THE ANALYSIS OF HIGH RESOLUTION SPECTRA OF ASYMMETRICALLY DEUTERATED METHOXY

RADICALS CH2DO AND CHD2O

(RI09)

MING-WEI CHEN1, JINJUN LIU2, DMITRY G. MELNIK1 and TERRY A. MILLER1, and ROBERT F. CURL3 and C. BRADLEY

MOORE4

1Laser Spectroscopy Facility Department of Chemistry The Ohio State University,2Laboratory of Physical Chemistry ETH, Zurich, Switzerland

3Department of Chemistry and Rice Quantum Institute, Rice University,4Department of Chemistry, University of California, Berkeley.

Outline

The goal:

•Understand the molecular properties of methoxy radicals “beyond numbers”

•Built the relationship between the molecular properties of different isotopomers

•Study the effect of symmetry reduction on the molecular parameters

Methods:

•Comparison of the molecular parameters of the symmetric methoxy species, CH3O and CD3O .

•High resolution spectroscopic study of asymmetrically deuterated methoxy species, CHD2O and CH2DO.

•Extension of global analysis to experimentally determined molecular parameters of substituted species.

The Benefits of the Isotopic Studies

( )V q

The potential hypothetical moleculealong normal mode q

q

Levels of Isotopomer 2

Isotopic scaling of rotationally resolved spectra:

• Molecular properties manifest themselves through the effective parameters of the rotational Hamiltonian:

• The Xi are the effective parameters that are co-factors to the terms with the unique functional dependence on quantum numbers fi(J, P,, etc...).

• Parameters Xi have different contributions:

• If F1, Fe and Fv have different functional dependence, they can be separated, e.g. through studying the isotopic dependencies.

( , , ,...) ( , , ,...)i ii

E J P X f J P

Interactions with excited vibrational statesInteractions with excited electronic states

1 2 2

1 1

2

2

( , ,...)

( ; , ,...)

( ; , ,...)

e vi i i i

e ei e

v vi v

X X X X

X ev X ev F r m

X F E A B

X F E A B

Levels of Isotopomer 1

Hamiltonian parameters and corrections

HEFF = HROT + HCOR + HSO + HSR + HJT + HCD

[1] J.Mol.Spectrosc., 81, 73 (1980)[2] J.Mol.Spectrosc., 140,112 (1990)[3] J. Chem. Phys, 42, 2283 (1965)[4] Can.J.Phys, 59, 428 (1981)[5] This work

2 1/ 2 1[3 5]2

1/ 2 1[5

1 2 [2] 2 [1]

1 1 2 2 2 21 1 1

2 2 2 22 2

2 21 3

22 4

2 21 1

222

1 32

2 42

2 4

]3

4

2

4

v e

v eH

v e

e

e

v eaa e

ebc

e

e

H

a

b

H

e

X X X X

A m K A K A K

B B K B K

h B K

h ABK

aA K aAK

aBK

B m K

ABm

aBK

aAK

aB

K

K

H

I

Note: we assume that the ratio of thevibrational frequency wi of the normal and substituted species is approximately the same for all modes.

A,B – rotational constants,mH – mass of the hydrogen isotopea – spin-orbit coupling constant – the ratio of the average vibational frequency of the protonated isotopomer ( ) to that of the species in question ( ).

Dominating terms are highlighted

HI

Isotopic Dependence and Structural Parameters

Experimentally obtained values and their ratios: Experiment vs. estimation

Experimentally obtained structural parameters of methoxy radical*:

, varied 0.003

, 1.1137(16) 1.1063(25) 1.1099(13)

, 1.1075(5) 1.1063 1.1069

, 1.3597(8) 1.3637(2) 1.3618(1)

,deg 111.1(1) 110.6(2) 110.8

CH CD CH CD CH CD

CH

CD

CO

Parameter r r r r r r A

r A

r A

r A

OCH OCD

13 [ ] 13 12 13 12 12 123 3 3

1

/ , / , / , / ,

154800(50) 154800 78391(23) 0.500 0.5064(2)

27930.36(4) 27283.9(38) 0.97687(8) 22194.05(2) 0.794621(1)

77.7(21) 73.9(24) 0.954 0.95(5) 88.7(1) 1

1 1

a D DX CH O CH O X X cal X X obs CD O X X cal X X obs

A

B

h

2

1

.171 1.142(31)

1326(3) 1370(318) 0.977 1.03(23) 847(1) 0.650 0.639(1)

37375(88) 40870(12664) 1.0 1.09(31) 23097(71) 0.650 0.618(2)

1111(3) 1312(260) 0.977 1.18(20) 841(2) 0.795 0.757(2)

172.65(13) 167(3) 0.

aa

bc

h

2

977 0.97(2) 142.09(15) 0.795 0.823(1)

534(86) 2204(9158) 1.0 -4(16) 192(42) 0.500 0.359(97)

1843703(113) 1849175(11461) 1.003(6) 1648732(101) 0.8941(1)

0.3375(8) 0.342(8) 1.01(2) 0.2844(6) 0.8427(24)

a

e

t

a d

[a] parameters obtained from re-fitting the 13CH3O data by Momose et al, J.Chem. Phys. 88, 5338 (1988)

What Happens When the Symmetry is Reduced (CHD2O)?

| 1 | ,u uu

ev v

C3vCs

E A

ABasis set:

1

22 21

2 2 2

e

SO ASYMe

a d E ev

H HE a d

ev

Vibronic eigenfunctions:

E

1

1

47 cm

62 cme

E

a d

a

aJ. Mol.Struct. 780, 163 (2006)

1( ) 0.31

2

1( ) 0.3

0.95

0.9 12

5

A ev ev

A ev ev

Vibronic problem: “asymmetry” Hamiltonian

02

02

ASYM

E

HE

| | | |eE a d

The effective rotational Hamiltonian:

• Treat asymmetry effects as perturbation.

• Use C3v vibronic functions.

• Use the obtained isotopic dependence to predict the properties of the asymmetrically substituted species.

HEFF = HROT + HCOR + HSO + HSR + HJT + HCD + HASYM

2 2

2ASYM

EH

L L

1. Traditional treatment, principal 2. Axis system with z axis placed axis system (PAS): along C-O bond, or “internal axis system” (IAS)

a

c

D

D

H

D

DH

z

2 2 2ROT a b c

a a a a

H AR BR CR

R J S L

2 2

2 ( )

ROT z y

x xz z x x z

H A

B R R R R

R BR

CR

cos sina xzJ J J 12

( )xJ J J

x

Coordinate System for Rotational Hamiltonian (CHD2O)

Mol.Physics, 105, 529 (2007)

1/ 2E

3/ 2E 2X E

21 6;A A

21 3;2A A

LIF –Rotational structure

of E3/2 state (=50MHz)

LIF –Rotational structure

of E3/2 state (=50MHz)

Direct microwave absorption –rotational structure of E3/2 state

across paritystacks (=2 MHz)

Direct microwave absorption –rotational structure of E3/2 state

across paritystacks (=2 MHz)

SEP –rotational structure

of E1/2 state(=70 MHz)

SEP –rotational structure

of E1/2 state(=70 MHz)

Rotational level parity:evenodd

Diagram of the Levels Accessed by the Measurements.

178995.3 MHz 199614.5 MHz

1.8 MHz

183250.5 MHz

2.7 MHz 3.2 MHz

1.2 MHz

187131.0 MHz

5 1, ; 1

2 2J P

7 3, , 1

2 2J P

7 1, , 1

2 2J P 5 1

, , 12 2

J P

CHD2OCHD2O

CH2DOCH2DO

Microwave Spectra.

32915 32920 32925 32930 32935 32940

Pa

inte

nsity

(a.

u.)

frequency / cm-1

LIF of CHD2O,

32

0 band of A2A

1-X 2E

3/2

high-res moderate-res

Pb

32915 32920 32925 32930 32935 32940

Pa

inte

nsity

(a.

u.)

frequency / cm-1

LIF of CHD2O,

32

0 band of A2A

1-X 2E

3/2

high-res moderate-res

Pb

32845.4 32845.6 32845.8 32846.00.58

0.60

0.62

0.64

0.66

0.68

0.70

0.72

0.74

0.76

0.78

norm

aliz

ed L

IF

frequency / cm-1

Depletion: ~15%

Linewidth (FWHM): ~200MHz

Freq. Accuracy (1): <100MHz

*

SEP dip by Pa

* LIF excited by dump laser32845.4 32845.6 32845.8 32846.0

0.58

0.60

0.62

0.64

0.66

0.68

0.70

0.72

0.74

0.76

0.78

norm

aliz

ed L

IF

frequency / cm-1

Depletion: ~15%

Linewidth (FWHM): ~200MHz

Freq. Accuracy (1): <100MHz

*

SEP dip by Pa

* LIF excited by dump laser

~2

3/2EX

~2

1AA

~2

1/2EX

LIF

SEP

LIF and SEP Spectra (CHD2O)

Parameters of the Effective Hamiltonian (CHD2O)

Number of assignedtransitions:

• microwave 14 • LIF 165• SEP 6

Exp. accuracy [std deviation],MHz

• microwave* 2.0 [ 1.52 ]• LIF 50 [ 36 ]• SEP 70 [ 76 ]

Number of parameters used:

16

5

5

2

21 3

21 6

2

X E

A A

A A

* due to partially unresolved hyperfine structure, centers-of-mass of transitions were used

1

2

1

2

Parameter Value

94721(93)

/ 2 23954(44)

/ 4 240(23)

5252(640)

27631(14)

1721677(804)

26800(50)

907

/ 4 87(15)

2349(57)

153

230

65(6)

1399(117)

1302844(105

xz

t

e

aa

bc

bb cc

xz

a

A

B C

B C

B

A

a d

fixed

fixed

fixed

h

h

E

0)

Molecular Parameters, Isotopic Trends

Isotopic trends of some of the effective Hamiltonian parameters

2 3( ) ( ) / 2CHD O CD O

5/3 Hm m, 1.3597

, 1.1137

, 1.1075

,deg 111.1

CO

CH

CD

Parameter Value

r A

r A

r A

OCH OCD

3 3 2 2

1

2

95232 94721(93)

23894 23954(4

84 65.5(63

, ,

154800(50) 78391(23)

/ 2 27930.36(4) 22194.05(2)

/ 4 0.0 0.0

0.0 0.0

77.7(21) 88.7(1)

13

4486 5252(6

4)

253 23

26(

9(16)

3) 847

40)

)

(

xz

Parameter CH O CD O CHD O pred CHD O obs

A

B C

B C

B

h

h

1)

37375(88) 23097(71)

1843703(113) 1648372(10

1031 13

1)

29

1721677(804)

0.3375(8) 0.2844(6) 0.291

99(117

403 26

7(2

800

)

( )

)

50aa

e

t

a d

Parameters used to predict values of CHD2O

Asymmetry effects in Rotational Jahn-Teller Hamiltonian

2 2 2 2 2 21 2JT z zH h N N h N N N N

L L L L

C3v case, effective Jahn-Teller Hamiltonian

Cs case, effective Hamiltonian:

2 2 2 2 2 21 2

2 2 2 2 2 21 2 ...

JT z z

z z

H h N N h N N N N

h N N h N N N N

L L L L

L L L L

The values of h1 and h2 are modified:

where are functions of derivatives of the Components of tensor of inertia with respect to normal Coordinates and energy difference E. These functions vanish in the C3v limit.

1 1 1

2 2 2

1 ( , )

1 ( , )

u

u

h h f E B

h h f E B

( , )uif E B

The potential sources of discrepanciesbetween the prediction and experiment:

• Neglect of the coupling between thequa components of the Jahn-Teller active modes with totally symmetric modes when the symmetry is reduced:

• Vibronic coupling in the system withreduced symmetry (new type of X2v

contributions).

terms?

A

A

A

1A

E

1 2,h h

Summary

Accomplished:

• The isotopic dependencies of various parameters of the effective rotationalHamiltonian are summarized end extended, including the h1 and h2 Jahn-Tellerterms.

• The global analysis of the symmetric species is performed. Its results allowedto approach the problem of the analysis of the asymmetrically substituted molecules.

• The analysis of the CHD2O is reasonably successful within the approximationof the model used. The higher order treatment is needed to achieve the agreementof the theory with observed data within the experimental error.

Future development:

• Refine the analysis of the Jahn-Teller terms in the asymmetrically substituted species.

• Global analysis of both asymmetric species with symmetric ones.

Funding: NSF

Acknowledgements

Colleagues:

Gabriel Just

Phillip Thomas

Linsen Pei

Rabi Chhantyal-Pun

Shenghai Wu (alumni)

Patrick Rupper (alumni)

John T. Yi (alumni)

Jinjun Liu (alumni)

Erin Sharp (alumni)