Excited-state radiative decay

The energy stored in an excited state is dissipated by the unimolecular radiative and radiationless relaxations. For strongly allowed electronic transitions, Strickler and Berg have obtained an expression for the rate constant of the excited-state radiative decay (Equation 6.67).31... 

Recent work by Lim and coworkers [11,12] on small thiones of C, and Cjv excited state symmetry has clearly demonstrated the symmetry requirements of vibronicaUy induced radiationless transitions. In the low pressure gas phase, Cjv molecules such as thioformaldehyde, HjCS, exhibit both strong Sj - Sq fluorescence and strong Tj - Sq phosphorescence. These molecules therefore exhibit rates of S, - Sq internal conversion and Tj - Sq intersystem crossing that are small in comparison with the excited state radiative decay rates, despite the fact that the density of states in Sq is sufficiently large that the molecule s radiationless transitions should fall into the statistical limit case. On the other hand similar thiones of C, excited state symmetry exhibit small quantum... 

The luminescence of an excited state generally decays spontaneously along one or more separate pathways light emission (fluorescence or phosphorescence) and non-radiative decay. The collective rate constant is designated k° (lifetime r°). The excited state may also react with another entity in the solution. Such a species is called a quencher, Q. Each quencher has a characteristic bimolecular rate constant kq. The scheme and rate law are... 

Time-resolved laser flash ESR spectroscopy generates radicals with nonequilibrium spin populations and causes spectra with unusual signal directions and intensities. The signals may show absorption, emission, or both and be enhanced as much as 100-fold. Deviations from Boltzmann intensities, first noted in 1963, are known as chemically induced dynamic electron polarization (CIDEP). Because the splitting pattern of the intermediate remains unaffected, the CIDEP enhancement facilitates the detection of short-lived radicals. A related technique, fluorescence detected magnetic resonance (FDMR) offers improved time resolution and its sensitivity exceeds that of ESR. The FDMR experiment probes short-lived radical ion pairs, which form reaction products in electronically excited states that decay radiatively. ... 

The finite lifetime of each excited state is the reflection of a fundamental law of nature - tendency towards minimum total energy of a system. The quantum mechanical system tends to occupy the state in which its total energy would be minimal. However, the transition of an atom to the lowest (ground) state depends on many circumstances (first of all, on the sort of excited configuration, on the presence of external fields, on the character of the matter itself - density of gas, vapours or plasma, etc.). There are two main channels of decay of the excited states radiative and radiationless. In the first case the electronic transition from the higher to the lower state is connected with the radiation of one or several quanta of... 

The rates of radiationless transitions between electronic states of porphyrins and their derivatives play a dominant role in their photochemistry because they are the major decay channels of the electronically excited states. Radiative channels, such as fluorescence, rarely exceed 10% of the overall decay rate constant at room temperature. The lifetimes of the lowest electronic states of free-base porph3nins and closed-shell metalloporphyrins vary by more than 10 orders of magnitude with the nature of the substituents. The understanding of such variations is essential to design and control the photochemistry of porphyrins and justifies an incursion on the fundamentals of radiationless transitions. 

The complexes often undergo radiative decay from their lowest excited state both in fluid solutions at room temperature and in glassy media at 77 K [51, 63, 64, 71]. Emission lifetimes are typically 20 ns to 2 ps at room temperature and are summarized in Table 7. The excited state can decay by two nonradiative pathways by internal conversion to the ground state and by a thermally activated process through a higher energy excited state that rapidly decays to the ground state. The exact parameters for the two pathways depend on X, L, solvent and temperature. 

Despite the unfavourable branching ratio, interference processes can occur between autoionisation and radiative decay. These are discussed in detail in section 8.30. One should also note that, as a result of autoionisation, the remaining parent ion may find itself in an excited state which decays by fluorescence. Thus, the study of fluorescence at wavelengths different from the original excitation may actually be used to detect the presence of autoionisation into a specific channel. 

A One in ten - at most. Even if the excitation pulse were intense enough to excite the molecule every time, there is only a 10% probability that the electronically excited state will decay radia-tively. The rest of the time (90%) the decay will be non-radiative, and the energy will dissipate as heat. (Note that fluorescence lifetimes are quite short, and that decay back to ground state will be complete before the next excitation pulse arrives.)... 

When electrons and holes meet, they can initially form charge-transfer excitons and then electronically-excited singlet or triplet states. Both excitation states can decay radiatively and thus contribute to the electroluminescence. Every non-radiative contribution to the decay reduces the light yield of the OLED. As a rule, fluorescence from the singlet excitons is predominant in OLEDs. There are however also important triplet emitters (see below). 

Radiative capture Is any such process in which the capture results in an excited state that decays by emission of photons. A common example is neutron capture to yield an excited nucleus, which decays by emission of a gamma ray. 

It follows from Eq. (14.8) that the decay parameters of the nucleus excited state (radiative lifetime and shift of excited level) are determined by the position of poles cd = co + ico" of integrand function A(ft>) in upper semiplane of complex values Q). From the general structure of the integral (14.8) it follows that the total lifetime of the excited nucleus Ttot corresponds to the condition mco = co" = I /2Ttot-... 

Still, however, competitive processes that can occur and result in the return of unreacted starting material. The excited state can decay to the ground state by emission of light, a radiative transition. The rate of emission is very high k = 10 -10 sec ) for radiative transitions between electronic states of the same multiplicity, and somewhat lower k = lO -lO sec ) between states of different multiplicity. The two processes are known as fluorescence and phosphorescence, respectively. Once energy has been emitted as light, the reactant is no longer excited, of course, and a photochemical reaction will not occur. 

The broadening Fj is proportional to the probability of the excited state k) decaying into any of the other states, and it is related to the lifetime of the excited state as r. = l/Fj . For Fjt = 0, the lifetime is infinite and O Eq. 5.14 is recovered from O Eq. 5.20. Unfortunately, it is not possible to account for the finite lifetime of each individual excited state in approximate theories based on the response equations (O Eq. 5.4). We would be forced to use a sum-over-states expression, which is computationally intractable. Moreover, the lifetimes caimot be adequately determined within a semiclassical radiation theory as employed here and a fully quantized description of the electromagnetic field is required. In addition, aU decay mechanisms would have to be taken into account, for example, radiative decay, thermal excitations, and collision-induced transitions. Damped response theory for approximate electronic wave functions is therefore based on two simplifying assumptions (1) all broadening parameters are assumed to be identical, Fi = F2 = = r, and (2) the value of F is treated as an empirical parameter. With a single empirical broadening parameter, the response equations take the same form as in O Eq. 5.4 with the substitution to to+iTjl, and the damped linear response function can be calculated from first-order wave function parameters, which are now inherently complex. For absorption spectra, this leads to a Lorentzian line-shape function which is identical for all transitions. 

Assuming that at time t = 0 the external radiation field is removed and that all atoms are in the excited state, the decay to the ground state follows the (first-order) radiative decay law... 

Light absorption leading to electronic excitation is commonly accompanied by radiative reemission as the electron decays back to the ground potential energy surface. However, in certain cases (dependent on excited-state radiative lifetime and potential features to be described below) the system returns to the ground electronic surface without optical emission, a so-called radiationless transition. Such non-radiative transition processes are important features of reaction pathways on both ground and excited surfaces. 

For thermalized neutrons, the most probable interactiOTi is radiative capture. Neutrons are captured by a nucleus, forming a compound nucleus in an excited state. It decays to the ground state and emits a gamma radiation with an energy that is characteristic for the host element. Thus, die characteristic properties are ... 

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,... 

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