Electronic transitions, intensity

These so-called interaction perturbations Hint are what induces transitions among the various electronic/vibrational/rotational states of a molecule. The one-electron additive nature of Hint plays an important role in determining the kind of transitions that Hint can induce. For example, it causes the most intense electronic transitions to involve excitation of a single electron from one orbital to another (recall the Slater-Condon rules). 

One of the earliest series of metal complexes which showed strong, redox-dependent near-IR absorptions is the well-known set of square-planar bis-dithiolene complexes of Ni, Pd, and Pt (Scheme 4). Extensive delocalization between metal and ligand orbitals in these non-innocent systems means that assignment of oxidation states is problematic, but does result in intense electronic transitions. These complexes have two reversible redox processes connecting the neutral, monoanionic, and dianionic species. 

Electronic absorption data for the neutral complexes reveal that two intense electronic transitions dominate the absorption spectra. The solution spectra of [Re(S2C2Ph2)3], [W(S2C2Ph2)3], and [Mo(tdt)3] are presented in Fig. 58. The first band is the more intense of the two and is generally found at 15,000 cm-1 (s = 20.000-30,000 M em-1) while the second is observed at 24,000 cm-1 (s 15.000 M em ). The general similarity of the electronic absorption... 

Because of the high sensitivity required, this generally involves the measurement of intense electronic transitions. In principle, infrared or Raman detection could be more widely applicable, but, except for resonance Raman methods, which again depend on the presence of UV-visible bands, these methods are too insensitive to be of much use at present. 

Intense electronic transitions (470-520 and 350-390 nm) exhibited by the complexes Fe(MeNNNNMe)(CO) Lj (L = P-donor, n = 1 3) have been attributed to the presence of a low-lying unoccupied metallocycle n orbital 115, 213). Electronic spectra have also been reported and analyzed for [Co(ArNNNNAr)(C5Hs)]- 143), Co(ArNNNNAr)(CsH5) 164), and Ni(ArNNNNAr)2 167). 

Spectral and electrochemical properties are listed in Tables I and II. The complexes are all quite stable as solids and as acetonitrile solutions. They aU display intense electronic transitions in the ultraviolet that represent bpy and BL-based 7T 7T transitions. In the visible spectrum they display metal-to-ligand charge transfer (MLCT) transitions associated with each metal center and its coordinated ligands. The lowest-lying electronic transition in all the complexes reported is a Os BL CT transition. 

Fig. 12.33 According to the Franck-Condon principle, the most intense electronic transition is from the ground vibrational state to the vibrational state that lies vertically above it in the upper electronic state. Transitions to other vibrational levels also occur, but with lower intensity.

The electronic transition moment of equation (B1.1.5) is related to the intensity that the transition would have if the nuclei were fixed in configuration Q, but its value may vary with that configuration. It is often usefiil to expand Pi CQ) as a power series in the nonnal coordinates, Q. ... 

The Franck-Condon principle says that the intensities of die various vibrational bands of an electronic transition are proportional to these Franck-Condon factors. (Of course, the frequency factor must be included for accurate treatments.) The idea was first derived qualitatively by Franck through the picture that the rearrangement of the light electrons in die electronic transition would occur quickly relative to the period of motion of the heavy nuclei, so die position and iiioiiientiim of the nuclei would not change much during the transition [9]. The quaiitum mechanical picture was given shortly afterwards by Condon, more or less as outlined above [10]. 

Equation (B1.1.10) and equation (B1.1.11) are the critical ones for comparing observed intensities of electronic transitions with theoretical calculations using the electronic wavefiinctions. The transition moment integral... 

Often it is possible to resolve vibrational structure of electronic transitions. In this section we will briefly review the symmetry selection rules and other factors controlling the intensity of individual vibronic bands. 

A very weak peak at 348 mn is the 4 origin. Since the upper state here has two quanta of v, its vibrational syimnetry is A and the vibronic syimnetry is so it is forbidden by electric dipole selection rules. It is actually observed here due to a magnetic dipole transition [21]. By magnetic dipole selection rules the A2- A, electronic transition is allowed for light with its magnetic field polarized in the z direction. It is seen here as having about 1 % of the intensity of the syimnetry-forbidden electric dipole transition made allowed by... 

Figure Bl.25.6. Energy spectrum of electrons coming off a surface irradiated with a primary electron beam. Electrons have lost energy to vibrations and electronic transitions (loss electrons), to collective excitations of the electron sea (plasmons) and to all kinds of inelastic process (secondary electrons). The element-specific Auger electrons appear as small peaks on an intense background and are more visible in a derivative spectrum.

Zare R N 1964 Calculation of intensity distribution in the vibrational structure of electronic transitions the B... 

The electronic transitions which produce spectra in the visible and ultraviolet are accompanied by vibrational and rotational transitions. In the condensed state, however, rotation is hindered by solvent molecules, and stray electrical fields affect the vibrational frequencies. For these reasons, electronic bands are very broad. An electronic band is characterised by the wave length and moleculai extinction coefficient at the position of maximum intensity (Xma,. and emai.). 

Molecular point-group symmetry can often be used to determine whether a particular transition s dipole matrix element will vanish and, as a result, the electronic transition will be "forbidden" and thus predicted to have zero intensity. If the direct product of the symmetries of the initial and final electronic states /ei and /ef do not match the symmetry of the electric dipole operator (which has the symmetry of its x, y, and z components these symmetries can be read off the right most column of the character tables given in Appendix E), the matrix element will vanish. 

The measurements are predicted computationally with orbital-based techniques that can compute transition dipole moments (and thus intensities) for transitions between electronic states. VCD is particularly difficult to predict due to the fact that the Born-Oppenheimer approximation is not valid for this property. Thus, there is a choice between using the wave functions computed with the Born-Oppenheimer approximation giving limited accuracy, or very computationally intensive exact computations. Further technical difficulties are encountered due to the gauge dependence of many techniques (dependence on the coordinate system origin). 

Intensities for electronic transitions are computed as transition dipole moments between states. This is most accurate if the states are orthogonal. Some of the best results are obtained from the CIS, MCSCF, and ZINDO methods. The CASPT2 method can be very accurate, but it often requires some manual manipulation in order to obtain the correct configurations in the reference space. 

If the absorption is due to an electronic transition then/, , the oscillator strength, is often used to quantify the intensity and is related to the area under the curve by... 

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