Polarization of Electronic Transitions

From Equation (1.33) it is seen that the transition moment is a vector quantity. The square of its absolute value determines the transition probability, whereas its direction is called the polarization direction. If one of the principal axes of a molecule is the long axis, the transition as well as the corresponding absorption band is often called parallel or long axis polarized if the direction of the transition moment vector is perpendicular to the long axis, the transition and the absorption band are called perpendicular or short-axis polarized. The longest wavelength transition of s-cis-buta- 

The polarization direction can be measured by investigating oriented molecules, most often with polarized light. From Equation (1.32) the oscillator strength /o r is seen to be proportional to the squared scalar product of the transition moment and the electric field vector of the light. The absorption reaches its maximum if the direction of the transition moment and the polarization direction of the light coincide, whereas no light is absorbed if they are perpendicular to each other. 

From Equation (1.32) it is seen that for the extinction coefficient, which is proportional to the absorption cross section, one obtains 

So- r is fh two-photon transition moment tensor that can be visualized as a (3 X 3) matrix with elements (So r)a which contain the sums of the products If the ground state % s of even (g) parity the inter- 

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. 

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Figure 3. Polarization of electronic transitions in a flat a-helix vs. a flat irregular structure.

The absorption spectra of oriented and amorphous films of naphthacene, pentacene, perylene, and coronene,169 the polarization of electronic transitions in coronene, pentahelicene, and hexahelicene,160 electronic spectra of perylene and... 

The origin of FA is the polarization of electronic transition of molecules to each transition is associated a vector called transition moment (see Sect. 1.5) which as a given orientation with respect to the molecular structure, In Fig. 6.15, the absorption transitions Sq —> 5i and 5o —> S2 of perylene are depicted. Transition 5i —> Sq responsible for the fluorescence is almost parallel to 5q —> 5i. In general, when the deactivation of an excited state takes place radiatively, the emitted photon is polarized parallel to the transition moment. Hence, if a single molecule is observed, the polarization of the emitted light is parallel to the direction defined by the transition responsible for the fluorescence. 

The stepwise reduction method was proposed by Thulstrup and Eggers [5] as an efficient development of the differential approach. Initially, this method was employed for the determination of the polarization of electron transitions. Later, Michl and Radziszewski [72] adapted it for processing IR-LD spectra of compounds, oriented within a poly(ethylene) matrix. Generalized analysis of both the theory and application of this method was made by Jordanov [16,19]. 

We now discuss the annular tautomerism of azoles. For 5-phenyltetra-zole, the 2//-tautomer was found predominant in polyvinyl alcohol film (based on the determination of polarization angles of electronic transition... 

Direct probe of ligand field and charge transfer excited states Greater sensitivity than ABS in observing weak transitions and greater resolution due to differences in circular polarization complimentary selection rules aiding in assignment of electronic transitions... 

If the electron solvent polarization is neglected, the study of electron transitions and the determination of the solvent shift do not require appreciable modifications in the basic scheme of ASEP/MD. During a Franck-Condon transition the solute and solvent nuclei remain fixed and hence the ASEP obtained for the initial state can be used for the rest of the states of interest. However, it is known that the electron degrees of freedom of the solvent can respond to the sudden change of the solute electron charge distribution. In fact, the polarization component can contribute appreciably to the final value of the solvent shift. The determination of this component requires additional calculations where the solute and solvent charge distributions are equilibrated. Each electronic state requires a separate calculation of the solvent polarization component. It is hence necessary to perform as many polarization calculations as electronic states being considered. 

For this study we have used methylen-cyclopropene (MCP) and acrolein (ACRO) in two solvents, an apolar (dioxane) and a polar one (acetonitrile). The selected transitions can be seen as representative examples of different types of electronic transitions for which different solvent responses can be studied for MCP the first 77 - 77 transition for MCP, and the first n -> 77 and 77 -> 77 transitions for ACRO. We note that in MCP the resulting excited state is characterized by a dipole moment which has an opposite direction with respect to that of the ground state, whereas in ACRO, the n -> 77 and 77 -> 77 transitions are characterized by a decrease and an increase in the dipole moment passing from ground to excited state, respectively. 

Several solvent polarity scales were proposed to quantify the polar effects of solvents on physical properties and reactivity parameters in solution, such as rate of sol-volyses, energy of electronic transitions, and solvent-induced shifts in IR or NMR... 

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