Transition dipole electronic

Fig. 20. A schematic representation of the emission of an isolated large molecule following internal conversion from the second to the first singlet, a" and 6J1 denote the amplitudes of the second singlet and quasi-degenerate vibrational levels of the first singlet, respectively, in the excited molecular state >/in. /v, and m are the corresponding electronic dipole transition matrix elements coupling < >n and as indicated.

Among these, the 612 nm emission from the Dq - 2 electronic dipole transition is dominant. The intensity ratio of Dq - 2 to Dq " Fi transitions is defined as monochromaticity, which is determined by the symmetry environment where europium ion is located the poorer the symmetry environment, the larger will be the monochromaticity. Usually, in the inorganic matrix, for example in YVO3 Eu matrix, the monochromaticity is about one, while in the Eu(DBM)3L complex (see Eigure 11.7) it is larger than ten. Thus a pure saturated red emission can be observed when the europium complexes are used as emitters. 

Since the Franck-Condon factors for all vibrational levels of the excited state add up to unity, the total intensity of a transition is given by the electronic dipole transition moment The resulting intensity distribution of the vibrational fine structure is depicted in Figure 1.13 for some typical cases. 

Table 5 Oscillator strengths of electronic dipole transitions between the five lowest electronic states of the fluorinated benzene cations. An empty entry (—) means that the quantity vanishes by symmetry...

Consider, as before, an initial state >, and let the letter i in Feynman graphs stand for the transition ( — /). We can write the single electron (independent electron) dipole transition as the diagram... 

Am n= Bm n- Thus, the absorption probability can be calculated as Wmn = Bn mp(wmn)- Through quantum-mechanism derivation, the electron-dipole transition optic absorption is Wmn = with the excited state... 

Eu Eu -" is a typical and efficient activator for red-emitting phosphor due to its transitions from the excited Dq level to the Fj (J = 0-4) levels of the 4/ configuration. Its photoluminescence emission strongly depends on the symmetry of the crystal stmcture of Eu " occupied site in the host. The optical transitions of Eu " ions originating from the electronic dipole and magnetic dipole interaction of the internal 4/electrons are deeply affected by the crystal environment. If the Eu " ions occupy the sites with inversion symmetry, the emission will peak at 590-600 nm from the Dq Fi magnetic-dipole transition. This will dominate the emission, which is not affected much by the site symmetry. In contrast, the emission peaks at approximately 610-630 nm, due to the Dq p2 electronic dipole transition, will dominate the emission if the Eu " ion substitutes the site with no inversion symmetry [56], Moreover, Eu -doped phosphors usually have intense intrinsic... 

The first factor is associated with the electronic dipole transition probability between the electronic states the second factor is associated between vibrational levels of the lower state v" and the excited state V, and is commonly known as the Franck-Condon factor, the third factor stems from the rotational levels involved in the transition, J" and /, the rotational line-strength factor (often termed the Honl-London factor). In particular, the Franck-Condon information from the spectrum allows one to gain access to the relative equilibrium positions of the molecular energy potentials. Then, with a full set of the spectroscopic constants that are used to approximate the energy-level structure (see Equations (2.1) and (2.2)) and which can be extracted from the spectra, full potential energy curves can be constructed. 

In the calculations of the Rb2 PA, we estimate the -X E+ — electronic-dipole moment to be p, = 3 au. This value corresponds to die 55 i/2(m = 1/2) — 5P3/2(m = 3/2) transition in Rb in a circularly polarized field, and is consistent with all the other 5S - 5P matrix elements for the Rb atom in a polarized laser field. The exact values of the atomic reduced dipole matrix elements can be found in Ref. [92]. The electronic-dipole transition matrix elements in KRb are taken as 3.5 eao fortheXiE+ o- transition, and 0.5 eao for the -o- l n transition, the order-of-magnitude estimate based on the data from Refs. [93,94],... 

Moffit, the electronic dipole transition moments and the optical activity of helical molecules are coupled. The electronic transition 7i° — n occurs at around 190 nm, while that of rii — n occurs at around 225 nm. The actual values, of course, depend on the stmcture of the molecules at specific conditions. They are not exactly at 190 and 225 nm, respectively. Still, it is worthwhile to focus on the curve near these two wavelengths. 

In order to evaluate the vibrational polarizability, Eq. (8.8), one needs the energies of all vibrational states of the electronic ground state and the corresponding vibrational dipole transition moments, which requires knowledge of the potential energy and electric dipole moment surface of this single electronic state. For the electronic-vibrational polarizability, Eq. (8.7), however, one would need to know not only all excited electronic states, and the electronic dipole transition moments to them but also all the vibrational states, of these excited states, which makes this... 

For the single proton transfer, the donor-acceptor distance of only one of the two H-chelate rings has to be compressed. This is achieved by an antisymmetric bending motion. This example demonstrates that different reaction channels result in different coherent wavepacket dynamics. BP(OH)2 exhibits inversion symmetry, and direct optical excitation of the antisymmetric bending mode is not possible because of selection rules for electronic dipole transitions [74]. This proves that the observed coherent wavepacket motions result from ultrafast intramolecular reactions. 

The integer k mns in the range 0-7 and the parameters containing even values of k are responsible for the crystal field splitting, while those with odd values influence the intensity of the induced electronic dipole transitions (see Section 1.3.10 for more details) [8,9]. q is also an integer and its values depend on the symmetry of the crystal field and the magnitude of k, since < k. The possible combinations of k and q for the crystal field parameters are given in Table 1.6 and the symmetry elements contained in the crystal field parameters are summarised in Table 1.7. 

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