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

Intensity, Frequency and Relaxation time

in the CH stretch overtones

Brant Billinghurst

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

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

Geometries

Gauche: 1.0847 ÅTrans: 1.0956 Å

Gauche: 1.0823 ÅTrans: 1.0832 Å

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

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

Second Overtone TMA d8

|3,0>|0> Fermi Resonance*




|0,0>|3> FermiResonance*


0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

8000 8500

Arbitrary units

Second Overtone TMA

|2,0>+|1>, |2,0>-|1>, |1,1>|1>, |2,1>+|0>*




|1,0>+2>




|2,1>-|0>

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

8000 8500

Wavenumbers (cm-1)


|2,0>-|1>, |1,1>|1>, |2,1>+|0>*

|2,0>+|1>




|1,0>-|2>

|1,0>+|2>




|2,1>-|0>

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

0.018

0.020

0.022

0.024

0.026

0.028

0.030

0.032

0.034

0.036

0.038 0.040

8000 8500

Arbitrary units

Third Overtone TMA

|3,1>-|0>, |2,1>+|1>, |2,1>-|1>, |2,2>|0>

|3,0>+|1>, |3,0>-|1>, |1,1>|2>, |3,1>+|0>

Fermi*

|4,0>|0>

Fermi*

|0,0>|4>

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

0.050

0.055

0.060

0.065

0.070

0.075

0.080

10500 11000 11500

Wavenumbers (cm-1)

Fourth Overtone TMA

|0,0>|5>|4,0>|1>, |1,1>|3>, |3,0>-|2>

Fermi*

|5,0>|0>

Fermi*

|1,0>|4>

Fermi*

|4,1>|0>, |2,1>|2>, |3,1>|1>, |2,2>|1>

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035

0.0040

0.0045

0.0050

0.0055

0.0060

0.0065

0.0070

13000 14000

Wavenumbers (cm-1)

Fourth Overtone DMS

See text

|0,0>|5>

|5,0>|0>

Fermi*

Fermi*

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035

0.0040

0.0045

0.0050

0.0055

0.0060

0.0065

13500 14000

Wavenumbers (cm-1)

Relative Intensities

Intensities: % of given overtone regionFor this discussion Intensities are reported on a per bond

basis L-L intensities given as a single value

Comparison of the intensities of Trimethyl amine d8

0

5

10

15

20

25

30

35

40

Second OvertoneThird OvertoneFourth Overtone

Gauche ExperimentalGauche Calculated

Trans ExperimentalTrans Calculated

Comparison of the Second Overtone intensities of Trimethyl

amine d0,d3,d6

0

5

10

15

20

25

30

N(CH3)3N(CH3)2(CD3)N(CD3)2(CH3)Calculated

Gauche Trans L-L

Comparison of the Third Overtone intensities of Trimethyl amine

d0,d3,d6

0

10

20

30

40


Gauche

Trans

L-L

Comparison of the Fourth Overtone intensities of Trimethyl amine

d0,d3,d6

0

10

20

30

40


Gauche Trans L-L

Comparison of the intensities of Dimethyl Sulfide

10

20

30

40


Gauche Experimental

Gauche Calculated

Trans Experimental

Trans Calculated

L-L Experimental

L-L Calculated

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

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

Experimental

Spectra collected on an Nicolet Nexus 870Metallocenes in Carbon tetrachlorideSodium cyclopentadienyl in THF

The first and second overtones Metallocenes 1 cm path lengthSodium cyclopentadienyl 3mm path length

The third overtone Metallocenes 10 cm path lengthSodium cyclopentadienyl 3mm path length

Bond length: Gaussian 98 at the BLYP/hybrid level.

First Overtone

NaCp-0.0

0.2

0.4

MgCp2 0.2

0.4

0.6

FeCp2 2

CoCp2-0.15

-0.10

NiCp2 1.0

RuCp2-0.8

-0.6

5500 6000

Wavenumbers (cm-1)

Second Overtone

0.00

0.02

0.00

0.05

0.10

0.00

0.01

0.000

0.002

0.00

0.01

0.02

0.000

0.005

0.010

8500 9000 9500

Wavenumbers (cm-1)

NaCp

MgCp2

FeCp2

CoCp2

NiCp2

RuCp2

Third Overtone

0.000

0.001

0.002

0.000

0.005

0.010

0.000

0.005

0.000

0.001

0.005

11200 11400 11600 11800 12000

Wavenumbers (cm-1)

NaCp

MgCp2

FeCp2

CoCp2

RuCp2

Bond Length Frequency Correlations

5650 5750 5850 5950

1.074

1.079

1.084

1.089

Frequency (cm -1)

Bo

nd

len

gth

(Å

)

8200 8300 8400 8500 8600 8700 8800

1.074

1.079

1.084

1.089

Frequency (cm-1)

Bo

nd

len

gth

(Å

)

10600 10800 11000 11200 11400 11600

1.074

1.079

1.084

1.089

Frequency (cm -1)

Bo

nd

len

gth

(Å

)

5650 5750 5850 59501.090

1.095

1.100

1.105

Frequency (cm -1)

Bo

nd

len

gth

(Å

)

8200 8300 8400 8500 8600 8700 8800

1.094

1.099

1.104

Frequency (cm -1)

Bo

nd

len

gth

(Å

)

10600 10800 11000 11200 11400 11600

1.094

1.099

1.104

Frequency (cm -1)

Bo

nd

len

gth

(Å

)

First Overtone Second Overtone Third Overtone

HF

/6-3

11G

(d,p

)B

LY

P/6

-311

G(d

,p)

Bond length Frequency Correlations

BasisBasisBasisCH SIR

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

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

Summary

Combination bands:Not due to metalLikely due to aromatic character of Na(Cp)

Mg(Cp)2 is likely not ionic

The nature of metal has little effect on rCH

V-T relaxation of Overtones

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

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

Cell design

Experimental setup

Flow Chart of ICL-PARPS

ICL-PARPS Signal

Possible Interpretations

Case 1: The wire takes longer to relax than V-T relaxationCase 2: V-T relaxation causes a phase shift > 180ºCase 3: Resonance causes “Inversion of phase shift”

Test for Case 1

Signal of the heated wire with a 50 khz frequency

In theory the relaxation of the wire cannot takelonger than 0.00002 sec

Analysis for Case 1

Negative apparent relaxations

|0,0>|6> < |6,0>|0>|0,0>|7> < |0,0>|6>All values < -0.00002 sec

0.0 2.5 5.0

-0.002

-0.001

-0.000

Relaxation time (sec)

TMA |0,0>|6> -0.0002+/- 0.0001TMA |6,0>|0> -0.00009 +/- 0.00002TMA |0,0>|7> -0.00023 +/- 0.00003Methane -0.0008 +/- 0.0004

1/Pressure (ATM)

Re

lax

ati

on

tim

e (

se

c)

tan

p

Analysis for Case 2

0.0 2.5 5.0

0.002

0.003


TMA |0,0>|6> -0.00005+/- 0.00003TMA |6,0>|0> -0.00025 +/- 0.000004TMA |0,0>|7> -0.000055 +/- 0.000004Methane 0.00011 +/- 0.00002

1/Pressure (ATM)

Re

lax

ati

on

tim

e (

se

c)

All relaxation times for TMA are negative

Positive relaxation time for Methane

3 6 0 oL H

p

Analysis for Case 3

0 1 2 3 4 5 6 70.0000

0.0025

TMA |0,0>|6> 0.0002 +/- 0.0001TMA |6,0>|0> 0.00009 +/- 0.00002TMA |0,0>|7> 0.00023 +/- 0.00003Methane 0.0009 +/- 0.0004


1/Pressure (ATM)

Re

lax

ati

on

tim

e (

se

c)

All relaxation times are positive|0,0>|6> > |6,0>|0>

|0,0>|6> < |0,0>|7> |6,0>|0> < |0,0>|7> Methane 450 Times

greater then what has been observed for the fundamental mode

tan ( )

p

Conclusions and Future Work

Case 3 seems to be the correctMore experimentationError unacceptably high Replace resonance with a lock-in

amplifier Collect both signals simultaneously

Overall the system shows promise

Acknowledgements

Supervisor:– Dr. K. M. Gough

Committee Dr. A. SeccoDr. TabiszDr. HenryDr. Wallace

My Family & FriendsMy fellow Graduate studentsThe Faculty and staff at the University of Manitoba

CollaboratorsDr. H. G. KjaergaardDr. G. LowDr. FedorovDr. SnavelyDr. T. Gough

Funding NSERCUMGFBrock award for Physical ChemistryMedicure

(HCAO)LM Model Theory

The oscillator strength between the ground state g and excited state e is given by:

f cmDeg eg eg 4 7 0 2 22

.

Where:

eg eg e g

Is the frequency of the transition in wavenumbers

Is the dipole momment function

|e> and |g> are the vibrational wavefunctions

LM Parameters

LM FrequencyAnharmonicityMazannares et.alFang et al.Mazannares et.alFang et al.Trimethyl Amine3074 4 cm-13085 26 cm-13069 5 cm-163 1 cm-164 6 cm-162 1 cm-1Gauche2892 8 cm-12877 15 cm-12915 8 cm-166 2 cm-165 3 cm-169 2 cm-1Trans

Dimethyl Sulfide3060 32 cm-13062 7 cm-154 5 cm-155 1 cm-1Gauche3038 34 cm-13070 4 cm-158 6 cm-162 2 cm-1Trans

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


For a methyl group the Hamiltonian is that of three Morse oscillators

333233333

112122

21121

00\00|

0

~)(~~

~)(~)(/)(

hcEH

Where:

E0

0|00|

i

i~

ii~

Is the energy at the ground vibrational state

Is the vibrational quantum number

Is the LM frequency

Is the anharmonicity


H hc a a a a a a a a a a a arain t, ,/ ( ) ( )11 2 1 2 1 2 1 3 1 3 1 3 2 3 2 3

a and a+ are annihilation and creation operators, with approximately step down and step up properties

The remaining terms are the coupling parameters


The coupling parameters are

12 12 12 1, ( ) ~

1 3 1 3 1 3 1 3, ( ) ~ ~

Where ij

ij

ii jj

G

G G

1

2

0

0 0 ij

ij

ii jj

F

F F

1

2

0ijG

ijFAre elements of the G matrix

Are elements of the force matrix


ijki j k

ijk

q q q1 2 3

ijk 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

Fermi Resonance

W W dn i n i 0 0

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

E E W

W E Eno

n i

in i

0 0

W E Wn i n i 1

24

2 2

Fermi Resonance

n n i

i n i

a bb a

0 0

0 0

aW

W

bW

W

n i

n i

n i

n i

4

2 4

4

2 4

2 2

2 2

1 2

2 2

2 2

1 2

/

/

=0 then 50/50 as increases approaches unperturbed

First Overtone

|1,0>+|1>|2,0>+|0>|2,0>-|0>

|1,1>|0>

TMA d0

0.05

|1,0>+|1>

|2,0>+|0>|2,0>-|0>

|1,1>|0>

TMA d3

0.05

|1,0>+|1>

|2,0>|0>

|1,1>|0>

TMA D6

0.05

|2,0>|0>

TMA d8

0.0

0.1

|2,0>|0>|0,0>|2>|1,1>|0>

DMS

2

4

5600 5800 6000

Wavenumbers (cm-1)


|2,1>-|0>

|2,0>+|1>, |2,0>-|1>, |1,1>|1>, |2,1>+|0>*




|1,0>+|2>




0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

8000 8500

Wavenumbers (cm-1)

Third Overtone TMA d8

|4,0>|0>

|0,0>|4>

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035

0.0040

0.0045

0.0050

0.0055

0.0060

0.0065

0.0070

0.0075

0.0080

0.0085

0.0090

10500 11000 11500

Wavenumbers (cm-1)


|3,1>-|0>, |2,1>+|1>, |2,1>-|1>, |2,2>|0>

|3,0>+|1>, |3,0>-|1>, |1,1>|2>, |3,1>+|0>

|2,0>+|2>, |2,0>-|2>

|4,0>|0>

Fermi* |0,0>|4>

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

0.0016

0.0018

0.0020

0.0022

0.0024

10500 11000 11500 Wavenumbers (cm-1)


|3,1>-|0>, |2,1>+|1>

|3,0>+|1>, |3,0>-|1>, |1,1>|2>, |3,1>+|0>

Fermi*

|4,0>|0>

Fermi*

Fermi*

|0,0>|4>

|2,1>-|0>, |2,2>|0>

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.010

0.011

0.012

10500 11000 11500

Wavenumbers (cm-1)

Fourth Overtone TMA d3

Fermi*

|5,0>|0>

|1,0>|4>

|0,0>|5>

Fermi*

Fermi*

|4,1>-|0> +

0.0000

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0.0010

0.0011

0.0012

0.0013

0.0014

13000 14000 Wavenumbers (cm-1)


|5,0>|0>

|0,0>|5>

10 -4

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

8.0

13000 14000

Wavenumbers (cm-1)


Fermi*

|5,0>|0>

Fermi*

|0,0>|5>

Fermi*

Fermi*

|4,1>-|0> +

0.0000

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0.0010

0.0011

0.0012

13000 14000

Wavenumbers (cm-1)

Second Overtone DMS

|1,0>-|2>

|2,0>-|1>

|2,0>+|1>

|2,1>-|0>,|1,0>-|2>

|2,1>+|0>

|0,0>|3>

|3,0>|0>

Fermi*

Fermi*

-0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

8400 8600 8800 Wavenumbers (cm-1)

Third Overtone DMS

|1,0>+|3>*

|3,1>|0>, |3,0>|1>

|0,0>|4>

|4,0>|0>

Combination*

Combination*

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

0.050

0.055

0.060

10500 11000 11500

Wavenumbers (cm-1)

Density Functional Theory

HF energy has the form:

E V hP PJ P PK PHF 1 2 1 2/ ( ) / ( )

V is the nuclear repulsion energy P is the density matrix<hP> is the one-electron energy1/2<PJ(P)> is the classical coulomb repulsion of the electrons-1/2<PK(P)> is the exchange energy

DFT energy has the form:

E V hP PJ P E P E PKS X C 1 2/ ( ) [ ] [ ]EX[P] is the exchange functionalEC[P] is the correlation functional

Comparison of the intensities of Trimethyl amine d0

0

10

20

30

40


Gauche Experimental

Gauche Calculated

Trans Experimental

Trans Calculated

L-L Experimental

L-L Calculated

Excitation of the acoustic wave

q

k E NC

B Ie

v c

i t

12 2

0

2 2 1 222

1

/( / )

2 01B I For the most common case

Energy Transfer Physics

The collisional deexcitation rate is given by

c Z Pi j A B i j

ZA Bnumber of kinetic collisions per cm3 persecond.

P i j probability of energy transfer

P ei j

u E

k Tc

2

2

1 3

/

u = relative velocity

Helmholtz Resonator Cell

c

A

lV Ar

1 2 2 21 2

4/

/

c =speed of sound l =length of the channel

Vr=VVc/V+Vc V =tube volume Vc =cavity volume

=viscosity of the gas =mass density of the gas

A = area of the channel

Test: Equivalence of Resonance

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

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

Effect of Voltage

Amplitude increases with voltageIncrease is not linearNo systematic change of phase with voltagePhases do differ between trialsThe difference is less for the phase differences

Heated Reference Wire Laser Induced PhaseDiff.Volt. Freq. Amp. Phase Freq. Amp. Phase

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

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

Documents

overtone slide

overtone tma slide

metal slide

overtone dms slide

sec slide

overtone tma d6 slide

r ch slide

overtone tma d8 slide