1. Microwave Rotational Spectroscopy
CHE 6416
Michael Evans

2. How does Microwave relate to other spectroscopies
Different types of motion
Translational
Vibrational
Rotational.

3. What is Microwave Spectroscopy?
Microwave stimulates Rotational translations
Measures the rotational states of molecules
Gas Phase
Must have a dipole.
Tjb – Fix bullets throughout,
The use of photons in the Microwave region to cause measureable translations in the Quantum Rotational Levels of a gas phase molecule

4. Applications of MW Measurement of bond lengths
Observation by radio telescopes for life precursors in interstellar clouds
Precise observation of translating stereochemistries and confirmation verification
Tjb- fix bullets, needs to be earlier in talk

5. Microwave Spectroscopy
RADAR was impetus for its invention
1948, Walter Gordy, first published review
Tjb- fix bullets Microwave Spectroscopy, Reviews of Modern Physics, Volume 20, Number 4, October 1948, Gordy, Walter.
Gordy, W., Microwave Spectroscopy, Reviews of Modern Physics, Volume 20, Number 4, October 1948,

6. Microwaves

7. TJB this needs to be shown early
TJB this needs to be shown early!!! The theory and data makes more sense if shown earlier, references
In the conventional Stark-modulated spectrometer, the sample is contained in a long (1- to 3-metre, or 3.3- to 9.8-foot) section of a rectangular waveguide, sealed at each end with a microwave transmitting window (e.g., mica or Mylar), and connected to a vacuum line for evacuation and sample introduction. The radiation from the source passes through a gaseous sample and is detected by a crystal diode detector that is followed by an amplifier and display system (chart recorder). In order to increase the sensitivity of the instrument, signal modulation by application of a high-voltage square wave across the sample is used.  (Note the above is a cut and paste, there are some references to flight tubes up to 20M)

8. Rotational vs. Vibrational
Where J = rotational
V= vibrational
Observed from
lowest vibration state
𝐸 𝐽 =𝐵 𝐽(𝐽+1)
Where does e(j) come from?

9. Motion of Rotation 3 Possible moments of inertia 𝐼 𝑎 , 𝐼 𝑏 , 𝐼 𝑐
𝐼 𝑎 , 𝐼 𝑏 , 𝐼 𝑐
Graph…needs one.

10. Diatomic molecule Rotation E from Schrodinger. 𝐼 𝑎 = 𝐼 𝑏 , 𝐼 𝑐 =0
𝐼 𝑎 = 𝐼 𝑏 , 𝐼 𝑐 =0
𝐵= ℎ 8𝐼 𝑐𝜋 2
𝐼= 𝑅 2 𝑢= ( 𝑀 1 𝑀 2 ) ( 𝑀 1 + 𝑀 2 ) 𝑅 2
Line spacing is 2B.

11. Theory of Microwave Spectroscopy
Microwave wavelength photon
Highest probability of transition
Molecules with dipoles
Tjb- fix bullets

12. How do we measure if it will translate?
Probability of Transition=∫ψrot(F)μ^ ψrot(I) dτ
Where: ψrot(F) is the complex conjugate of the final rotational state
ψrot(I) is the wave function of the initial rotational state
μ is the dipole moment operator with X, y, z coordinates.
The function is positive.
Only tells if is allowed.
might need graph of probability
Per Dr Burkey, a comparison of the sin and antisine waves may be appropriate

13. But there are limits. Photons limited ΔJ±1 Only one transition per
Each photon has one unit of momentum
ΔJ±1
Only one transition per

14. Is it available to translate?
Boltzmann distribution
Where nJ=number of molecules excited
n0=number of molecules in ground state
R=gas constant
T=temperature
ErotJ=molar energy of the rotational state

15. Plot of Probability Probability of Population Similar to spectra

16. Types of Molecules that are MW-Active
Linear
Tjb- line structure are ineffective - show structures here not later!!! Break up into two slides if needed, don’t make audience interpret line formula because they will be distracted and stop listening to you, get ChemDraw from the University if you don’t have it already.

17. Types of Molecules that are MW-Active
Symmetric Tops

18. Types of Molecules that are MW-Active
Antisymmetric tops

19. Types of Molecules that are MW-Active
Spherical tops-Not active

20. Linear Molecules. Linear molecules(Rigid rotors)
Bond length directly calculated
𝐼 𝑎 = 𝐼 𝑏 , 𝐼 𝑐 =0
𝐼= 𝑅 2 𝑢= ( 𝑀 1 𝑀 2 ) ( 𝑀 1 + 𝑀 2 ) 𝑅 2
Tjb- fix bullets

21. http:// en.wikipedia.org/wiki/Rotational_spectroscopy#Asymmetric_top
Linear Molecules.
Linear molecules(Rigid rotors)
∆𝐽= 𝐽 ′ − 𝐽 ′′ =±1
𝑣 𝐽 ′ ↔ 𝐽 ′′ =𝐸 𝐽 ′ −𝐸 𝐽 ′′ =2𝐵 𝐽 " +1
Where 𝐽 ′′ =𝐿𝑜𝑤𝑒𝑟 𝑙𝑒𝑣𝑒𝑙
𝐽 ′ =𝑈𝑝𝑝𝑒𝑟 𝐿𝑒𝑣𝑒𝑙
en.wikipedia.org/wiki/Rotational_spectroscopy#Asymmetric_top

22. Symmetric Tops (Rotors)
Two rotational axes same, one different
Oblate
𝐼 𝑎 ≠ 𝐼 𝑏 = 𝐼 𝑐
Oblate.
Benzene, XeF4
Prolate
𝐼 𝑎 = 𝐼 𝑏 ≠ 𝐼 𝑐
Prolate.
CH3Cl, NH3
Tjb- fix bullets

23. Symmetric Top Spectra
On the Cl⋅⋅⋅N Halogen Bond: A Rotational Study of CF3Cl⋅⋅⋅NH3
Gang Feng, 
Dr. Luca Evangelisti, 
Nicola Gasparini and
Prof. Dr. Walther Caminati*
Chemistry - A European Journal
Volume 18, Issue 5, pages 1364–1368, January 27, 2012
Fengm G., Evangelisti, L, Gaspartini, N., Caminati, W., On the Cl⋅⋅⋅N Halogen Bond: A Rotational Study of CF3Cl⋅⋅⋅NH3, Chemistry-A European Journal, Vol 18, #5 pg

24. Why more complicated? With more axis, more complicated
Symmetrical molecules gain 2 terms
K = vector about the symmetry axis
Must be between –J and +J
M = rotational momentum about a external field
Also between –J and +J
0 if no external field

25. Why more complicated? With more axis, more complicated
𝐸 𝐽, 𝐾 =𝐵𝐽 𝐽+1 + 𝐴−𝐵 𝐾 2
Where B= ℎ 8 𝜋 2 𝑐 𝐼 𝑏
A= ℎ 8 𝜋 2 𝑐 𝐼 𝑎 , Prolate
A= ℎ 8 𝜋 2 𝑐 𝐼 𝑐 , Oblate

26. Why more complicated? Which leads to Lines at:
𝑣 𝐽 ′ ↔ 𝐽 ′′ , 𝐾 =𝐸 𝐽 ′ , 𝐾 −𝐸 𝐽 ′′ , 𝐾 =2𝐵 𝐽 " +1

27. Why more complicated? With more axis, more complicated Stark Effect
- Hyperfine splitting

28. Stark Effect Similar to Zeeman effect Lifts level degeneracy
Due to external electric field
1rst Order-Linear
2nd Order-Quadratic

29. Stark Effect 𝐸 𝑆𝑡𝑎𝑟𝑘 𝐽, 𝐾, 𝑀 =− 𝑢𝐸𝐾𝑀 𝐽(𝐽+1) M = 0, no stark
𝐸 𝑆𝑡𝑎𝑟𝑘 𝐽, 𝐾, 𝑀 =− 𝑢𝐸𝐾𝑀 𝐽(𝐽+1)
M = 0, no stark
K, M ≠0 splitting occurs
-M inc, + M dec
Post note, uE is the energy of the level, with K and M quantum numbers

30. Hyperfine Splitting Coupling of Nuclear spin and molecular rotation.
If J > l, 2l+1 levels
If J < l, 2J+1 levels.

31. Hyperfine splitting CF3I, Splitting due to 127I

32. Asymmetrical Tops Three different axes, 3 different inertias
Most molecules.
Very complex spectra.

33. Effect of Isotope Substitution
12C16O13C16O, mass ↑, B ↓ (~1/I), E ↓.

34. Isotope splitting c-C3HD

35. Isotopic Substitution
As Isotopic Mass ↑, Energy ↓
Example (CO)
12CO J=0->J=1 @ cm-1
13CO @ cm-1
Tjb- fix bullets

36. Instrumentation Most homemade. Two types spectrometers.
Stark Modulated
Fortier Transform Microwave Spectroscopy
Similar in concept to FTIR
Tjb- fix bullets

37. Stark Modulated MW Spectrometer
Samples introduced as a gas.
Can be heated.
Generally high vacuum.

38. TJB this needs to be shown early
TJB this needs to be shown early!!! The theory and data makes more sense if shown earlier, references
In the conventional Stark-modulated spectrometer, the sample is contained in a long (1- to 3-metre, or 3.3- to 9.8-foot) section of a rectangular waveguide, sealed at each end with a microwave transmitting window (e.g., mica or Mylar), and connected to a vacuum line for evacuation and sample introduction. The radiation from the source passes through a gaseous sample and is detected by a crystal diode detector that is followed by an amplifier and display system (chart recorder). In order to increase the sensitivity of the instrument, signal modulation by application of a high-voltage square wave across the sample is used. 

39. FTMW Spectrometer Similar in principle to FTIR
Broader Frequency, Greater Precision

40. Chipped Pulse FTMW Add waveform generators
Widens Bandwidth several 1000x
Decreases spectral search time
Tjb- fix bullets

41. Chipped Pulse FTMW
This is not needed, spend more time on spectra and interpretation

42. FTMW Spectrometer Typical setup

43. Sample Preparation/Introduction
Gas samples
As is
As a diluted analyte in a non-MW reactive gas such as Neon
Solids
Laser abatement
Vaporization
Liquids
Supersonic Expansion

44. Supersonic Expansion/Laser Ablatement
I don’t think this is important for your audience,

45. Applications of MW Measurement of bond lengths
Observation by radio telescopes for life precursors in interstellar clouds
Precise observation of translating stereochemistries and confirmation verification

46. Measuring Bond Length.
For example, we will use the easiest case, a diatomic molecule, HCL.
cm-1
J->J+1
R(nm)
83.03
3-4
.1288
103.73
4-5
124.3
5-6
.1289
145.03
6-7
165.51
7-8
.1290
185.86
8-9
.1291
206.38
9-10
.1292
226.5
10-11
.1293

47. Calculation example (HCL)
𝐵= ℎ 8𝐼 𝑐𝜋 2 R= ℎ 8 𝜋 2 𝑐𝐵𝑢 R= 6.626𝑒−34 𝐽.𝑆 8 (3.14) 2 ( 𝑒10 𝑐𝑚.𝑠)( ∗1.661𝑥10−27 𝑘𝑔)(10.3 𝑐𝑚−1) R=1.29x10-10 M or nm

48. Problem Calculate bond length for CO Given= 2B = 3.8626 cm-1
h = x J.S
c = x 1010 cm.s
Amu to kg = 1.661x kg

49. Calculation example (CO)
𝐵= ℎ 8𝐼 𝑐𝜋 2 R= ℎ 8 𝜋 2 𝑐𝐵𝑢 R= 6.626𝑒−34 𝐽.𝑆 8 (3.14) 2 ( 𝑒10 𝑐𝑚.𝑠)( 48 7 )∗1.661𝑥10−27 𝑘𝑔)( 𝑐𝑚−1) R=1.13x10-10 M or nm
Reference value is nm for CO

50. Identification of Organics in Interstellar Space
Gas phase molecules and radicals
Observed using a radio telescope.
Linear molecule
Simple spectra

51. Identification of Organics in Interstellar Space
Symmetric Molecule
Complicated due to symmetric top
Many more possible states

52. Glycine? in interstellar clouds
Other more complicated molecules may be observed
Data too complicated

53. Molecular Confirmation
Resolve rapidly interchanging conformers.
17000 scans/52 hrs.
27 yrs on standard unit.
B C Dian et al, Science, 2008, 320, 924 (DOI: /science
B C Dian et al, Science, 2008, 320, 924 (DOI: /science

54. Conformers Cyclopropane carboxaldehyde

55. Conclusion Useful for Gas Molecules Can determine bond length.
Diverse usages for the technique.
Tjb- fix bullets, never ever write out sentences like this, Ughh!!!