Intensity, Frequency and Relaxation time in the CH stretch overtones

1
Intensity, Frequency and Relaxation time in the
CH stretch overtones

• Brant Billinghurst

2
Summary

• CH Overtone Intensities TMA and DMS
• Structural information from CH overtones
  Metallocenes
• ICL-PARPS A instrument for determining the V-T
  relaxation of Overtone Vibration

3
CH-Stretch Overtone Study of Trimethyl amine and
Dimethyl Sulfide

• Lone pair trans effect on TMA and DMS
• Different CH bond lengths in methyl group
• Different CH stretching frequencies
• Different intensities
• Project goals
• Measure the experimental intensities
• Compare with prediction of the (HCAO)LM model

4
Geometries
Gauche 1.0823 Å Trans 1.0832 Å
Gauche 1.0847 Å Trans 1.0956 Å
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HCAO/LM Model

• Calculations H. G. Kjaergaard and G. Low
• The Hamiltonian 3 Morse oscillators
• Dipole moment function from Grid
• LM parameters from Birge-Spöner plots
• No coupling between methyl groups

6
Experimental

• The 1st through 4th overtones of
• Trimethyl amine d0,d3,d6,d8,and d9
• Dimethyl Sulfide
• All spectra
• Collected on a Nicolet 870 FT-IR
• With a 10 m Gas cell
• Curve fit analysis was done for the second
  through fourth overtones
• Win-IR software was used for all curve fitting
• In all cases correlation (R2) better then .99 was
  achieved

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Second Overtone TMA d8
8
Second Overtone TMA
9
Second Overtone TMA d6
10
Third Overtone TMA
11
Fourth Overtone TMA
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Fourth Overtone DMS
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Relative Intensities

• Intensities of given overtone region
• For this discussion
• Intensities are reported on a per bond basis
• L-L intensities given as a single value

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Comparison of the intensities of Trimethyl amine
d8
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Comparison of the Second Overtone intensities of
Trimethyl amine d0,d3,d6
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Comparison of the Third Overtone intensities of
Trimethyl amine d0,d3,d6
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Comparison of the Fourth Overtone intensities of
Trimethyl amine d0,d3,d6
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Comparison of the intensities of Dimethyl Sulfide
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Summary

• Spectra collected
• 1st-4th overtones of TMA d0-d9
• 1st-4th overtones of DMS
• Most peaks were assigned
• Predicted and experimental intensities match well
• (HCAO)LM model showed bias towards trans CH
• Possible evidence of coupling between the methyl
  groups

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Metallocenes Overtone Frequencies and C-H Bond
length

• Study 5 metallocenes
• 3 overtones observed
• rCH-?CH correlation
• Goal To determine
• The effect of metal on CH bond length
• Mg(C2H5)2 ionic ?
• If the combination bands are brightened by metal

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Experimental

• Spectra collected on an Nicolet Nexus 870
• Metallocenes in Carbon tetrachloride
• Sodium cyclopentadienyl in THF
• The first and second overtones
• Metallocenes 1 cm path length
• Sodium cyclopentadienyl 3mm path length
• The third overtone
• Metallocenes 10 cm path length
• Sodium cyclopentadienyl 3mm path length
• Bond length Gaussian 98 at the BLYP/hybrid
  level.

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First Overtone
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Second Overtone
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Third Overtone
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Bond Length Frequency Correlations
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Bond length Frequency Correlations
I Error in I S Error in S R2 of Fit
HF/6-311G
First Overtone 1.323 .01 4.16E-5 1.77E-06 0.9875
Second Overtone 1.287 .008 2.42E-5 8.81E-07 .09869
Third Overtone 1.273 .006 1.73E-5 5.59E-07 0.9876
BLYP
First Overtone 1.319 .01 3.58E-5 2.15E-06 0.9755
Second Overtone 1.270 .02 1.88E-5 2.1E-06 0.8891
Third Overtone 1.248 .02 1.23E-5 1.35E-06 0.8732
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Results
First Second Third BLYP
HF/6-311G BLYP HF/6-311G BLYP HF/6-311G BLYP Calc.
Mg(C5H5)2 1.071 1.085 1.071 1.085 1.072 1.083 1.087
Fe(C5H5)2 1.071 1.084 1.071 1.085 1.072 1.086 1.086
Co (C5H5)2 1.070 1.084 1.070 1.084 1.071 1.085 1.086
1.071 1.086 1.085
1.072 1.087 1.086
Ni (C5H5)2 1.071 1.084 1.070 1.084 1.085
Ru (C5H5)2 1.071 1.084 1.070 1.084 1.072 1.086 1.086
Na (C5H5)2 1.073 1.088 1.074 1.088 1.075 1.090 1.090
.002 .002 .002 .003 .002 .003
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Summary

• Combination bands
• Not due to metal
• Likely due to aromatic character of Na(Cp)
• Mg(Cp)2 is likely not ionic
• The nature of metal has little effect on rCH

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V-T relaxation of Overtones

• The phase shift of a PA signal can determine V-T
  relaxation times
• Little work on V-T relaxation of overtone
  vibrations.
• V-T relaxation is of interest because
• Lazing of gases
• Chemical kinetics
• Transport properties

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Dealing with variables

• Previous studies have been hampered by many
  variables that effect V-T relaxation. These
  include
• Pressure
• Incident radiation intensity
• Presence of a buffer gas
• Cell design
• Electronics causing lag times
• Heat relaxation of the gas
• The use of a wire as a reference to eliminate
  problems with many of these variables

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Cell design
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Experimental setup
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Flow Chart of ICL-PARPS
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ICL-PARPS Signal
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Possible Interpretations

• Case 1 The wire takes longer to relax than V-T
  relaxation
• Case 2 V-T relaxation causes a phase shift gt
  180º
• Case 3 Resonance causes Inversion of phase
  shift

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Test for Case 1
Signal of the heated wire with a 50 khz frequency
In theory the relaxation of the wire cannot
take longer than 0.00002 sec
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Analysis for Case 1

• Negative apparent relaxations
• 0,0gt6gt lt 6,0gt0gt
• 0,0gt7gt lt 0,0gt6gt
• All values lt -0.00002 sec

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Analysis for Case 2

• All relaxation times for TMA are negative
• Positive relaxation time for Methane

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Analysis for Case 3

• All relaxation times are positive
• 0,0gt6gt gt 6,0gt0gt
• 0,0gt6gt lt 0,0gt7gt
• 6,0gt0gt lt 0,0gt7gt
• Methane 450 Times greater then what has been
  observed for the fundamental mode

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Conclusions and Future Work

• Case 3 seems to be the correct
• More experimentation
• Error unacceptably high
• Replace resonance with a lock-in amplifier
• Collect both signals simultaneously
• Overall the system shows promise

41
Acknowledgements

• Supervisor
• Dr. K. M. Gough
• Committee
• Dr. A. Secco
• Dr. Tabisz
• Dr. Henry
• Dr. Wallace
• My Family Friends
• My fellow Graduate students
• The Faculty and staff at the University of
  Manitoba

• Collaborators
• Dr. H. G. Kjaergaard
• Dr. G. Low
• Dr. Fedorov
• Dr. Snavely
• Dr. T. Gough
• Funding
• NSERC
• UMGF
• Brock award for Physical Chemistry
• Medicure

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(HCAO)LM Model Theory
The oscillator strength between the ground state
g and excited state e is given by
Where
Is the frequency of the transition in wavenumbers
Is the dipole momment function
egt and ggt are the vibrational wavefunctions
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LM Parameters

• The values shown here a larger difference in
  anharmonicity
• By using more values the previous work lower
  error was achieved
• Agreement with previous work is generally within
  experimental error
• In all cases the presence of Fermi resonance
  contributed to the error

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(HCAO)LM Model Theory
For a methyl group the Hamiltonian is that of
three Morse oscillators
Where
Is the energy at the ground vibrational state
Is the vibrational quantum number
Is the LM frequency
Is the anharmonicity
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(HCAO)LM Model Theory
a and a are annihilation and creation operators,
with approximately step down and step up
properties
The remaining terms are the coupling parameters
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(HCAO)LM Model Theory
The coupling parameters are
Where
Are elements of the G matrix
Are elements of the force matrix
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(HCAO)LM Model Theory
Is the derivative of the dipole moment multiplied
by (1/i!j!k!), obtained from 2D grids of the
dipole moment as a function of both (q1,q2) and
(q1,q3)
q coordinates are displacements from equilibrium
bond length
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Fermi Resonance
W is the perturbation function given by the
anharmonic terms in the potential energy
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Fermi Resonance
?0 then 50/50 as ? increases approaches
unperturbed
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First Overtone
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Second Overtone TMA d3
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Third Overtone TMA d8
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Third Overtone TMA d3
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Third Overtone TMA d6
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Fourth Overtone TMA d3
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Fourth Overtone TMA d8
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Fourth Overtone TMA d6
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Second Overtone DMS
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Third Overtone DMS
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Density Functional Theory
HF energy has the form
V is the nuclear repulsion energy P is the
density matrix lthPgt is the one-electron
energy 1/2ltPJ(P)gt is the classical coulomb
repulsion of the electrons -1/2ltPK(P)gt is the
exchange energy
DFT energy has the form
EXP is the exchange functional ECP is the
correlation functional
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Comparison of the intensities of Trimethyl amine
d0
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Excitation of the acoustic wave
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Energy Transfer Physics
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Helmholtz Resonator Cell
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Test Equivalence of Resonance
Side 1 Side 2 Phase
Freq. Amp. Phase Amp. Phase Diff.
560.036 11.536 266.061 11.792 266.829 0.768
560.035 11.516 265.943 11.935 266.650 0.707
560.037 11.543 265.978 11.671 266.907 0.929
560.036 11.482 265.689 11.743 266.819 1.13

• There is some difference between the sides
• The difference is not significant
• The difference also varies and is likely not due
  to a lack of symmetry

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Effect of Voltage
Heated Reference Wire Heated Reference Wire Heated Reference Wire Heated Reference Wire Laser Induced Laser Induced Laser Induced Phase Diff.
Volt. Freq. Amp. Phase Freq. Amp. Phase Phase Diff.
10 345.02 59.31 24.63 345.05 14.74 -26.46 -51.08
1 345.02 40.99 22.94 345.02 18.24 -29.45 -52.40
0.7 345.02 21.36 19.79 345.02 19.34 -32.30 -52.10
0.5 345.02 11.10 20.79 345.02 18.86 -30.49 -51.29

• Amplitude increases with voltage
• Increase is not linear
• No systematic change of phase with voltage
• Phases do differ between trials
• The difference is less for the phase differences