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Intensity, Frequency and Relaxation time in the CH stretch overtones Brant Billinghurst

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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

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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

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Geometries Gauche: 1.0847 Å Trans: 1.0956 Å Gauche: 1.0823 Å Trans: 1.0832 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

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Experimental The 1 st through 4 th 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 (R 2 ) better then.99 was achieved

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Second Overtone TMA d8

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Second Overtone TMA

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Second Overtone TMA d6

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Third Overtone TMA

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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 r CH - CH correlation Goal: To determine The effect of metal on CH bond length Mg(C 2 H 5 ) 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 IError in I SError in SR 2 of Fit HF/6-311G** First Overtone1.323.014.16E-51.77E-060.9875 Second Overtone1.287.0082.42E-58.81E-07.09869 Third Overtone1.273.0061.73E-55.59E-070.9876 BLYP First Overtone1.319.013.58E-52.15E-060.9755 Second Overtone1.270.021.88E-52.1E-060.8891 Third Overtone1.248.021.23E-51.35E-060.8732

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Results FirstSecondThirdBLYP HF/6- 311G** BLYPHF/6- 311G** BLYPHF/6- 311G** BLYPCalc. Mg(C 5 H 5 ) 2 1.0711.0851.0711.0851.0721.0831.087 Fe(C 5 H 5 ) 2 1.0711.0841.0711.0851.0721.086 Co (C 5 H 5 ) 2 1.0701.0841.0701.0841.0711.0851.086 1.0711.0861.085 1.0721.0871.086 Ni (C 5 H 5 ) 2 1.0711.0841.0701.0841.085 Ru (C 5 H 5 ) 2 1.0711.0841.0701.0841.0721.086 Na (C 5 H 5 ) 2 1.0731.0881.0741.0881.0751.090 ±.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 r CH

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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 > 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 |0,0>|6> |0> |0,0>|7> |6> All values < -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 |0,0>|6> > |6,0>|0> |0,0>|6> |7> |6,0>|0> |7> 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

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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 |e> and |g> 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 (q 1,q 2 ) and (q 1,q 3 ) 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 is the one-electron energy 1/2 is the classical coulomb repulsion of the electrons -1/2 is the exchange energy DFT energy has the form : EX[P] is the exchange functional EC[P] 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 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 Side #1Side #2Phase Freq.Amp.PhaseAmp.PhaseDiff. 560.03611.536266.06111.792266.8290.768 560.03511.516265.94311.935266.6500.707 560.03711.543265.97811.671266.9070.929 560.03611.482265.68911.743266.8191.13

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Effect of Voltage 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 Heated Reference WireLaser InducedPhase Diff. Volt.Freq.Amp.PhaseFreq.Amp.Phase 10345.0259.3124.63345.0514.74-26.46-51.08 1345.0240.9922.94345.0218.24-29.45-52.40 0.7345.0221.3619.79345.0219.34-32.30-52.10 0.5345.0211.1020.79345.0218.86-30.49-51.29

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