Electronic spectra calculated from Raman

Thus 2a2 is experimentally found from the electronic spectrum, ratios of the A s are found from the Raman spectrum, and the Ak s are calculated (except for sign) by pairwise comparison of the Raman intensities. Once the Ak s are calculated, the electronic spectra are calculated by using eq. 2 or 3. 

The electronic spectrum is calculated by using equations 3 and 5. The distortions used in these equations are determined from the pre-resonance Raman intensities by using equations 7 and 9. Both the vibrational frequencies of the normal modes and the displacements of the excited state potential surfaces along these normal modes are obtained from the pre-resonance Raman spectrum. 

Mo2(02CCF3)4 [4]. The analysis of the distortions of this molecule is included here for two reasons. First, the spectra provide a detailed check on the use of the combination of electronic and Raman spectroscopy to determine distortions. The electronic spectrum contains more highly resolved vibronic bands than that in the previous example and thus provides a more detailed check of the distortions calculated from the pre-resonance Raman data. Second, the analysis is of chemical interest because the distortions are caused by a transition between orbitals forming the Mo—Mo... 

The final two examples of the determination of excited state distortions are large bimetallic compounds whose electronic absorption spectra are broad and featureless. We must turn entirely to resonance Raman spectroscopy to measure the distortions because all of the information in the electronic spectrum is buried under the envelope. Fortunately, the resonance Raman profiles contain a great deal of information. These molecules were chosen as illustrative examples precisely because the resonance Raman spectra are so rich. The spectrum contains long overtone progressions and combination bands. Excitation profiles of not only the fundamentals but also of overtones and combination bands will be used to determine the distortions. The power of time-dependent theory from Section III.F and experimental examples of the effects of A on fundamentals, overtones, and combination bands are shown. The calculated distortions provide new insight about the orbitals involved in the electronic transition. 

It has been shown, from simple quantum chemical calculations (MNDO), that F is linearly related to molecular electronic properties, such as Eg, ionisation potential Ip and bandwidth. Fig. 8 [33]. It then becomes possible, in principle, to correlate directly Raman vibrational frequencies with the above electronic properties. The theoretical linear relation has also been verified experimentally, for the case of measured from the UV-visible spectrum, and Fjj derived from Raman experiments. Fig. 9 [3. ... 

Another related issue is the computation of the intensities of the peaks in the spectrum. Peak intensities depend on the probability that a particular wavelength photon will be absorbed or Raman-scattered. These probabilities can be computed from the wave function by computing the transition dipole moments. This gives relative peak intensities since the calculation does not include the density of the substance. Some types of transitions turn out to have a zero probability due to the molecules symmetry or the spin of the electrons. This is where spectroscopic selection rules come from. Ah initio methods are the preferred way of computing intensities. Although intensities can be computed using semiempirical methods, they tend to give rather poor accuracy results for many chemical systems. 

This expression for the complete overlap is Fourier transformed to give the electronic emission spectrum. In order to carry out the calculation it is necessary to know the frequencies and the displacements for all of the displaced normal modes. In addition, the energy difference between the minima of the two potential surfaces E0 and the damping r must be known. As will be discussed below, the frequencies and displacements can be experimentally determined from pre-resonance Raman spectroscopy, and the energy difference between the ground and excited states and the damping can be obtained from the electronic absorption spectrum and/or emission spectrum. 

Fig. 1. Experimental and theoretical electronic Raman Spectra of CaO Cu2+. The experimental spectrum (a), is reproduced from the work by Guha and Chase [1] and was collected at 4.2 K in a polarization geometry which facilitates the observation of transitions of Eg symmetry only. The theoretical spectrum was calculated using equation (9) employing the following parameters hco = 330 cm-1, Af = —1900 cm-1, Af = —0.65 cm-1, Sd 3 cm-1, Se = 3 cm-1, nv = 40, T = 7 K.

The UV resonance Raman spectrum of thymine was revisited in 2007, with a slightly different approach, by Yarasi, et al. [119]. Here, the absolute UV resonance Raman cross-sections of thymine were measured and the time-dependent theory was used to experimentally determine the excited-state structural dynamics of thymine. The results indicated that the initial excited-state structural dynamics of thymine occurred along vibrational modes that are coincident with those expected from the observed photochemistry. The similarity in a DFT calculation of the photodimer transition state structure [29] with that predicted from the UV resonance Raman cross-sections demonstrates that combining experimental and computational techniques can be a powerful approach in elucidating the total excited-state dynamics, electronic and vibrational, of complex systems. 

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