1. Lecture 13 APPLICATIONS OF GROUP THEORY 1) IR and Raman spectroscopy. Normal modes of H 2 O Three normal vibrations of H 2 O transform as 2 A 1 and 1 B 2 representations C 2v EC2C2  xz  yz A1A1 1111zx 2, y 2, z 2 A2A2 11 RzRz xy B1B1 11 x, R y xz B2B2 1 1y, R x yz

2. 2) Selection rules for IR and Raman active bands A normal vibration is IR active if it transforms as x, y, z or any of their linear combinations. A normal vibration is Raman active if it transforms as quadratic functions x 2, y 2, z 2, xy, xz or yz. C 2v EC2C2  xz  yz A1A1 1111zx 2, y 2, z 2 A2A2 11 RzRz xy B1B1 11 x, R y xz B2B2 1 1y, R x yz

3. 3) Selected vibrational modes For polyatomic species considering full set of normal modes is usually very time consuming. Consideration of only selected vibrational modes is simpler and often very important. The modes may be, for example, only stretching modes of a particular type. Combined with group theoretical analysis, vibration spectroscopy may allow for distinction of isomers. In the simplest cases the isomers can be distinguished by the number of stretching bands observed for particular bonds in IR spectra of these isomers (see the example below). Let us see, how group theory can help assign the proper configuration to these complexes. (a) assign the isomers to the appropriate symmetry point groups (b) chose vectors, 1 and 2, of two Pd-N bonds a basis function for a reducible representation corresponding to Pd-N stretching modes. (c) build the appropriate reducible representations, decompose them and find out which modes are IR active. C 2h EC2C2 i hh AgAg 1111RzRz x 2,y 2,z 2,xy BgBg 11 R x,R y xz, yz AuAu 11 z BuBu 1 1y, x

4. 4) IR and Raman spectroscopy based structure elucidation Consider two possible structures of Co(CO) 5 + (HF solution with [(CF 3 ) 3 BF - ] counterion), D 3h and C 4v. In an experiment two IR CO-stretching bands (, 2140, 2121 cm -1 ) and three Raman CO- stretching bands (, 2195, 2152, 2121 cm -1 ) are observed. Thus, Co(CO) 5 + is trigonal bipyramidal (D 3h ). Consider three possible structures of XeF 5 -, D 3h, C 4v and D 5h. In an experiment XeF 5 - exhibited in total three bands in the IR: 550, 290, 274 cm -1 and three bands in its Raman spectrum: 502, 423, 377 cm -1. This result matches D 5h symmetry only. Thus XeF 5 - is pentagonal planar (D 5h ). Total number of bands / number of stretching bands: