Symmetric states intensity

The v(CO) band can be observed in each of the five available redox states, and it shifts to progressively lower frequencies upon reduction from the (+4) state to the (—2) state due to the increasing 7i-backbonding ability of the metal centre. All of the redox states can be considered symmetric in that both cluster monomers are in the same oxidation state, with the exception of the singly reduced (—1) mixed-valence state. As such, the v(CO) band in each of the symmetric states is sharp (FWHM = 16 cm ), while the v(CO) band in the (—1) state is broad (FWHM 50-60 cm ) and is midway (with half-intensity) between the peaks for the (0) and (—2) states (Figure 5.4). 

It is evident from Eq. (88) that the radiation pattern is nonspherical unless Pss = Paa ancl then the pattern is spherically symmetric independent of the interatomic separation. Therefore, an asymmetry in the radiation pattern would be compelling evidence that the entangled states. y) and a) are not equally populated. If the fluorescence were detected in the direction perpendicular to the atomic axis, the observed intensity (if any) would correspond to the fluorescence field emitted from the symmetric state. v) and/or the upper state e). On the other hand, if there is no fluorescence detected in the direction perpendicular... 

Similar to the fluorescence intensity distribution, the visibility can provide us an information about the internal state of the system. When the system is prepared in the antisymmetric state or in a superposition of the antisymmetric and the ground states, p55 = pee = 0, and then the visibility has the optimum negative value V = — 1. On the other hand, when the system is prepared in the symmetric state or in a linear superposition of the symmetric and ground states, the visibility has the maximum positive value "V - 1. 

Figure 5. (a) The ( A, SO,) anion symmetric streching mode of polypropylene glycol)- LiCF,SO, for 0 M ratios of 2000 1 and 6 1. Solid symbols represent experimental data after subtraction of the spectrum corre-ponding to the pure polymer. Solid curves represent a three-component fit. Broken curves represent the individual fitted components, (b) Relative Raman intensities of the fitted profiles for the ( Aj, SO,) anion mode for this system, plotted against square root of the salt concentration, solvated ions ion pairs , triple ions, (c) The molar conductivity of the same system at 293 K. Adapted from A. Ferry, P. Jacobsson, L. M. Torell, Electrnchim. Acta 1995, 40, 2369 and F. M. Gray, Solid State Ionics 1990, 40/41, 637. 

The ground state spectrum in Figure 5 exhibits the typical features of the Raman spectrum of a bipyridine complex (40,51,52). Seven relatively intense peaks dominate the spectrum. These may be approximately described as the seven symmetric C-C and C-N stretches expected of bipyridine in any point group wherein the two pyridine rings are related by a symmetry element. 

If the "localized" formulation of the structure of Ru(bpy)3 as Ru(III)(bpy)2(bpy ) + is realistic, the resonance Raman spectrum of Ru(bpy)3+ can be predicted. A set of seven prominent symmetric modes should be observed at approximately the frequencies seen in Ru(III)(bpy)3, with approximately two thirds of the intensity of the ground state bpy modes. The intensity of the isolated 1609 cm - peak fits this prediction, as do the other "unshifted" peaks. A second set of seven prominent Raman modes at frequencies approximating those of bpy should also be observed. Figure 6 shows that this prediction is correct. The seven Ru(bpy)3+ peaks which show substantial (average 60 cm l) shifts from the ground state frequencies may be correlated one-for-one with peaks of Li+(bpy ) with an average deviation of 10 cm. In addition, the weak 1370 cm l mode in Ru(bpy)3 is correlated with a bpy mode at 1351 cnfl. It is somewhat uncertain whether the 1486 cm l bpy mode should be correlated with the Ru(bpy)3 mode at 1500 cm -1- or 1482 cm 1. It appears clear that the proper formulation of Ru(bpy)3 is Ru(III)(bpy)2(bpy ). This conclusion requires reinterpretation of a large volume of photophysical data (43,45,51 and references therein). 

Treating vibrational excitations in lattice systems of adsorbed molecules in terms of bound harmonic oscillators (as presented in Chapter III and also in Appendix 1) provides only a general notion of basic spectroscopic characteristics of an adsorbate, viz. spectral line frequencies and integral intensities. This approach, however, fails to account for line shapes and manipulates spectral lines as shapeless infinitely narrow and infinitely high images described by the Dirac -functions. In simplest cases, the shape of symmetric spectral lines can be characterized by their maximum positions and full width at half maximum (FWHM). These parameters are very sensitive to various perturbations and changes in temperature and can therefore provide additional evidence on the state of an adsorbate and its binding to a surface. 

Another type of DOUBLE ENDOR, called special TRIPLE , has been introduced by Dinse et al.90 to study proton hf interactions of free radicals in solution. In a special TRIPLE experiment two rf fields with frequencies vp + Av and vp — Av are swept simultaneously. For systems with Tln < T,i this leads to a considerable signal-to-noise improvement and to TRIPLE line intensities which are directly proportional to the number of nuclei with the same hf coupling constant. It should be remembered, however, that in transition metal complexes in the solid state the resonance frequencies are not, in general, symmetrically placed about the free proton frequency vp and that the condition Tln < Tj,i is not always fulfilled. 

A computation of Raman intensities can be done precisely in the same way as for infrared intensities. One needs here, in addition to the wave functions of the initial and final state, the polarizability tensor a(r,0, < )). This is a symmetric tensor of rank 2 that in Cartesian coordinates can be written as... 

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