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Chemical Applications of Group Theory Vibrational Spectroscopy

Chemical Applications of Group Theory Vibrational Spectroscopy. Edward A. Mottel Department of Chemistry Rose-Hulman Institute of Technology. Spectroscopy. Vibrational bands 100-5000 cm -1 (1.2 -60 kJ·mol -1 ) the stretching and bending motions of the molecule.

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Chemical Applications of Group Theory Vibrational Spectroscopy

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  1. Chemical Applicationsof Group TheoryVibrational Spectroscopy Edward A. Mottel Department of Chemistry Rose-Hulman Institute of Technology

  2. Spectroscopy • Vibrational bands • 100-5000 cm-1 (1.2 -60 kJ·mol-1) • the stretching and bending motions of the molecule. • depend on the symmetry of the molecule. • There are no restrictions on how a molecule can bend or stretch, but certain bands may not appear in a spectra because they are symmetry forbidden.

  3. Io Is sample cell ir light source ir detector Io Ir reference cell Infrared Spectroscopy An infrared spectra occurs because of an absorption of infrared light.

  4. - + 1 Å Electric Dipole Infrared bands will occur if the motion changes the electric dipole of the molecule. m = e r = (1.602 x 10-19 C)(1 x 10-10 m) = 4.803 x 10-18esu·cm = 4.803 D

  5. C O Infrared Spectroscopy Infrared bands will occur if the motion changes the electric dipole of the molecule. m = 0.1 D Absorption of some of the energy from the electric field causes the dipole to get bigger and smaller. Repulsion of the negative dipole and the negative wave of the electric field results in the atoms moving together.

  6. sample cell visible photon counter monochromatic light source scattered light (visible laser) Raman Spectroscopy A Raman spectra occurs because of a change in the frequency of scattered light.

  7. C O polarizability Raman Spectroscopy Raman bands will occur if the motion changes the polarizability of the molecule. Electron density moves towards positive electric field (and away from negative electric field) generating an induced dipole. mind = a e

  8. C O Raman Spectroscopy Raman bands will occur if the motion changes the polarizability of the molecule. The induced dipole is not permanent, adding to and subtracting from the frequency of the light. Differences in the frequency of the light generate the Raman spectra. Only about 0.1% of the light is actually scattered.

  9. Infrared Raman K.O. Christe, R.D. Wilson, E.C. Curtis, Inorg. Chem., 12, 1358 (1973)

  10. C O Carbon Monoxide Determine the reducible representation of carbon monoxide Cv E 2 C  sv Gred 6 2 2

  11. 2 cos 3F 2 cos 2F 2 cos F 2 2 2 0 0 0 Character Table of Cv Cv E 2 C  sv 1 1 1 z x2+y2, z2 A1 S+ 1 1 -1 Rz A2 S- (x,y);(Rx,Ry) (xz, yz) E1 P E2 D (x2-y2,xy) E3 F

  12. E 2 C  sv 1 1 1 z A1 S+ 2 cos F 2 cos F 2 2 0 0 (Rx,Ry) (x,y) E1 P E1 P 1 5 1 1 1 1 Gred 6 2 2 A1 S+ Carbon Monoxide Cv translation translation rotation vibration

  13. A is singly degenerate E is doubly degenerate Carbon Monoxide The irreducible representation for carbon monoxide is 2 A1 + 2 E1 it includes energy modes for 3 translations 2 rotations 6 energy modes 1 vibration

  14. Cv E 2 C  sv 1 1 1 z x2+y2, z2 A1 S+ 1 1 -1 Rz A2 S- 2 cos 3F 2 cos 2F 2 cos F 2 2 2 0 0 0 (x,y);(Rx,Ry) (xz, yz) E1 P E2 D (x2-y2,xy) 1 1 1 E3 F A1 S+ Character Table of Cv infrared active Raman active remaining unidentified mode .

  15. C O O E 2 C 2 S  C2  sv i Carbon Dioxide Determine the reducible representation of carbon dioxide Dh Gred -1 -3 -1 9 3 3

  16. E 2 C 2 S  C2  sv i 1 Sg+ 1 1 1 1 1 -1 Sg- 1 1 1 1 -1 0 -2 cosf 2 cosf Pg 2 2 0 0 Dg 2 cos2f 2 cos2f 2 2 0 -1 Su+ -1 -1 1 1 1 1 Su- -1 -1 1 1 -1 0 2 cosf 2 cosf Pu -2 2 0 0 Du -2 cos2f 2 cos2f -2 2 0 Character Table of Dh Dh

  17. doubly degenerate singly degenerate Carbon Dioxide The irreducible representation for carbon dioxide is Su++ Pu + Pg + 4 more energy modes it includes energy modes for 3 translations 2 rotations 9 energy modes 4 vibrations

  18. E 2 C 2 S  C2  sv i -1 Su+ -1 -1 1 1 1 0 -2 cosf 2 cosf Pg 2 2 0 0 2 cosf 2 cosf Pu -2 2 0 Character Table of Dh Dh -1 -1 -1 5 1 1 sum Gred 9 3 3 -3 -1 -1 0 -2 0 4 2 2 remainder

  19. E 2 C 2 S  C2  sv i 1 Sg+ 1 1 1 1 1 -1 Su+ -1 -1 1 1 1 0 -2 0 4 2 2 remainder 0 2 cosf 2 cosf Pu -2 2 0

  20. C C C C O O O O O O O O Vibrational Frequencies of CO2 symmetric stretch Sg+ Pu symmetric bend (2 degenerate modes) Su+ asymmetric stretch Which of the modes are infrared active and which are Raman active?

  21. Isotopic Substitution • To identify specific bands in a spectra (i.e., which bands are responsible for symmetric or asymmetric stretching or bending) isotopic substitution is often required. • If the substituted atom moves in a vibrational mode, then the band will shift. • If the isotope is heavier, the band shifts to a lower frequency.

  22. C C C C O O O O O O O O Vibrational Frequencies of CO2 symmetric stretch symmetric bend (2 degenerate modes) asymmetric stretch Which of the modes are affected if 13C is substituted for 12C?

  23. trifluorobenzene

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