Transition moment, for

Having assigned symmetry species to each of the six vibrations of formaldehyde shown in Worked example 4.1 in Chapter 4 (pages 90-91) use the appropriate character table to show which are allowed in (a) the infrared specttum and (b) the Raman specttum. In each case state the direction of the transition moment for the infrared-active vibrations and which component of the polarizability is involved for the Raman-active vibrations. 

The Franck-Condon approximation (see Section 7.2.5.3) assumes that an electronic transition is very rapid compared with the motion of the nuclei. One important result is that the transition moment for a vibronic transition is given by... 

Shang, Q., X. Dou, and B.S. Hudson. 1991. Off-axis orientation of the electronic transition moment for a linear conjugated polyene. Nature 352 703-705. 

From the sensing point of view, the adiabatic design is superior to any nonadiabatic systems because of its strong mixing between LE and CT states, resulting in a large transition moment for CT emission. Thus, the contrast of the on/off signal based on the intensity ratio for LE versus CT is remarkable. Conversely, the CT... 

The absorption intensity can then be expressed as the square of the transition moment. For example, the normalized intensity ratio of the second lowest to the... 

The optical transition moments for vibrational or electronic transitions between defect states have specific orientations with respect to the defect coordinates. The absorption strength of polarized light for each of the differently oriented centers is proportional to the square of the component of the transition moment that is along the polarization direction. Hence, a stress-induced redistribution of the defects among their different orientations will be detected as an anisotropy in the polarized optical absorption. A convenient measure of the anisotropy is the dichroic ratio, defined as... 

As the number of silicon atoms in the delocalized backbone cr-electron system increases, the number of HOMO and LUMO states increases, resulting in a band structure for high molecular weight polymers. Electronic absorptions from the HOMO (cr) to LUMO (essentially a ) are responsible for the characteristic UV absorption of polysilanes observed between 300 and 400 nm, the transition moment for which is in the direction of the Si chain.198 Polysilanes are... 

In this section, we report calculated values of the vibrational transition moments for vibrational transitions where V2 is the inversion mode, ... 

The diagrams of bond transition moments for the three excited states of 1 are given in Fig. 3. The comparison with the bond transition moment diagrams of the all-trans-hexaene (right hand side of Fig. 3) explains readily two intensity features peculiar to 1 ... 

A general theory of dichroism induced by strain in polymeric networks Is developed by adaptation of methods developed earlier for treating strain birefringence. It is generally applicable to dichrolc bands associated with any specified conformation involving sequences of one or more consecutive bonds. The transition dipole moment is introduced in the local framework of the skeletal bonds associated therewith. Possible differences in transition moments for various conformations and repeat units are taken into account. Numerical calculations for PE chains show gauche bonds, rather than trans, to be more favorably oriented with respect to the chain vector r. 

Figure 3.6 Graphical integration of transition moment for Is - 2s and Is - 2p transition to emphasize the selection rule M 0 for an allowed...

Finally, the interaction between the dipole and quadrupole of donor and acceptor molecules [13] is generally much weaker than the dipole-dipole interaction. The dipole—quadrupole term [/ (r) r-8] is typically 10—100 times weaker than the dipole—dipole term, though if the acceptor absorption spectrum is symmetry-forbidden (and so weak) but not spin-forbidden, the dipole transition moment for the acceptor is small [127]. Such is the case for energy transfer between rare-earth ions in tungstates typically separated by 1.7 nm [146]. The kinetics of dipole—quadrupole energy transfer are discussed in Chap. 4, Sect. 2.6. 

For polyatomic molecules, (7.2) and (7.6) give the wave numbers and transition moment for an electronic transition. Besides the S selection rule (7.7), there are electronic selection rules stating between which electronic symmetry species transitions are allowed these are derived using group theory (Section 9.11). Equation (7.13) applies to polyatomics, except that Pei is now a function of the 3N —6 (or 3Af —5) normal coordinates Qr... 

In fluid solutions only the third mechanism is of importance in transfer of triplet excitation. The trivial mechanism is usually excluded because most molecules do not phosphoresce in solution, and the second mechanism seems to be excluded because the transition moments for the T - S process in the donor and the T - S transition of the acceptor should both be vanishingly small. An interesting possibility which has yet to be explored experimentally is that heavy atom-containing solvents might so enhance T <- S transition probabilities that long-range triplet energy transfer may become important. 

A calculation of the oscillator strength of the y band was made by Erkovich.130 Using low-pressure absorption spectra, he obtained a value of0.043. This result is about 20 times as great as from other measurements, and the method used has been severely criticized by Penner.342 Erkovich and Pisarevskii,131 using a modification of Erkovich s method, calculated the electronic transition moments for the / and y systems. Because their computations were, as before, based on low-pressure absorption spectra, Penner s criticism still applies. 

In Sponer s treatment the probability for internal conversion from the zeroth vibrational level of a state S, to the isoenergetic vibrational level of a state St(i = j — 1) was assumed to be proportional to the ratio of the transition moments for absorption from the ground state to the corresponding levels. 

The study of oriented polymers with polarized infrared radiation is an equally important tool in the detailed analysis of the vibrational spectrum, since it permits us, within certain restrictions, to determine the orientation (with respect to the molecular structure) of the transition moment for a given normal mode. This makes it possible, as we shall see, not only to classify bands in the spectrum but to establish their origin. Although polarizers are available with commercial spectrometers, their use has not yet become as general as would be desirable. Some comments... 

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