Transition, radiative forbidden

As shown in Example 5.2, magnetic dipole transitions are much weaker than electric dipole transitions. Nevertheless, when a radiative transition is forbidden by an electric dipole process, it may happen due to a magnetic dipole process. In fact. 

The following conclusion of the theory (1 ) is extremely important. The radiative transition 2 > Sq in a sandwich dimer is forbidden. In case of a dimer of 04 symmetry, the transition 2 (4Eg) > Sg (A g) is forbidden because of parity. There is no principle difference in the splitting nature of 2 and states for sandwich type dimers with lesser than D4h symmetry and the 2 > Sq transition remains quasi forbidden. This makes it possible to explain low P2 values obtained in (1 ) by a decrease of the 2 > Sg transition radiative probability, i.e., by decreasing or 2 > Sq fluorescence quantum yield in dimeric TTA complexes. In the case of non-sandwich dimer structures with location of subunits in one plane, the So state also is split into two states (high 202y and low 2B3g). However, two radiative transitions S2(B2y)... 

SELECTION RLILES (Energy Levels). It was found early in the. study of atomic spectra that radiative transitions between certain pairs of energy levels seldom or never occur. A set of rules which are expressed in terms of the differences of the quantum numbers of the two states involved allow a prediction of allowed transitions and forbidden transitions. The conditions for allowed transitions are ... 

First approximation theory leads to certain wave mechanical selection rules on the basis of which a radiative electronic transition may be classified as allowed (high probability) or forbidden (vanishingly low probability). Some forbidden transitions are indeed too weak to observe easily but in actual practice with polyatomic molecules the selection rules often break down sufficiently to permit reasonably strong absorption processes to occur. The following kinds of transition are forbidden... 

Of course H2 is by far more abundant, but its rotational transitions cannot be excited in the cold parts of the interstellar medium. For H2, electric dipole transitions are forbidden, because no dipole moment exists in the molecule in this state. Transitions occur via electric quadrupole interaction, and only AJ = 2 transitions occur. The least energetic transition in H2, the excitation J = 0 — J = 1, occurs at an energy equivalent to 510 K. We want now to study the influence of radiative transfer effects on the radiative cooling by CO. 

Direct semiconductors have strongly allowed optical transitions, with relatively short radiative rate constants and thus short-lived excited states, which can be highly emissive following excitation. For indirect semiconductors optical transitions are forbidden, absorption coefiftcients are low, they have relatively long radiative lifetimes and therefore potentially long-lived excited states, and deactivation after excitation is not usually emissive. 

Weber and Laurence (1953) have described a series of substances that although completely nonfluorescent in water solution become strongly fluorescent on adsorption by native serum albumin, denatured ovalbumin, filter paper, or alumina. They are also spontaneously fluorescent in certain solvents. These substances are derivatives of 3-chloro-6-meth-oxy-9-aminoacridine or of one of several aminonaphthalene sulfonic acids, in which one of the amino hydrogens has been substituted by a benzene ring derivative. The explanation of the behavior on adsorption lies apparently in that the radiative transition is forbidden for the nonplanar molecule but is allowed when the molecule lies on a plane as it presumably does on adsorption. This is extensively discussed by Forster (1951). Although the causes of the phenomenon are interesting in themselves, its practical applications may be of importance. Laurence and Rees (1953) have developed a method for the rapid and accurate determination of albumin in blood serum by fluorimetry using 1 N phenyl-aminonaphthalene-5 sulfonic acid. The detection of ovalbumin dena-turation by this method also deserves consideration. The appearance of fluorescence on adsorption of auramin O by nucleic acids has been described by Oster (1951). 

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. ... 

As stated in Chapter 1, transitions involving a change in multiplicity are spin forbidden. However, for reasons which we will consider later, such transitions do indeed occur although with very low transition probabilities in most cases. The intensity of an absorption corresponding to a transition from the ground state S0 to the lowest triplet state Tx is related to the triplet radiative lifetime t ° by the following equation[Pg.114]

A third possible channel of S state deexcitation is the S) —> Ti transition -nonradiative intersystem crossing isc. In principle, this process is spin forbidden, however, there are different intra- and intermolecular factors (spin-orbital coupling, heavy atom effect, and some others), which favor this process. With the rates kisc = 107-109 s"1, it can compete with other channels of S) state deactivation. At normal conditions in solutions, the nonradiative deexcitation of the triplet state T , kTm, is predominant over phosphorescence, which is the radiative deactivation of the T state. This transition is also spin-forbidden and its rate, kj, is low. Therefore, normally, phosphorescence is observed at low temperatures or in rigid (polymers, crystals) matrices, and the lifetimes of triplet state xT at such conditions may be quite long, up to a few seconds. Obviously, the phosphorescence spectrum is located at wavelengths longer than the fluorescence spectrum (see the bottom of Fig. 1). 

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 lifetime of the singlet excited state (the fluorescence lifetime TF) is of the order of picoseconds to 100 nanoseconds (10—12 - 10-7 seconds) and can now be measured accurately using pulsed laser excitation methods and other techniques. Since the radiative transition from the lowest triplet state to the ground state is formally forbidden by selection rules, the phosphorescence lifetimes can be longer, of the order of seconds. 

Phosphorescence Photon emission. Phosphorescence involves a spin-forbidden radiative transition between states of different multiplicity, usually from the lowest vibrational level of the lowest excited triplet state, Tt. Ti(v = 0) - S0 + hv... 

Phosphorescence arises as the result of a radiative transition between states of different multiplicity, Ti —> So. Since the process is spin-forbidden, phosphorescence has a much smaller rate constant, kp, than that for fluorescence, kf ... 

Since the photon emitted by D is absorbed by A, the same rules will apply to radiative energy transfer as to the intensity of absorption. Because singlet-triplet transitions are spin-forbidden and singlet-triplet absorption coefficients are usually extremely small, it is not possible to build up a triplet state population by radiative energy transfer. For this... 

In solution at room temperature, non-radiative de-excitation from the triplet state Ti, is predominant over radiative de-excitation called phosphorescence. In fact, the transition Ti —> S0 is forbidden (but it can be observed because of spin-orbit coupling), and the radiative rate constant is thus very low. During such a slow process, the numerous collisions with solvent molecules favor intersystem crossing and vibrational relaxation in So-... 

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