Allowed Bands Using Group Theory

Yttrium aluminum borate, YAlj (603)4 (abbreviated to YAB), is a nonlinear crystal that is very attractive for laser applications when doped with rare earth ions (Jaque et al, 2003). Figure 7.9 shows the low-temperature emission spectrum of Sm + ions in this crystal. The use of the Dieke diagram (see Figure 6.1) allows to assign this spectrum to the " Gs/2 Hg/2 transitions. The polarization character of these emission bands, which can be clearly appreciated in Figure 7.9, is related to the D3 local symmetry of the Y + lattice ions, in which the Sm + ions are incorporated. The purpose of this example is to use group theory in order to determine the Stark energy-level structure responsible for this spectrum. 

In the footnote on page 271 it was claimed that infrared spectroscopy could distinguish three different M(CO)3 geometries. Substantiate this claim by working out the predicted allowed bands for each geometry (it will be necessary to use group theory). Could a similar claim be made for Raman spectroscopy ... 

The color and constitution of cyanine dyes may be understood through detailed consideration of their component parts, ie, chromophoric systems, terminal groups, and solvent sensitivity of the dyes. Resonance theories have been developed to accommodate significant trends very successfully. For an experienced dye chemist, these are useful in the design of dyes with a specified color, band shape, or solvent sensitivity. More recendy, quantitative values for reversible oxidation—reduction potentials have allowed more complete correlation of these dye properties with organic substituent constants. 

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