Transitions nonradiative

Once a center has been excited we know that, in addition to luminescence, there is the possibility of nonradiative de-excitation that is, a process in which the center can reach its ground state by a mechanism other than the emission of photons. We will now discuss the main processes that compete with direct radiative de-excitation from an excited energy level. 

Bound electronic states exhibit a discrete spectrum of rovibrational eigenstates below the dissociation energy. The interaction between discrete levels of two bound electronic states may lead to perturbations in their rovibrational spectra and to nonradiative transitions between the two potentials. In the case of an intersystem crossing, this process is often followed by a radiative depletion. Above the dissociation energy and for unbound states, the energy is not quantized, that is, the spectrum is continuous. The coupling of a bound state to the vibrational continuum of another electronic state leads to predissociation. 

Apart from the selection rules for the electronic coupling matrix element, spin-forbidden and spin-allowed nonradiative transitions are treated completely analogously. Nonradiative transitions caused by spin-orbit interaction are mostly calculated in the basis of pure spin Born-Oppenheimer states. With respect to spin-orbit coupling, this implies a diabatic behavior, meaning that curve crossings may occur in this approach. The nuclear Schrodinger equation is first solved separately for each electronic state, and the rovibronic states are spin-orbit coupled then in a second step. 

we confine the discussion to cases that can be reduced to one dimension. As far as bound-continuum interactions are concerned, we restrict ourselves to weak interactions. This condition is mostly fulfilled for 

From Eq. [239], it is apparent that the size of a particular is not only determined by the magnitude of the electronic coupling matrix element but also by the overlap of the vibrational wave functions v,- and i/. Squared overlap integrals of the type (Xi/, (Q) IXt/ (Q))q 2 are frequently called Franck-Con-don (FC) factors. In contrast to radiative processes, FC factors for nonradiative transitions become particularly unfavorable if two states differing considerably in their electronic energies exhibit similar shapes and equilibrium coordinates of their potential curves. Due to the near-degeneracy requirement, an upper state vibrational wave function, with just a few nodes 

Continuum wave functions are spatially extended and are not normalizable in the usual spatial sense. Instead an energy normalization is chosen.186 

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The mathematical definition of the Born-Oppenheimer approximation implies following adiabatic surfaces. However, software algorithms using this approximation do not necessarily do so. The approximation does not reflect physical reality when the molecule undergoes nonradiative transitions or two... 

Figure 9.1. A Jablonski diagram. So and Si are singlet states, Ti is atriplet state. Abs, absorption F, fluorescence P, phosphorescence IC, internal conversion and ISC, intersystem crossing. Radiative transitions are represented by full lines and nonradiative transitions by dashed lines...

M.L) it may be a MMCT state (see text). The arrow indicates the nonradiative transition from the charge-transfer state d to the ground state, so that c b and c - a emission is quenched... 

Internal conversion is a nonradiative transition between states of like multiplicity (e.g., singlet to singlet, triplet to triplet, but not singlet to triplet) ... 

A nonradiative transition between states of different multiplicity is called intersystem crossing ... 

As discussed in Chapter 1, the probability of a nonradiative transition is proportional to the square of the vibrational overlap integral J xiXa drv ... 

It has been possible to employ the heavy-atom solvent effect in determining the rate constants for the various intercombinational nonradiative transitions in acenaphthylene and 5,6-dichIoroacenaphthylene.<436,c,rate constants, which are not accessible in light-atom solvents due to the complexity of the mechanism and the low efficiency of intersystem crossing from the first excited singlet to the first excited triplet, can be readily evaluated under the influence of heavy-atom perturbation. 

Of the different kinds of forbiddenness, the spin effect is stronger than symmetry, and transitions that violate both spin and parity are strongly forbidden. There is a similar effect in electron-impact induced transitions. Taken together, they generate a great range of lifetimes of excited states by radiative transitions, 109 to 103 s. If nonradiative transitions are considered, the lifetime has an even wider range at the lower limit. 

The above dynamical description of the polymerisation strongly parallels that of nonradiative transitions and this is not accidental althouth the monomer crystal from which the polymeric one is issued, do fluoresce, the polymeric one does not, despite its strong absorption at 2 eV. This strongly indicates efficient nonradiative relaxation of the excitation and strong electron-phonon coupling. 

Radiative and radiationless (nonradiative) transitions may be pictured as competing vertical and horizontal crossings, respectively, between the... 

Figure 2.6 An energy-level scheme for (a) four- and (b) three-level lasers, transition =, laser transitions , fast nonradiative transitions.

A further possibility is that molecules undergo a nonradiative transition from the excited singlet states to the triplet states (intersystem crossing). This is the origin of some loss mechanisms for dye lasers. 

NONRADIATIVE TRANSITIONS IN RARE EARTH IONS THE ENERGY-GAP LAW... 

Figure 5.61 summarizes the temperature behavior of decay time r and quantum efficiency xj of the blue luminescence from benitoite in the forms ln(r) and ln(q) as a function of reciprocal temperature 1/T. Figure 5.62.a demonstrates a suitable energy levels scheme. After excitation the metastable level 1 is populated due to nonradiative fast transition from excited level. Between levels 1 and 2 the equilibrium population is established due to nonradiative transition. The relative quantum yield of the blue emission may be described by simple Arrhenius equation ... 

Figure 2 Variation of the quantum efficiencies of photodissociation of photoionization and of nonradiative transition to the ground state, r] r = l — — t]i, in liquid water as a function of...

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