1. Vibrational Spectroscopy CHE 626 Alex Nazarenko nazareay@buffalostate.edu

3. Energy (kJ/mol) Frequency(Hz) Wavelength (m) NMR IR Raman UV-vis

4. Only photons of one specified wavelength are absorbed Ground state Excited state

5. Width Doppler Speed of light 300,000,000 m/s Velocity of a particle >1000 m/s collisions Approximately as Doppler Both effects increase with the temperature and decrease with the size of the molecule/atom Multiple energy levels Width is around 0.01-0.001 nm in visible area

6. Energy levels of ground state Energy levels of excited state Energy sublevels

7. A primitive rule: Molecular spectra - wide bands Atomic spectra - narrow lines

8. Frequency Wavenumber

9. Carbon Monoxide in gas

10. Rayleigh scattering No changes!

11. Raman scattering Escaping photon has smaller energy because the molecule did not return to the ground state

13. Raman scattering

14. http://symmetry.otterbein.edu/tutorial/pointgroups.html

15. EThe identity transformation (E coming from the German Einheit, meaning unity). CnCn Rotation (clockwise) through an angle of 2π/n radians, where n is an integer. The axis for which n is greatest is termed the principal axis. CnkCnk Rotation (clockwise) through an angle of 2kπ/n radians. Both n and k are integers. SnSn An improper rotation (clockwise) through an angle of 2π/n radians. Improper rotations are regular rotations followed by a reflection in the plane perpendicular to the axis of rotation. Also known as alternating axis of symmetry and rotation- reflection axis. i The inversion operator (the same as S 2 ). In Cartesian coordinates, (x, y, z)→(−x, −y, −z). Irreducible representations that are even under this symmetry operation are usually denoted with the subscript g for gerade (german=even), and those that are odd are denoted with the subscript u for ungerade (german=odd). σA mirror plane (from the German word for mirror - Spiegel). σhσh Horizontal reflection plane - passing through the origin and perpendicular to the axis with the ‘highest’ symmetry. σvσv Vertical reflection plane - passing through the origin and the axis with the ‘highest’ symmetry. σdσd Diagonal or dihedral reflection in a plane through the origin and the axis with the ‘highest’ symmetry, but also bisecting the angle between the twofold axes perpendicular to the symmetry axis. This is actually a special case of σ v.