Molecule radiationless transitions

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. ... 

Sensitivity levels more typical of kinetic studies are of the order of lO molecules cm . A schematic diagram of an apparatus for kinetic LIF measurements is shown in figure C3.I.8. A limitation of this approach is that only relative concentrations are easily measured, in contrast to absorjDtion measurements, which yield absolute concentrations. Another important limitation is that not all molecules have measurable fluorescence, as radiationless transitions can be the dominant decay route for electronic excitation in polyatomic molecules. However, the latter situation can also be an advantage in complex molecules, such as proteins, where a lack of background fluorescence allow s the selective introduction of fluorescent chromophores as probes for kinetic studies. (Tryptophan is the only strongly fluorescent amino acid naturally present in proteins, for instance.)... 

Fig. 11. (a) Diagram of energy levels for a polyatomic molecule. Optical transition occurs from the ground state Ag to the excited electronic state Ai. Aj, are the vibrational sublevels of the optically forbidden electronic state A2. Arrows indicate vibrational relaxation (VR) in the states Ai and Aj, and radiationless transition (RLT). (b) Crossing of the terms Ai and Aj. Reorganization energy E, is indicated. 

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

Sodium Acetate-Sodium Chloride Mixtures. Ramasamy and Hurtubise (12) obtained RTF and RTF quantum yields, triplet formation efficiency, and phosphorescence lifetime values for the anion of p-aminobenzoic acid adsorbed on sodium acetate and on several sodium acetate-sodium chloride mixtures. Rate constants were calculated for phosphorescence and for radiationless transition from the triplet state. The results showed that several factors were important for maximum RTF from the anion of p-aminobenzoic acid. One of the most important of these was how efficiently the matrix was packed with sodium acetate molecules. A similar conclusion was found for RTF however, the RTF quantum yield increased more dramatically than the RTF quantum yield. 

E. S. Medevedev and V. I. Osherov, Radiationless Transitions in Polyatomic Molecules, Springrer Series in Chemical Physics, Springer, Berlin, 1994, voL 57. 

Robinson and Frosch<84,133> have developed a theory in which the molecular environment is considered to provide many energy levels which can be in near resonance with the excited molecules. The environment can also serve as a perturbation, coupling with the electronic system of the excited molecule and providing a means of energy dissipation. This perturbation can mix the excited states through spin-orbit interaction. Their expression for the intercombinational radiationless transition probability is... 

Internal conversion refers to radiationless transition between states of the same multiplicity, whereas intersystem crossing refers to such transitions between states of different multiplicities. The difference between the electronic energies is vested as the vibrational energy of the lower state. In the liquid phase, the vibrational energy may be quickly degraded into heat by collision, and in any phase, the differential energy is shared in a polyatomic molecule among various modes of vibration. The theory of radiationless transitions developed by Robinson and Frosch (1963) stresses the Franck-Condon factor. Jortner et al. (1969) have extensively reviewed the situation from the photochemical viewpoint. 

Hamiltonians expressed in matrix forms have been extensively employed in the theory of radiationless transitions of electronically excited states of larger molecules (Bixon and Jortner, 1968 Schlag et al., 1971 Freed, 1972 Nitzan et al., 1972 Avouris et al., 1977 Jortner and Levine, 1981 Felker and Zewail, 1988 Seel and Domcke, 1991). 

Radiationless transitions have an associated rate constant (/ radiationless) intcrsystcm crossings have a corresponding rate constant (/ crossing) and fluorescence is characterized by its own rate constant, designated here as / fluorescence [Each of these competing events are first-order relaxation processes. See Chemical Kinetics (9. Relaxation Kinetics)] A photo-excited molecule rarely re-emits every photon by fluorescence, and the quantum yield is the ratio of the number of photons produced by fluorescence to the number of photons originally absorbed. Accordingly, the quantum yield (f) is formally... 

An analytical theory for the study of CC of radiationless transitions, and in particular, IC leading to dissociation, in molecules possessing overlapping resonances is developed in Ref. [33]. The method is applied to a model diatomic system. In contrast to previous studies, the control of a molecule that is allowed to decay during and after the preparation process is studied. This theory is used to derive the shape of the laser pulse that creates the specific excited wave packet that best enhances or suppresses the radiationless transitions process. The results in Ref. [33] show the importance of resonance overlap in the molecule in order to achieve efficient CC over radiationless transitions via laser excitation. Specifically, resonance overlap is proven to be crucial in order to alter interference contributions to the controlled observable, and hence to achieve efficient CC by varying the phase of the laser field. 

The radiationless transitions are indicated by wavy lines with the corresponding rate constants or lifetimes. The rates of thermalization of a dye molecule after an absorptive or emissive transition, namely k in the excited singlet state Si and k" in the ground state So, axe so fast that they have not yet been reliably measured. From indirect evidence they are believed to be k k" rs 1012 — 1013 sec-1. The rate 21 °f radiationless internal conversion from S2 to Si has recently been measured for several dyes and was found to be in the range kzi = 1011 —1012 sec-1 5>6 While has not yet been measured directly, there is no reason to believe that it should be much different from A 21, and indirect evidence seems to... 

The authors believe that the decreases in decay times are associated primarily with changes in quantum yield. This may be inferred from the fact that both the emission intensities and lifetimes are falling off at about the same rate with temperature. One thus concludes that the luminescence of sulfuric acid solutions of terbium sulfate is subjected to much greater temperature quenching than the luminescence in aqueous solution of the same salt. The increasing probability of radiationless transitions is undoubtedly connected in some manner with greater interaction of the radiating ion with the solvent molecules. 

The selection rules for radiationless transitions are just the opposite of those for radiative transitions. The nuclear kinetic operator is symmetric. The symmetric aromatic molecules normally have symmetrical ground state and antisymmetrical excited state. Therefore, allowed transitions are ... 

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. 

Figure 18-13 Physical processes that can occur after a molecule absorbs an ultraviolet or visible photon. S0 is the ground electronic state. S, and T, are the lowest excited singlet and triplet electronic states. Straight arrows represent processes involving photons, and wavy arrows are radiationless transitions. R denotes vibrational relaxation. Absorption could terminate in any of the vibrational levels of S,. not just the one shown. Fluorescence and phosphorescence can terminate in any of the vibrational levels of Sq.

Fluorescence and phosphorescence are relatively rare. Molecules generally decay from the excited state by radiationless transitions. The lifetime of fluorescence is always very short (10-8 to 10-4 s). The lifetime of phosphorescence is much longer (10-4 to 102 s). Therefore, phosphorescence is even rarer than fluorescence, because a molecule in the T] state has a good chance of undergoing intersystem crossing to S0 before phosphorescence can occur. 

Radiationless transitions among electronic states of molecules represent a class of relaxation processes that are electronic in nature. The general term electronic relaxation appears to be appropriate for these processes,23 but it is convenient to divide those transitions involving a change in the bound electronic states of a molecule into two categories Transitions between states of the same multiplicity, referred to as internal conversion, and transitions between states of different multiplicity, referred to as intersystem crossing. Although there are several early experimental... 

Parameters Descriptive of Radiationless Transitions in Large Molecules... 

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