Selection rules and intensities of absorption bands

The most important use of energy level diagrams described in 3.5 is to interpret visible to near-infrared spectra of transition metal compounds and minerals. The diagrams provide qualitative energy separations between split 3d orbitals and convey information about the number and positions of absorption bands in a crystal field spectrum. Two other properties of absorption bands alluded to in 3.3 are their intensities and widths. 

Several factors affect intensities of crystal field spectra. In addition to enhancement by increased temperature and pressure discussed in chapter 9 ( 9.4), intensities of absorption bands depend on first, the spin-state or number of unpaired electrons possessed by a transition metal ion second, whether or not the cation is located at the centre of symmetry of a coordination site and third, interactions with next-nearest-neighbour cations. 

Symmetry of crystal field Symmetry notation Crystal field states Mineral examples 

Intensities of absorption bands are governed by probabilities of electronic transitions between the split 3d orbital energy levels. The probabilities are expressed by selection rules, two of which are the spin-multiplicity selection rule and the Laporte selection rule. 

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The relative intensities of absorption bands are governed by a series of selection rules. On the basis of the symmetry and spin multiplicity of ground and excited electronic states, two of these rules may be stated as follows ... 

The strength or intensity of absorption is related to the dipole strength of transition D or square of the transition moment integral M m , and is pressed in terms of oscillator strength / or integrated molar extinction jfe Jv. A transition with /= 1, is known as totally allowed transition. But the transitions between all the electronic, vibrational or rotational states are not equally permitted. Some are forbidden which can become allowed under certain conditions and then appear as weak absorption bands. The rules which govern such transitions are known as selection rules. For atomic energy levels, these selection rules have been empirically obtained from a comparison between the number of lines theoretically... 

Fig. 13. Surface selection rules linking the transition moment orientation and the sign and intensity of the absorption band at the air-water interface. Taken from Ref. [91] with permission from American Chemical Society.

Charge transfer transitions are allowed by the selection rules, and as a result, the intensities of CT absorptions are much greater than those of d-d bands (Table 20.4). 

The phenomenon of surface-enhanced infrared absorption (SEIRA) spectroscopy involves the intensity enhancement of vibrational bands of adsorbates that usually bond through contain carboxylic acid or thiol groups onto thin nanoparticulate metallic films that have been deposited on an appropriate substrate. SEIRA spectra obey the surface selection rule in the same way as reflection-absorption spectra of thin films on smooth metal substrates. When the metal nanoparticles become in close contact, i.e., start to exceed the percolation limit, the bands in the adsorbate spectra start to assume a dispersive shape. Unlike surface-enhanced Raman scattering, which is usually only observed with silver, gold and, albeit less frequently, copper, SEIRA is observed with most metals, including platinum and even zinc. The mechanism of SEIRA is still being discussed but the enhancement and shape of the bands is best modeled by the Bruggeman representation of effective medium theory with plasmonic mechanism pla dng a relatively minor role. At the end of this report, three applications of SEIRA, namely spectroelectrochemical measurements, the fabrication of sensors, and biochemical applications, are discussed. 

It is well known that the oscillator strengths of electronic absorption bands are directly proportional to Hua, and that factors such as selection rules and the distance separating the donor and acceptor (through the overlap integral), etc. affect these band intensities. The relationship of the experimental parameters and the electronic coupling matrix element for a Gaussian shaped absorption band is usually described as in Equation (22), ... 

In collaboration with E.L. Sibert, we have learned to interpret these Franck-Con-don forbidden, pure torsional band intensities in S,-S0 absorption spectra quantitatively and thus place the key ml+ assignment on firm ground.27 The forbidden bands follow the selection rule Am = 3, so we need a perturbation of the form Vel cos 3a. Working in an adiabatic representation with the S0 and S, electronic states denoted by y0(g a) and /,( a) and the torsional states by m" and m, the electric dipole transition moment is,... 

Some characteristics of, and comparisons between, surface-enhanced Raman spectroscopy (SERS) and infrared reflection-absorption spectroscopy (IRRAS) for examining reactive as well as stable electrochemical adsorbates are illustrated by means of selected recent results from our laboratory. The differences in vibrational selection rules for surface Raman and infrared spectroscopy are discussed for the case of azide adsorbed on silver, and used to distinguish between "flat" and "end-on" surface orientations. Vibrational band intensity-coverage relationships are briefly considered for some other systems that are unlikely to involve coverage-induced reorientation. 

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