Radiationless transitions states

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. ... 

Figure lb shows a four-level system. The terminal level, level 2, is ordinarily empty. Atoms are optically pumped to level 4. From level 4, the atoms make a rapid radiationless transition to level 3. The first few atoms to arrive begin to contribute to the population inversion. Therefore, laser operation can begin with much less intense pumping light. After the laser transition, the atoms return to the ground state (level 1) by a radiationless transition. 

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. 

Because of the dense spectrum of the highest vibrational sublevels and their rapid vibrational relaxation in the A2 state, this radiationless transition (RLT) is irreversible and thus it may be characterized by a rate constant k. The irreversibility condition formulated by Bixon and Jortner [1968] reads... 

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

If certain quanta suitable for the excitation of a line are absorbed without photon emission, a radiationless transition is likely. This transition is known as the Auger effect,39 and it may be thought to involve an absorption by the atom of the photon produced when the hole in the K shell is filled by an electron from one of the external shells such as the L shell. The absorption of this photon results in the ejection of a second electron from one of the shells to leave a doubly charged residue of what had been a normal atom. The atom in this condition is described by naming the two states in which the electron holes are to be found e.g., the atom is in the LL or LM or LN state. An atom in such a state is, of course, vastly different from the usual divalent cation. 

In the theory of radiationless transitions as covered in this paper (6,4g), the two non BO terms are treated as perturbations (not externally plied, but arising as imperfections within this model of molecular structure) that can induce transitions between unperturbed states each of which is taken to be a specific Bom-Oppenheimer product state ... 

Let us now consider how similar the expression for rates of radiationless transitions induced by non Bom-Oppenheimer couplings can be made to the expressions given above for photon absorption rates. We begin with the corresponding (6,4g) Wentzel-Fermi golden rule expression given in Eq. (10) for the transition rate between electronic states Ti,f and corresponding vibration-rotation states Xi,f appropriate to the non BO case ... 

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. 

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... 

In Chapters 4 and 5 we made use of the theory of radiationless transitions developed by Robinson and Frosch.(7) In this theory the transition is considered to be due to a time-dependent intramolecular perturbation on non-stationary Bom-Oppenheimer states. Henry and Kasha(8) and Jortner and co-workers(9-12) have pointed out that the Bom-Oppenheimer (BO) approximation is only valid if the energy difference between the BO states is large relative to the vibronic matrix element connecting these states. When there are near-degenerate or degenerate zeroth-order vibronic states belonging to different configurations the BO approximation fails. 

Figure 6.11. Electronic transitions to the first excited singlet (s) and lowest triplet (0 states from the ground states (g) of benzophenone (B) and naphthalene (N) moieties in compounds (4), n = 1-3. Possible radiative transitions are represented by straight arrows, radiationless transitions by wavy arrows.(80> Reprinted by permission of the American Chemical Society.

The development of comprehensive models for transition metal carbonyl photochemistry requires that three types of data be obtained. First, information on the dynamics of the photochemical event is needed. Which reactant electronic states are involved What is the role of radiationless transitions Second, what are the primary photoproducts Are they stable with respect to unimolecular decay Can the unsaturated species produced by photolysis be spectroscopically characterized in the absence of solvent Finally, we require thermochemical and kinetic data i.e. metal-ligand bond dissociation energies and association rate constants. We describe below how such data is being obtained in our laboratory. 

The palladium phthalocyanine (67), developed by Mitsui Toatsu and Ciba58,59 is one of the leading phthalocyanine infrared absorbers for CD-R (Compact Disk-Rewritable) (see Chapter 9.13). Bulky groups (R) reduce undesirable molecular aggregation, which lowers the extinction coefficient and hence the absorptivity and reflectivity. Partial bromination allows fine tuning of the film absorbance and improves reflectivity. The palladium atom influences the position of the absorption band, the photostability and the efficiency of the radiationless transition from the excited state.58 It is marketed by Ciba as Supergreen.60... 

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. 

To get a rough idea of the rate of radiationless transition from higher excited states, consider the quantum yield of fluorescence from that state as the ratio of nonradiative (t ) to radiative (t ) lifetimes as follows ... 

The radiationless transition between two states of same spin is called internal conversion, the one occuring with inversion of spin being termed intersystem crossing. In both processes the excess energy is liberated as heat. All these transitions between different electronic states are customarily preceded by vibrational relaxation, i.e. the deactivation from a higher vibronie level to the v0-level of the same electronic state (Fig. 5). 

This case is shown in Fig. 10.6c and d where through absorption of light a photohole in the vb and a photoelectron in the cb are formed. The probability that interfacial electron transfer takes place, i.e. that a thermodynamically suitable electron donor is oxidized by the photohole of the vb depends (i) on the rate constant of the interfacial electron transfer, kET, (ii) on the concentration of the adsorbed electron donor, [Rads]. and (iii) on the rate constants of recombination of the electron-hole pair via radiative and radiationless transitions,Ykj. At steady-state of the electronically excited state, the quantum yield, Ox, ofinterfacial electron-transfer can be expressed in terms of rate constants ... 

Internal conversion Involves radiationless transitions between vibronic states of the same total energy (isoenergetic states) and the same multiplicity. Internal conversion between excited states, e.g. S2-Wr> Si is much faster than internal conversion between Si and S0... 

Intersystem crossing Intramolecular spin-forbidden radiationless transitions between isoenergetic states of different multiplicity, e.g. SrWr Ti... 

Radiationless transitions (internal conversion and intersystem crossing) between electronic states are isoenergetic processes and are drawn as wavy arrows from the v = 0 level of the initial state to a vibrationally-hot (v > 0) level of the final state. 

Intersystem crossing involves intramolecular spin-forbidden radiationless transitions between isoenergetic states of different multiplicity, for example Si(v = 0) -Wr T v = n). Si AWr Ti intersystem crossing has a timescale of the order of KTn-l(T8s. 

The excited singlet-state radiative lifetime, o, of Si is the lifetime of Si in the absence of any radiationless transitions that is, the only... 

Understand that intermolecular radiationless transitions of excited states are caused by a breakdown of the Born-Oppenheimer approximation. 

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. 

In Chapters 2 and 4, the Franck-Condon factor was used to account for the efficiency of electronic transitions resulting in absorption and radiative transitions. The efficiency of the transitions was envisaged as being related to the extent of overlap between the squares of the vibrational wave functions, /2, of the initial and final states. In a horizontal radiationless transition, the extent of overlap of the /2 functions of the initial and final states is the primary factor controlling the rate of internal conversion and intersystem crossing. 

The variations in efficiency (rate) of radiationless transitions result from differences in the Franck-Condon factor, visualised by superimposing the vibrational wavefunctions, / (or /2 - the probability distributions), of the initial and final states. We will consider three cases illustrated in Figure 5.2. 

Figure 5.2 Overlap of /2 functions for a radiationless transition between the initial (i) and final (f) electronic states...

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