Transition moment polarization

Figure 7.7 Rotational fine structure of the 0 absorption band in aniline vapor. The experimental rotational contour is shown at top the theoretical simulations labeled (b), (c), and (d) were generated using identical rotational constants, but assumed 0 transition moments polarized along theib, a. and c principal rotational axes, respectively. This work established that the S, - transition in aniline is polarized along the b axis (Fig. 7.8), or equivalently, y-polarized (cf. Fig. 7.5). Reproduced by permission from J. Christofferen, J. M. Hollas, and G. H. Kirby, Mol. Phys. 16, 441 (1969).

Figure 6.22 Symmetry species of some overtone and combination levels of H2O together with directions of polarization of transition moments. The vibration wavenumbers are cO] = 3657.1 cm a>2 = 1594.8 cm m3 = 3755.8 cm ...

Acetylene (HC=CH) belongs to the point group whose character table is given in Table A.37 in Appendix A, and its vibrations are illustrated in Figure 6.20. Since V3 is a vibration and T T ) = 2"+, the 3q transition is allowed and the transition moment is polarized along the z axis. Similarly, since Vj is a vibration, the 5q transition is allowed with the transition moment in the xy plane. 

The three bands in Figure 9.46 show resolved rotational stmcture and a rotational temperature of about 1 K. Computer simulation has shown that they are all Ojj bands of dimers. The bottom spectmm is the Ojj band of the planar, doubly hydrogen bonded dimer illustrated. The electronic transition moment is polarized perpendicular to the ring in the — Ag, n — n transition of the monomer and the rotational stmcture of the bottom spectmm is consistent only with it being perpendicular to the molecular plane in the dimer also, as expected. 

For films on non-metallic substrates (semiconductors, dielectrics) the situation is much more complex. In contrast with metallic surfaces both parallel and perpendicular vibrational components of the adsorbate can be detected. The sign and intensity of RAIRS-bands depend heavily on the angle of incidence, on the polarization of the radiation, and on the orientation of vibrational transition moments [4.267]. 

A powerful characteristic of RAIR spectroscopy is that the technique can be used to determine the orientation of surface species. The reason for this is as follows. When parallel polarized infrared radiation is specularly reflected off of a substrate at a large angle of incidence, the incident and reflected waves combine to form a standing wave that has its electric field vector (E) perpendicular to the substrate surface. Since the intensity of an infrared absorption band is proportional to / ( M), where M is the transition moment , it can be seen that the intensity of a band is maximum when E and M are parallel (i.e., both perpendicular to the surface). / is a minimum when M is parallel to the surface (as stated above, E is always perpendicular to the surface in RAIR spectroscopy). 

Intermediate methods include the earliest procedure based on Stein s equation [33] and one based on Samuels equation [34]. Among the direct methods is an IR spectroscopic method based on the measurement of the dichroic ratio (R), of amorphous absorption bands. In the investigations [35], the amorphous bands 898 cm" and 1368 cm", for which the angles of transition moment are a898 = 39 and aneg = 80 , respectively, were used. Other methods are spectroscopy of polarized fluorescent radiation [35,36], measurement of color di-... 

The form of the Plmn will be discussed later, because it is instructive to develop the argument by considering next the information which is obtained from any spectroscopic technique. Figure 2a shows a direction within a unit of structure which is defined by the polar and azimuthal angles (, r ). For example, this could be the direction defining the change in dipole moment (the transition moment vector) in an infra-red spectroscopic measurement. The spectroscopic measurements provide... 

We now report that in the region of the absorption band the flow linear dichroism of a solution of 1 is positive (Fig. 3). Assuming that the nature of the flow orientation is of the usual kind, i.e., that the polymer chains in a random coil conformation which dominates in solution (34) tend to align with the flow direction, this observation provides additional support for the absolute assignment of the transition moment direction along the chain direction, even in solution. Similar conclusions based on polarization studies on a stretched film of poly(di-n-hexyl silane) have recently been reported (36). 

The values of P range from + to — (0 = 0 or 90°). This equation would be considerably simpler if only those molecules with their transition moments parallel to the electric vector were capable of absorption or if the molecules were perfectly aligned, that is, 0 = 0. Then the angle between the two transition moments could be directly determined from the observed degree of polarization P. 

Normal incidence transmission IRLD measurements are used to study thin films (typically 100 pm thickness and less, depending on the molar extinction coefficient of the bands) with in-plane uniaxial orientation. Two spectra are recorded sequentially with the radiation polarized parallel (p) and perpendicular (s) to the principal (machine) direction of the sample. The order parameter of the transition moment of the studied vibration is calculated from either the dichroic ratio (R — Ap/As) or the dichroic difference (AA = Ap—As) as ... 

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... 

In the normal-incident transmission measurements of LB films deposited on transparent substrates, the electric vector of the infrared beam is parallel to the film surface (Figure 5A). Therefore, only absorption bands which have the transition moments parallel to the film surface can be detected by this method. On the other hand, in the above-mentioned RA measurements, in which the p-polarized infrared beam is incident upon the LB film prepared on Ag-evaporated substrates at a large angle of incidence, we have a strong electric field perpendicular to the film surface as shown in Figure 5B. Therefore, in this case, only absorption bands which have the transition moments perpendicular to the film surface can be detected with a large intensity enhancement. Thus, if the molecules are highly oriented in the LB films, the peak intensities of particular bands should be different between the transmission and RA spectra. 

The concept of transition moment is of major importance for all experiments carried out with polarized light (in particular for fluorescence polarization experiments, see Chapter 5). In most cases, the transition moment can be drawn as a vector in the coordinate system defined by the location of the nuclei of the atoms4 therefore, the molecules whose absorption transition moments are parallel to the electric vector of a linearly polarized incident light are preferentially excited. The probability of excitation is proportional to the square of the scalar product of the transition moment and the electric vector. This probability is thus maximum when the two vectors are parallel and zero when they are perpendicular. 

If the incident light is linearly polarized, the probability of excitation of a chro-mophore is proportional to the square of the scalar product MA.E, i.e. cos2 0A, 8 being the angle between the electric vector E of the incident light and the absorption transition moment MA (Figure 5.2). This probability is maximum when E is parallel to MA of the molecule it is zero when the electric vector is perpendicular. 

Thus, when a population of fluorophores is illuminated by a linearly polarized incident light, those whose transition moments are oriented in a direction close to that of the electric vector of the incident beam are preferentially excited. This is called photoselection. Because the distribution of excited fluorophores is anisotropic, the emitted fluorescence is also anisotropic. Any change in direction of the transition moment during the lifetime of the excited state will cause this anisotropy to decrease, i.e. will induce a partial (or total) depolarization of fluorescence. 

Let us consider a population of N molecules randomly oriented and excited at time 0 by an infinitely short pulse of light polarized along Oz. At time t, the emission transition moments ME of the excited molecules have a certain angular distribution. The orientation of these transition moments is characterized by 0E, the angle with respect to the Oz axis, and by (azimuth), the angle with respect to the Oz axis (Figure 5.5). The final expression of emission anisotropy should be independent of

[Pg.134]

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