Polarization, of transition moment

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 ...

Polarization of transition moment perpendicular to the molecular plane in the molecular plane perpendicular to the molecular plane... 

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 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. 

With vertically polarized exciting light, p0 — when p = 0. But when P = n/2, p0 becomes negative and is equal to —1/3. The values are +1/3 and—1/7 for unpolarized radiation. Thus negative polarization appears when 6 is small, i.e. absorption probability is high and the transition moment in emission is perpendicular to that in absorption. These observations provide a suitable method for assigning the polarization directions of transition moments in different absorption bands of a given molecule from polarization of the fluorescence excitation spectra. 

Equation (11.1) indicates that values of P occur between 1 (I = 0) and —1 (I = 0). Natural or unpolarized light, where I = I, yields a P value of 0. These two extreme values of P are observed when the polarized absorption transition moment and that of the emission are colinear (7j = 0) or perpendicular (I = 0). However, in a rigid medium where motions are absent, the absorption and emission transition dipoles can be oriented by an angle 9, one relative to the other. 

F . 3. Polarization of fluorescence in isolated chromophore as function of orientation angle e of transition moment with respect to plane of polarization of exciting radiation (i) e = 0°, (ii) e = 45 . tiii) e = 90 ... 

The elements of transition moment tensors reflect the symmetry of the states involved, so even the allowed transitions can be observed only if the polarization of the photons in the molecular frame matches the nonzero components of the tensor. A major difference with respect to one-photon spectroscopy lies in the fact that this dependence on polarization does not vanish upon averaging over all orientations, and two-photon measurements on isotropic samples such as liquid solutions provide polarization information. 

The orientation of transition moments in the molecular framework can be predicted by quantum mechanical calculations (Sections 2.1.4 and 4.4). Experimentally, the direction of transition moments can be assessed by studying the absorption of linearly polarized light by samples in which the molecules are preferentially oriented. Complete orientation is available in single crystals. However, optical measurements on single crystals are demanding and rarely practicable, not least because extremely thin crystals are required for absorption studies. 

Fig. 6.1 S left) and R (right) enantiomers of DCPH. The directions of transition moments (jilg and (tHG of an R enantiomer are shown as weU as those of photon polarization vectors e defined asfii Q-e = The magnitudes of p, LG and (iHG are 2.02euo and 1.63eoo, respectively...

Polarized infrared radiation is used to obtain information about the direction of transition moments of normal modes of vibration in solid oriented compounds. If one knows the molecular orientation in a solid, he can use polarization studies in making band assignments. (See Chapters 6 and 10 for such applications in carbohydrate and polypeptide chemistry.) The measured direction of the transition moment of the vibration producing a band must coincide with the direction deduced from the structure if the assignment is correct. On the other hand, knowing the band assignment but not the molecular orientation in the solid, one can deduce some knowledge of the molecular orientation. 

If symmetry constrains the directions of transition moments and the principal axes of the orientation tensor to the symmetry axes x, y, z, the results are the simplest. If the first photon is absorbed in a transition purely polarized along u and the second is absorbed or emitted in a transition purely polarized along the degree of anisotropy shows a double exponential decay in time ... 

Figure 16 Distribution of the transition moment /W of a particular vibration in a uniaxially oriented polymer (f, electric vectors of the incoming polarized radiation 9, angle of polymer chain axis with the draw direction j/, angle of transition moment with the polymer chain axis).

The polarization properties of single-molecule fluorescence excitation spectra have been explored and utilized to detennine botli tlie molecular transition dipole moment orientation and tlie deptli of single pentacene molecules in a /7-teriDhenyl crystal, taking into account tlie rotation of tlie polarization of tlie excitation light by tlie birefringent... 

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). 

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