Probability of electronic transition

On the basis of qualitative reasoning we might think that the probability of charge exchange per unit time, W(p), is proportional to the probability of electron transition through the potential barrier (Fig. 5), i.e. 

As we have seen, the line and oscillator strengths as well as the probabilities of electronic transitions between configurations of any type are expressed in terms of the submatrix elements of the appropriate operators. These submatrix elements may be found in a similar way as for the energy operator (see Part 5). Therefore, further on we shall consider only submatrix elements and present only final results. It is convenient to write the submatrix element of the non-relativistic operators of E/c-radiation (4.12) and (4.13) for transitions of the type (25.2), namely Zf Z2 — Zf Z3, as follows ... 

Intensities of absorption bands are governed by probabilities of electronic transitions between the split 3d orbital energy levels. The probabilities are expressed by selection rules, two of which are the spin-multiplicity selection rule and the Laporte selection rule. 

In Experiment 5.2, we saw that the mathematical model describing electronic transitions in solution is Beer s law (A = sbc). Using visible spectroscopy we were able to determine s, the molar absorptivity, which gives us information about the probability of electronic transitions occurring in coordination complexes. Similarly, E° from the Nernst equation (A.2.1) gives us information about redox activity of species in solution, where n is the number of electrons transferred. 

Spectrophotometric methods of identification and determination of substances are based on the existence of relationships between the position and intensity of absorption bands of electromagnetic radiation, on the one hand, and molecular structure on the other. Electronic spectra result from changes in the energy states of electrons [o, ti, and free electron pairs (n)] in a molecule as a result of absorption in the UV-VIS region. The changes depend on the probability of electronic transitions between the individual energy states of the molecule. The number of absorption bands, and their positions, intensities and shapes are the spectral parameters utilized in qualitative and quantitative chemical analyses [1-3]. 

The UV-VIS radiation gives rise to changes in the energy of electronic states of a molecule. The probability of electronic transitions in a molecule depends on the presence of multiple bonds in the molecule and on the kind, number and positions of the substituent groups. Determination of the kind of transitions corresponding to the observed bands of absorption spectra enables one to determine the structure of the molecule. 

Molecules in electronic excited states are highly reactive. The presence of any dissolved oxygen or impurities makes it possible for the excited species to react with oxygen or the impurities, or to dimerize this decreases the probability of electronic transitions to the ground state. Note that fluorescence and phosphorescence are both radioactive decay processes, therefore they are both subject to the sarnie influences the differences that would exist would be the differences in reactions and reactivity of singlet vs. triplet states. 

The position and intensity of the absorption bands for the 2,4,6-triaminobenzenium ion and its analogue ate sununari in Table 35 the molomlar-orbital calculations for the energies and probabilities of electron transitions for ions of this type can be found in... 

The probability of electronic transitions across the band gap is higher in materials with a direct band gap and this results in higher efficiency in devices such as lasers and LEDs. 

The probability of a transition —>/resulting from any external perturbation which impulsively transfers momentum q to the internal momenta of the electrons of the target system is... 

The physical picture of the transition is different here from that for nonadiabatic reaction. Equation (34.34) shows that the probability of electron transfer becomes equal to 1 when the acceptor energy level passes a small energy interval Ae 1/(2jiYlzP) near the Fermi level. However, unUke the nonadiabatic case,... 

The ro-vibronic spectrum of molecules and the electronic transitions in atoms are only part of the whole story of transitions used in astronomy. Whenever there is a separation between energy levels within a particular target atom or molecule there is always a photon energy that corresponds to this energy separation and hence a probability of a transition. Astronomy has an additional advantage in that selection rules never completely forbid a transition, they just make it very unlikely. In the laboratory the transition has to occur during the timescale of the experiment, whereas in space the transition has to have occurred within the last 15 Gyr and as such can be almost forbidden. Astronomers have identified exotic transitions deep within molecules or atoms to assist in their identification and we are going to look at some of the important ones, the first of which is the maser. 

The total rate of electron transfer is calculated by summing over the probability of the transitions for the multiple passes of the system through... 

The induced magnetic dipole moment has transformation properties similar to rotations Rx, Rt, and Rz about the coordinate axes. These transformations are important in deducing the intensity of electronic transitions (selection rules) and the optical rotatory strength of electronic transitions respectively. If P and /fare the probabilities of electric and magnetic transitions respectively, then... 

Experimentally, S02 shows a region of absorption from ca. 2400 to 1800 A ca. 2000 A). Its maximum molecule extinction coefficient is several times that of the 3400— 2600-A system. Duchesne and Rosen (J. Chem. Phys., 1947, 15, 631) have shown, by vibrational analysis, that at least two and probably three electronic transitions arc involved in the region. The first of these has its origin at 42,170 cm.-1 (2371 A), the vibrational frequencies appearing in the upper state being 963 (symmetrical stretching)... 

The cross-section of electron transfer to a multiply charged ion can be calculated by solving a set of coupled equations which take into account the probability of electron transfer on to different levels. Such calculations are extremely tedious (for a review, see ref. 21). At the same time, the presence of transitions into a large number of states makes it possible to describe the charge transfer in terms of the formalism, based on the idea of electron tunneling from one potential well to another. Using such an approach, Chibisov [22] has obtained an analytical expression for the charge transfer cross-section. 

Here t is the time elapsed from the moment the light is switched on, z 1 is the probability of the transition of an electron to a quasi-free (mobile) state per unit time under the action of light, Rz = (ae/2)lnver is the distance of electron tunneling from a trap to an acceptor within the time z. 

Owing to a relatively high (compared with molecules in the ground electron state) probability of electron tunneling for excited molecules, this process, at sufficiently short distances between the excited molecules and the particles of electron acceptors, can compete with the ordinary over-barrier electron transfer (see the scheme in Fig. 9). In practice this effect manifests itself in the transition, as the concentration of acceptor rises, from the usual... 

H. H. Michels, Theoretical Determination of Electronic Transition Probabilities for Diatomic Molecules , technical report No. AFWL-TR-72-1, 1972. 

Line and multiplet strengths are useful theoretical characteristics of electronic transitions, because they are symmetric, additive and do not depend on the energy parameters. However, they are far from the experimentally measured quantities. In this respect it is much more convenient to utilize the concepts of oscillator strengths and transition probabilities, already directly connected with the quantities measured experimentally (e.g. line intensities). Oscillator strength fk of electric or magnetic electronic transition aJ — a J of multipolarity k is defined as follows ... 

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