Vibrational SpectroscopyCHE 626

Alex Nazarenkonazareay@buffalostate.edu

Energy (kJ/mol)

Frequency(Hz)

Wavelength (m)

NMRIRRaman

UV-vis

Only photons of one specified wavelength areabsorbed

hchE

Ground state

Excited state

Width

Dopplerc

v

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

Energy levels of ground state

Energy levels of excited state

Energy sublevels

A primitive rule:

Molecular spectra - wide bands

Atomic spectra - narrow lines

21

21 where,2

1

mm

mmk

Frequency

21

21 where,2

1

mm

mmk

cc

Wavenumber

Carbon Monoxide in gas

Rayleigh scattering

No changes!

Raman scattering

Escaping photon has smaller energy because the molecule did not return to the ground state

Raman scatteringRaman scattering

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

E The identity transformation (E coming from the German Einheit, meaning unity).

CnRotation (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.

Cnk Rotation (clockwise) through an angle of 2kπ/n radians. Both n and k are integers.

Sn

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 S2). 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).

σ A mirror plane (from the German word for mirror - Spiegel).

σhHorizontal reflection plane - passing through the origin and perpendicular to the axis with the ‘highest’ symmetry.

σvVertical reflection plane - passing through the origin and the axis with the ‘highest’ symmetry.

σd

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 σv.