Spectroscopy

1
Spectroscopy

• Microwave (Rotational)
• Infrared (Vibrational)
• Raman (Rotational Vibrational)
• Texts
• Physical Chemistry, 6th edition, Atkins
• Fundamentals of Molecular Spectroscopy, 4th
  edition, Banwell McCash

2
Introduction-General Principles

• Spectra - transitions between energy states
• Molecule, Ef - Ei hu photon
• Transition probability
• selection rules
• Populations (Boltzmann distribution)
• number of molecules in level j at equilibrium

3
Typical energies
4
Fate of molecule?

• Non-radiative transition M M M M heat
• Spontaneous emission M M hn (very fast for
  large DE)
• Stimulated emission (opposite to stimulated
  absorption)
• These factors contribute to linewidth to
  lifetime of excited state.

5
MCWE or Rotational SpectroscopyClassification of
molecules

• Based on moments of inertia, Imr2
• IA ¹ IB ¹ IC very complex eg H2O
• IA IB IC no MCWE spectrum eg CH4
• IA ¹ IB IC complicated eg NH3
• IA 0, IB IC linear molecules eg NaCl

6
Microwave spectrometer

• MCWE 3 to 60 GHz X-band at 8 to 12 GHz 25-35 mm
• Path-length 2 m pressure 10-5 bar Ts up to
  800K vapour-phase
• Very high-resolution eg 12C16O absorption at
  115,271.204 MHz
• Stark electric field each line splits into (J1)
  components

7
Rotating diatomic molecule

• Degeneracy of Jth level is (2J1)
• Selection rules for absorption are
• DJ 1
• The molecule must have a non-zero dipole
  moment, p ¹ 0. So N2 etc do not absorb microwave
  radiation.
• Compounds must be in the vapour-phase
• But it is easy to work at temperatures up to 800K
  since cell is made of brass with mica windows.
  Even solid NaCl has sufficient vapour pressure to
  give a good spectrum.

8
Rotational energy levels

• For DJ1
• DE 2 ( J1) h2/8p2I
• 01 DE 2 h2/8p2I
• 12 DE 4 h2/8p2I
• 23 DE 6 h2/8p2I
• etc., etc., etc.
• Constant difference of
• DE 2 h2/8p2I

9
Populations of rotational levels
10
Example

• Pure MCWE absorptions at 84.421 , 90.449 and
  96.477 GHz on flowing dibromine gas over hot
  copper metal at 1100K.
• What transitions do these frequencies represent?
• Note 96.477 - 90.449 6.028 and
• also 90.449 - 84.421 6.028
• So, constant diff. of 6.028 GHz or 6.028109 s-1.
• DE 2 h2/8p2I h (6.028109 s-1)
• So 84.421 6.028 14.00 ie J13 J14
• 90.449 6.028 15 ie J14 J15
• 96.477 6.028 16 ie J15 J16

11
Moment of inertia, I

• DE 2 h2/8p2I hv h(6.028109 s-1)
• I 2 h/(8p2 6.028109 )
• I 2 (6.62610-34)/(8p2 6.028109 )
• I 2.78410-45
• Units?
• Þ (J s)/(s-1) J s2 kg m2 s-2 s2 kg m2
• But I mr2
• m (0.0630.079)/(0.0630.079)NA 5.8210-26 kg
• Þ r Ö(I/m) 218.610-12 m 218.6 pm

12
Emission spectroscopy?

• Radio-telescopes pick up radiation from
  interstellar space. High resolution means that
  species can be identified unambiguously.
• Owens Valley Radio Observatory 10.4 m telescope
• Orion A molecular cloud 300K, 10-7 cm-3
• 517 lines from 25 species
• CN, SiO, SO2, H2CO, OCS, CH3OH, etc
• 13CO (220,399 MHz) and 12CO (230,538 MHz)

13
IR / Vibrational spectroscopy

• Ev (v 1/2) (h/2p) (k/m)1/2
• v 0, 1, 2, 3,
• Selection rules
• Dv 1 p must change during vibration
• Let we wavenumber of transition then energy
• ev (v 1/2) we
• Untrue for real molecules since parabolic
  potential does not allow for bond breaking.
• ev (v 1/2) we - (v 1/2)2 we xe
• where xe is the anharmonicity constant

14
Differences?

• Energy levels unequally spaced, converging at
  high energy. The amount of distortion increases
  with increasing energy.
• All transitions are no longer the same
• Dv gt 1 are allowed
• fundamental 01
• overtone 02
• hot band 12

15
Example

• HCl has a fundamental band at 2,885.9 cm-1, and
  an overtone at 5,668.1cm-1.
• Calculate we and the anharmonicity constant xe.
• ev (v 1/2) we - (v 1/2)2 we xe
• e2 (2 1/2) we - (2 1/2)2 we xe
• e1 (1 1/2) we - (1 1/2)2 we xe
• e0 (0 1/2) we - (0 1/2)2 we xe
• e2 - e0 2we - 6we xe 5,668.1
• e1 - e0 we - 2we xe 2,885.9
• \ we 2,989.6 cm-1 we xe 51.9 cm-1 xe
  0.0174

16
High resolution infrared

• Ev (v 1/2) (h/2p) (k/m)1/2
• ev (v 1/2) we
• EJ J(J1) (h2/8I)
• eJ J(J 1) Bv
• Vibrational rotational energy changes
• e(v,J) (v 1/2) we J(J 1) Bv
• Selection rule Dv1, DJ1
• Rotational energy change must accompany a
  vibrational energy change.

17
Vibrational rotational changes in the IR
18
Hi-resolution spectrum of HCl

• Above the gap DJ 1
• Below the gap DJ 1
• Intensities mirror populations of starting levels

19
Example HBr

• Lines at 2590.95, 2575.19, 2542.25, 2525.09,
  ... cm-1
• Difference is roughly 15 except between 2nd 3rd
  where it is double this. Hence, missing
  transition lies around 2560 cm-1.
• So 2575 is (v0,J0) (v1,J1) 2590 is
  (v0,J1) (v1,J2)
• So 2542 is (v0,J1) (v1,J0) 2525 is
  (v0,J2) (v1,J1)
• (2575.19 - 2525.25) 6B0 B08.35 cm-1
• (2590.95 - 2542.25) 6B1 B18.12 cm-1
• Missing transition at 2542.25 2B0 2558.95 cm-1

20
Raman spectroscopy

• Different principles. Based on scattering of
  (usually) visible monochromatic light by
  molecules of a gas, liquid or solid
• Two kinds of scattering encountered
• Rayleigh (1 in every 10,000) same frequency
• Raman (1 in every 10,000,000) different
  frequencies

21
Raman

• Light source? Laser
• Monochromatic, Highly directional, Intense
• He-Ne 633 nm or Argon ion 488, 515 nm
• Cells? Glass or quartz so aqueous solutions OK
• Form of emission spectroscopy
• Spectrum highly symmetrical eg for liquid CCl4
  there are peaks at 218, 314 and 459 cm-1
  shifted from the original incident radiation at
  633 nm (15,800 cm-1).
• The lower wavenumber side or Stokes radiation
  tends to be more intense (and therefore more
  useful) than the higher wavenumber or anti-Stokes
  radiation.

22
(No Transcript)
23
Why?

• Rayleigh scattering no change in wavenumber of
  light
• Raman scattering either greater than original or
  less than original by a constant amount
  determined by molecular energy levels
  independent of incident light frequency

24
Raman selection rules

• Vibrational energy levels
• Dv 1
• Polarisability must change during particular
  vibration
• Rotational energy levels
• DJ 2
• Non-isotropic polarisability (ie molecule must
  not be spherically symmetric like CH4, SF6, etc.)
• Combined

25
Vibrational Raman

• Symmetric stretching vibration of CO2
• Polarisability changes
• therefore Raman band at 1,340 cm-1
• Dipole moment does not
• no absorption at 1,340 cm-1 in IR

26
Vibrational Raman

• Asymmetric stretching vibration of CO2
• Polarisability does not change during vibration
• No Raman band near 2,350 cm-1
• Dipole moment does change
• CO2 absorbs at 2,349 cm-1 in the IR

27
Example

• In an experiment jets of argon gas and tin vapour
  impinged on a metal block cooled to 12 K in
  vacuo. The Raman spectrum of the frozen matrix
  showed a series of peaks beginning at 187 cm-1
  and with diminishing intensity at 373, 558, 743,
  etc cm-1.
• What species is responsible for the observed
  spectrum?
• Shifts of ca. 200 cm-1 indicate vibrational
  energies diatomic tin? Is 187 the fundamental?
  With the second peak at 373 (note 2 x 187 374),
  the third at 558 being 3 x 187 561, etc.
• Use ev (v 1/2) we - (v 1/2)2 we xe
• Substitute in v0, v1, v2, etc then compute
• e1-e0 187 e2-e0 373 e3-e0 558
  calculate we, xe

28
Pure Rotational Raman

• Polarisability is not isotropic
• CO2 rotation is Raman active
• some 20 absorption lines are visible on either
  side of the Rayleigh scattering peak with a
  maximum intensity for the J7 to J9 transition.
• The DJ 2 and DJ -2 are nearly equal in
  intensity
• Very near high intensity peak of exciting
  radiation needs good quality spectrometers

29
Rotational Raman
30
Raman applications

• Structure of Hg(I) in aqueous solution
• Is it Hg ? or (Hg2)2 ?
• Aqueous solutions of HgNO3 show Raman band at 169
  cm-1 (as well as NO3- bands), solid HgCl shows a
  band at 167 cm-1
• Conclusion Hg(I) exists as a diatomic cation
  (note that a symmetrical diatomic would vibrate
  but would not absorb in the IR different
  selection rule)
• Very little sample preparation required easy to
  get good quality spectra of solids, powders,
  fibers, crystals
• Drawbacks coloured samples may overheat burn up

31
Raman spectra of KNO3N.B. strong symmetric
stretch band at 1,050 cm-1
32
Raman spectrum of aspirin tablet no sample
preparation
33
Raman vs IR

• CHCl3
• Which?
• Very similar
• Diffs.?