between chemical and physical pathways for decay of excited states. If the chemical pathway is inefficient, then the physical pathway will lead to relaxation of M to its ground electronic state M. 

Let us generalize the quantum yield of a multi-step process x is equal to the product of the efficiencies of all steps required to complete that process. This allows us to determine rate constants by measuring quantum yields and lifetimes. Kinetic measurements such as time-resolved fluorescence or kinetic flash photolysis yield observed rate laws for the decay of excited states or of reactive intermediates. When the decay of an intermediate x obeys first-order kinetics, as is frequently the case, then the observed lifetime t = l/kobs is equal to the inverse of the sum of the rate constants of all processes contributing to the decay of the species observed.1... 

Another alternative for the decay of excited states is the transfer of electronic energy to suitable acceptors. Such a process can be represented by... 

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