Radiationless transitions energy transfer

Once the excited molecule reaches the S state it can decay by emitting fluorescence or it can undergo a fiirtlier radiationless transition to a triplet state. A radiationless transition between states of different multiplicity is called intersystem crossing. This is a spin-forbidden process. It is not as fast as internal conversion and often has a rate comparable to the radiative rate, so some S molecules fluoresce and otliers produce triplet states. There may also be fiirther internal conversion from to the ground state, though it is not easy to detemiine the extent to which that occurs. Photochemical reactions or energy transfer may also occur from S. ... 

A may also return to the ground state via a radiationless transition, most commonly by collisional transfer of energy to a solvent molecule. 

Instead of the quantity given by Eq. (15), the quantity given by Eq. (10) was treated as the activation energy of the process in the earlier papers on the quantum mechanical theory of electron transfer reactions. This difference between the results of the quantum mechanical theory of radiationless transitions and those obtained by the methods of nonequilibrium thermodynamics has also been noted in Ref. 9. The results of the quantum mechanical theory were obtained in the harmonic oscillator model, and Eqs. (9) and (10) are valid only if the vibrations of the oscillators are classical and their frequencies are unchanged in the course of the electron transition (i.e., (o k = w[). It might seem that, in this case, the energy of the transition and the free energy of the transition are equal to each other. However, we have to remember that for the solvent, the oscillators are the effective ones and the parameters of the system Hamiltonian related to the dielectric properties of the medium depend on the temperature. Therefore, the problem of the relationship between the results obtained by the two methods mentioned above deserves to be discussed. 

In the quantum mechanical formulation of electron transfer (Atkins, 1984 Closs et al, 1986) as a radiationless transition, the rate of ET is described as the product of the electronic coupling term J2 and the Frank-Condon factor FC, which is weighted with the Boltzmann population of the vibrational energy levels. But Marcus and Sutin (1985) have pointed out that, in the high-temperature limit, this treatment yields the semiclassical expression (9). 

The probability of intramolecular energy transfer between two electronic states is inversely proportional to the energy gap, AE, between the two states. The value of the rate constant for radiationless transitions decreases with the size of the energy gap between the initial and final electronic states involved. This law readily provides us with a simple explanation of Kasha s rule and Vavilov s rule. 

The molecular ion will be of low symmetry and have an odd electron. It will have as many low-lying excited electronic states as necessary to form essentially a continuum. Radiationless transitions then will result in transfer of electronic energy into vibrational energy at times comparable to the periods of nuclear vibrations. 

The mechanisms of luminescence decay from an optical center are of critical importance. In particular we have to know if there are any processes internal to the center or external to it, which reduce the luminescence efficiency. It is possible to define two decay times, ir, the true radiative decay time which a transition would have in absence of all non-radiative processes, and r, the actual observed decay time, which maybe temperature dependent, as will usually occur when there are internal non-radiative channels, and which may also be specimen dependent, as when there is energy transfer to other impurities in the mineral. The quantum yield may be close to unity if the radiationless decay rate is much smaller than the radiative decay. 

The decay time of the Cr " band of approximately 150 ns is very short for such emission. Radiative energy transfer may not explain it because in such a case the decay curves of each of the ions are independent of the presence of the other. Thus non-radiative energy transfer may also take part, probably via multipolar or exchange interactions. In such cases the process of luminescence is of an additive nature and the lifetime of the sensitizer from which the energy is transferred is determined, apart from the probability of emission and radiationless transitions, by the probability of the energy transfer to the ion activator. 

The luminescence spectrum of the Canada apatite contains the yellow band, which is similar to Mn + emission in the Ca(II) site (Fig. 5.71). Nevertheless, this band has short decay time, which is not suitable for strictly forbidden d-d transitions in Mn +. It dominates in the time-resolved spectrum with a delay of 10 ps and gate of 100 ps when the shorter-lived centers are quenched, while the longer-Hved ones are not detected. A change in the lifetime may be indicative of the energy transfer from Mn + by a radiationless mechanism. A condition necessary for this mechanism is coincidence or a close distance between energy level pairs of the ion sensitizer and the ion activator. Here, the process of luminescence is of an additive nature and a longer duration and greater quantum yield of the activator luminescence accompany a reduced... 

These three factors are included in the expression derived by Robinson and Frosch from time-dependent perturbation theory, for the nonradiative energy transfer or radiationless transition probability kNR per unit time,... 

Suppose that absorption promotes a molecule from the ground electronic state, S0, to a vibra-tionally and rotationally excited level of the excited electronic state S, (Figure 18-13). Usually, the first process after absorption is vibrational relaxation to the lowest vibrational level of Sj. In this radiationless transition, labeled R, in Figure 18-13, vibrational energy is transferred to other molecules (solvent, for example) through collisions, not by emission of a photon. The net effect is to convert part of the energy of the absorbed photon into heat spread through the entire medium. 

In 1969, Suppan reviewed experimental data about dipole moment changes in excited states of substituted aromatic molecules and suggested a theoretical approach according to which charge transfer occurs if the lowest vacant orbitals are very close in energy.41 In 1978, Birks introduced the term horizontal radiationless transition, which was applied to intramolecular rotation in stilbene and polyene derivatives.37 In this... 

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