27 : 3/ Quantum Mechanical Basis of Molecular Spectra 513 



well with chemical data; the spectroscopic data are often more precise. 



If the change in the vibrational-energy level involves a change in the 



average electrical dipole, radiation can occur. The selection rules are 



Ar> = ±1 



AJ = ± 1, except 0^0 



(Read expression 0^0 as "zero to zero is forbidden.") For every 

 change in v, there will be a band of changes in J. (In fact, there will be 

 three bands, one for A J = +1, one for A J = — 1, and one for A J = 0. 

 They are different because the energy and the moment of inertia / both 

 depend on J and v.) 



Qualitatively, the foregoing concept is valid for all molecular bonds. 

 For the more complex molecules, however, the sharp lines within a 

 band are smeared out by interactions with other groups within the 

 molecules and with neighboring molecules. To some extent, these 

 interactions can be reduced by taking the spectrophotometric measure- 

 ments at very low temperatures, but the smearing out of the rotational 

 bands associated with a vibrational transition cannot be completely 

 removed. 



A variety of covalent bonds have characteristic absorption peaks due 

 to vibrational transitions. From the location and relative magnitude 

 of these absorption peaks, it is sometimes possible to determine the bond 

 types present and also the number of bonds of a given type. So many 

 peaks occur in the spectral region of 3 -> 20/jl that this type of analysis is 

 most successful for choosing one of several structures for a given molecule 

 or determining the amounts of two or, at most, three different types of 

 molecules after purification. Spectra in this region are complex but 

 characteristic of the particular molecular species present. This band 

 is often called the fingerprint region of the spectrum. 



A characteristic spectrum is shown in Figure 2. Many more are 

 shown in the book by Randal, et al. included in the references. When 

 their book was published in 1949, the actual type of vibration was not 

 known for all absorption bands. They do, however, identify a large 

 number. Since then, additional studies have multiplied the known 

 absorption spectra manyfold. 



The problems of comparing different data from different laboratories 

 have been complicated by lack of absolute calibrations and failure to 

 appreciate the limitations of the equipment. Infrared measurements of 

 vibrational bands are also difficult because of the extremely high absorp- 

 tion of water in this spectral region. Some experiments have compared 

 spectra in H 2 and D 2 to eliminate the high background absorptions. 

 Most experiments involved specimens prepared either in a hydrocarbon 



