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

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Presentation on theme: "Intensity, Frequency and Relaxation time in the CH stretch overtones Brant Billinghurst."— Presentation transcript:

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: Å Trans: Å Gauche: Å Trans: Å

5 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 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

7 Second Overtone TMA d8

8 Second Overtone TMA

9 Second Overtone TMA d6

10 Third Overtone TMA

11 Fourth Overtone TMA

12 Fourth Overtone DMS

13 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

14 Comparison of the intensities of Trimethyl amine d8

15 Comparison of the Second Overtone intensities of Trimethyl amine d0,d3,d6

16 Comparison of the Third Overtone intensities of Trimethyl amine d0,d3,d6

17 Comparison of the Fourth Overtone intensities of Trimethyl amine d0,d3,d6

18 Comparison of the intensities of Dimethyl Sulfide

19 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

20 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

21 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.

22 First Overtone

23 Second Overtone

24 Third Overtone

25 Bond Length Frequency Correlations

26 Bond length Frequency Correlations IError in I SError in SR 2 of Fit HF/6-311G** First Overtone E-51.77E Second Overtone E-58.81E Third Overtone E-55.59E BLYP First Overtone E-52.15E Second Overtone E-52.1E Third Overtone E-51.35E

27 Results FirstSecondThirdBLYP HF/6- 311G** BLYPHF/6- 311G** BLYPHF/6- 311G** BLYPCalc. Mg(C 5 H 5 ) Fe(C 5 H 5 ) Co (C 5 H 5 ) Ni (C 5 H 5 ) Ru (C 5 H 5 ) Na (C 5 H 5 ) ±.002 ±.003±.002±.003

28 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

29 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

30 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

31 Cell design

32 Experimental setup

33 Flow Chart of ICL-PARPS

34 ICL-PARPS Signal

35 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

36 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 sec

37 Analysis for Case 1 Negative apparent relaxations |0,0>|6> |0> |0,0>|7> |6> All values < sec

38 Analysis for Case 2 All relaxation times for TMA are negative Positive relaxation time for Methane

39 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

40 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

42 (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

43 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

44 (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

45 (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

46 (HCAO)LM Model Theory The coupling parameters are Where Are elements of the G matrix Are elements of the force matrix

47 (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

48 Fermi Resonance W is the perturbation function given by the anharmonic terms in the potential energy

49 Fermi Resonance =0 then 50/50 as increases approaches unperturbed

50 First Overtone

51 Second Overtone TMA d3

52 Third Overtone TMA d8

53 Third Overtone TMA d3

54 Third Overtone TMA d6

55 Fourth Overtone TMA d3

56 Fourth Overtone TMA d8

57 Fourth Overtone TMA d6

58 Second Overtone DMS

59 Third Overtone DMS

60 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

61 Comparison of the intensities of Trimethyl amine d0

62 Excitation of the acoustic wave

63 Energy Transfer Physics

64 Helmholtz Resonator Cell

65 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

66 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

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