Vibronic transitions polarizability

When the lanthanide ion is surrounded by voluminous polarizable anions like chloride, bromide, or sulfide ions, the Stokes shift is generally small. At low temperatme, a zero-phonon line is present in absorption and emission spectra, in addition to the band corresponding to transitions involving absorption or emission of phonons (vibronic transitions). Low... 

Linear response polarizability theory of spectral bandshapes was applied to the numerical analysis of the chiroptical spectra obtained for DNA-acridine orange complexes [85]. After analysis of various models of conformation, it was concluded that a dimer-pairs repeating sequence model was best able to account for the observed spectral trends. In another work, the CD induced in the same band system was studied at several ionic strengths [86]. The spectra were able to be interpreted in terms of the long-axis-polarized electronic transitions of the dyes, with the induced CD being attributed to intercalated and non-intercalated dye species superimposed by degenerate vibronic exciton interactions between these. 

Symmetry-lowering effects of the solvent are referred to as the Ham effect (Ham, 1953 Platt, 1962). Thus, in rigid or fluid solutions, symmetry-forbidden vibrational components of the Bju ( Lb) absorption band of benzene appear with increasing intensity as the polarizability and the polarity of the solvent increase. The fact that for pyrene and 2-methylpyrene the direction of the Lb transition moment is inclined on the average 40° and 20° away from the y axis, respectively, has also been ascribed to a symmetrylowering perturbation by the environment, related to the Ham effect (Lang-kilde et al., 1983). The associated intensification of otherwise weak vibronic peaks in the Lb band can be used for an investigation of microenvironments such as micelles. 

Formally, one can think of the Raman transition probability being proportional to the elements of the polarizability tensor of a bound electron as the exciting frequency approaches the resonance frequency, these elements are enhanced in a Lorentz model of the bound electron. A common example of this mechanism is furnished by the ring-breathing (in-plane expansion) modes of porphyrins. Another mechanism, called vibronic enhancement, involves vibrations which couple two electronic excited states. In both mechanisms, the enhancement factors are nearly proportional to the intensities in the absorption spectrum of the adsorbate. 

These equations have been tested for several short polyenes and for jS-carotene (Sklar et al., 1977 Snyder et al., 1985 Andersson et al., 1991). For So(l Ag) — SgCl BJ transitions, k s are typically lO" cm. In addition to the linear dependence of transition energies on solvent polarizability, another critical test of Eq. (1) is its abdity to predict gas phase (n= 1) transition energies. Forthe So(l Ag) - 2( u) transitions of diphenylpolyenes with one to four double bonds, extrapolations of solution data and transition energies obtained from gas phase measurements agree within experimental error (Hudson etal., 1976,1982). Equation 1 also accounts for the shifts in spectra in the few cases where solvent studies have been carried out on vibronically-resolved S,(2 Ag) ->So(l Ag) transitions. The k s are considerably smaller but not insignificant, -1000-2000 cm for unsubstituted polyenes (Snyder et al.,... 

After separation, the polarizability in Equation (9.22) is the sum of four terms (i) the A-term, also known as the Condon approximation, is a result of the pure electronic transition moment and vibrational overlap integrals (ii) the B-term results from vibronic coupling of the resonant excited state with other excited states (iii) the C-term has to do with the vibronic coupling of the ground state with one or more excited states and (iv) the D-term results from vibronic coupling of the resonant excited state to other excited states coupling in both the electronic transition moments. 

In the main text we arrive at the same conclusion regarding the possible frequency shifts based on a qualitative discussion of vibronic states. The complete quantum model of Raman spectroscopy also has to take into account the change of polarizability accompanying the transition between stationary vibrational states, which leads to the coupling factor in Equation (6.15). 

The Stark effect of a rotational transition of a specific vibronic state will only yield the permanent electric dipole moment and the anisotropy of the electric polarizability (an - ax). In principle, both molecular... 

The Stark effect of a rotational transition of a specific vibronic state will only yield the permanent electric dipole moment and the anisotropy of the electric polarizability (an — aj.). In principle, both molecular parameters are functions of the intemuclear distance. The measured Stark effect yields, therefore, the vibrational average of the molecular parameter which in trun is represented as a power series expansion in (t) + 1/2) and J J + 1) ... 

The molecular probe pyrene is commonly employed to elucidate solute-solvent interactions in normal liquids (18,35). Because of the high molecular symmetry, the transition between the ground and the lowest excited singlet state is only weakly allowed, subject to strong solvation effects (36-39). As a result, in the fluorescence spectrum of pyrene the relative intensities of the first (/i) and third I2) vibronic bands vary with changes in solvent polarity and polarizability. The ratio h/h serves as a convenient solvation scale, often referred to as the Py solvent polarity scale. Py values for an extensive list of common liquid solvents have been tabulated (15,16). 

The changes in molecular polarizability during vibrational transitions determine the intensities of Raman lines. The aj polarizability matrix element for a transition from a vibronic state m to a vibronic state n can be presented as follows [4,254-256]... 

The tfaeoiy of intensities of re onantly>enhanced Raman lines is based on the Kramers-Heisenberg-Dirac dispersion equation [266,267], The problem is analyzed in teims of vibronic interactions in die molecule. The JK matrix component of the molecular polarizability for the gi gf transition in die Raman spectrum can be expressed as follows [256,257]... 

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