DMITRY G. MELNIK1 MING-WEI CHEN1, JINJUN LIU2, and TERRY A. MILLER1, and ROBERT F. CURL3 and C. BRADLEY MOORE4

EFFECTS OF ASYMMETRIC DEUTERATION ON THE ROTATIONALLEVEL STRUCTURE OF JAHN-TELLER ACTIVE METHOXY

RADICALS

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.

Motivation

• Jahn-Teller active molecule with spin-orbit interaction

• High resolution spectroscopy: characterize the effects of lowering of the nuclear symmetry on the rotational level structure

• Connect the spectra of the molecule to intrinsic geometric properties and the properties of the electronic wavefunction

• Use isotopic relationships and the data obtained from the study of the normal species to facilitate the analysis

Methoxy spectroscopy

1/ 2E

3/ 2E 2X E

21 6;A A

21 3;2A A

LIF –Rotational structure

of E3/2 state (=50MHz)P = -1, 0, +1

LIF –Rotational structure

of E3/2 state (=50MHz)P = -1, 0, +1

Direct microwave absorption –rotational structure of E3/2 state

across paritystacks (=1 MHz)

=0P=0

p: +1 <-> -1

Direct microwave absorption –rotational structure of E3/2 state

across paritystacks (=1 MHz)

=0P=0

p: +1 <-> -1

SEP –rotational structure

of E1/2 state(=70 MHz)

Pump+Dump:= -1

p = +1<-> +1 -1<->-1

SEP –rotational structure

of E1/2 state(=70 MHz)

Pump+Dump:= -1

p = +1<-> +1 -1<->-1

Rotational level reflection parity:p = +1p = -1

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

Experimental data: LIF and SEP (CHD2O)

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

Experimental data: microwave spectra

C3vCs

EA

A

00

0 0

1

22 21

2 2 2

e

SVEe

a d E evEH

a dEE ev

E

(a)

aI.Kalinovsky Ph.D. Thesis, U.of California, Berkeley, (2001)

0 0

0 0

10.31

2

10.3

0.95

0.95 12

ev ev ev

ev ev ev

1

1

| | | |

47 cm

62 cm

e

e

E a d

E

a d

• Treat nuclear asymmetry effects as perturbation.

• Use C3v vibronic functions.

• Ignore the effects of the totally symmetric modes (i.e. limit the discussion to the components of doubly-degenerate modes)

Spin-Vibronic problem

0EV JTSVE SO ASYMHH HH H

Basis set:

-- eigenfunctions of

in unsubstituted (normal)species

ev

0EV EV JTH H H

Difference in ZPE along A” and A’ components

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

D.Melnik, J. Liu, R.F. Curl and T.A.Miller et al Mol.Physics, 105, 529 (2007)

Choice of the axis system

General form:HEFF = HSO + HROT + HCD + HCOR + HSR + HJT + HCDJT+ HSRJT+ HASYM

Basis set:

Effective Rotational Hamiltonian

1/ 2, 1 2 ( 1)J P SJPS p e JP S e J P S

Two types of rotational matrix elements:

,ˆˆ

R Sev S J P Oe e PO J S

Matrix element of the vibronic part of microscopic rotational Hamiltonian

,ˆ(ˆ 1)ev R SS J P O J P S

J P

e

S

O e

-diagonal in vibronic component, or“parity-independent”

-off-diagonal in vibronic component, or“parity-dependent”. In the absecne of vibronic interaction all parity-dependentterms vanish.

Expressions for HROT and HJT

2 2 21 2 1

1

0 2 0 0 0 0

2

1

2

2

2 2 0

12

81

2

1 1 1,

4 4

4

1

2

12

8

4

R

JT z z A

xx yy xy

xz yz

xx yy x

OT

zz z yy xx yy xx

z

z

y

z B

x

xz

H

H h N h N N h

N N N N N

h ev i ev

h ev i ev

h ev i ev

h ev i

N

N h N N h N h N

N

N

N

1

21

2

yz

A zz

B xx yy

ev

h ev ev

h ev ev

Nuclear asymmetry-induced terms. These terms

vanish in the limit of symmetric molecule

Spin-rotation in an asymmetrically substituted molecule

00

(2) . .COR SO

i

COR SOR

i iiS

e H i i e H i i H e

E

H e

EH c c

EE

Spin-rotation interaction is dominated by the second order contribution:

The parity-independent part: derived using relationships by J. Brown, T.J. Sears and J.K.G. Watson (a)

The parity dependent part. Only two types of the interactionin C3v group(b):

-- with nondegenerate states

-- with doubly degenerate states

The isotopic substitution does not alter the electronic wavefunctions,therefore we expect exactly the same number of independent spin-rotationalparameters in the isotopically substituted species!

2 2

2 1

10 0

20

2

i i

xx yy

i ii i

i iz

zzi i

A L e A L eB Ba

E E E E

e L E E L eaB

E E

(a) J.M. Brown, T.J. Sears, J. K. G. Watson, Mol. Phys.  41, 173, (1980)(b) J. T. Hougen, J. Mol. Spectroscopy, 81, 73 (1980)

Effective spin-rotational Hamiltonian

2 2 2 2 2 21 2 2

2 21

2 22

21

1 1

4 8

, ,4 4

SR zz z z xx yy xx yy

xz zxz z

SRJT a z z b z z

a z z

a z z

b

H N S N S N S N S N S

N N S S S N

H L N S L N S L N S L N S L N S L N S

L L N S

L N S L N S

L N

2

2 22

2 2, ,

b z z

S L N S

L N S L N S

L N N S L N N S

Parity-independent terms, incl. asymmetry-induced

Parity-dependent terms in normal species

Nuclear asymmetry-induced parity-dependent terms. None of these parameters are independent.

(a) J. T. Hougen, J. Mol. Spectroscopy, 81, 73 (1980)

Parameter constraints

HSR :

2

2

xx yy

xx yy

xzxz zz

zz

xzzx xx yy

xx yy

xx yy

xx yy xx yyxx yy

nbcn

B B

B

B

B

B B

B B

B B

B

11

2 2

2xx yy

zza

nn

an

B

A

B B

B

HSR :

1 2

2 1

1 1

2 2

12

2

2

2

2 4

xza a

zz

xza

xx yy

xx yy

b

xx yy

xx yy

b azz

xz aa

zz

B

B

B

B B

B B

B B

B B

B

B

B

Additional constraints: HCD

Parameters are derived from the corresponding values in the normal species using 2nd order PT (a)

• A total of 18 ground state parameters were constrained in the actual fits.

N NK K D e e t K tD D D a d

(a) R. N. Zare, Angular Momentum (Wiley Interscience, New Yourk, 1988)

1 2, , ,n n n naA B Where are the values of the

corresponding parameters in normal species

Numerical analysis: statistics

CH2DO CHD2O

Number of assigned transitions:

MW 13 14

LIF 126 165

SEP 8 6

Fit standard deviation (MHz)

MW 0.26 0.36

LIF 38 36

SEP 55 54

Number of independently fit parameters

17 17

5 5

5 5

2

21 3

21 6

2

X E

A A

A A

Experimental accuracy: MW: 1 MHzLIF: 50 MHzSEP: 70 MHz

1

2

1

2

94900(15) 95180

/ 2 23884(5) 23917

/ 4 271(3) 253

4339(92) 4482

27638(13)

1722481(1

Parameter Value (exp) Valu

55)

26757(

72(4) 85.5

1011

29(1) 0

136(26) 234

41) 2

e

66

(pre

90

d)

zz

xx yy

yy xx

xz

zz t

e

zz

B

B B

B B

B

B

h

h

h

h

h

a d

299(15) 1144

19(1) 25.8

1301843(204)

A

Bh

E

1

2

1

2

119028(20) 119171

/ 2 25836(7) 25876

/ 4 434(3) 426

6350(97) 6577

36989(12)

Parameter Value (exp) Value (

1790517(2

79(11) 84.3

1221

26(2) 1

17)

31660(60) 33475

p

7

269(2

red)

zz

xx yy

yy xx

xz

zz t

e

zz

B

B B

B B

B

B

a d

h

h

h

h

6) 321

1003(21) 2329

10(1) 0

1367281(288)

A

B

h

h

E

Molecular constants of the ground state

CH2DO CHD2O

NOTE: for brevity, CDJT terms are not shown

Conclusions

• A simple mechanical model is used to construct the effective rotationalHamiltonian of the asymmetrically substituted methoxy radical.

• The parameters of this model are shown to have straightforward physicalmeaning by relation to the corresponding parameters in the symmetric species.

• The model is successfully used to calculate a number of parameters tobreak correlations in the fit procedure and reduce dimensionalityof the problem.

• The model is used to describe all available high resolution spectra to the experimental error.

Acknowledgements

• Colleagues:

Gabriel Just,Dr. Phillip Thomas,Rabi Chhantyal PanTerrance Codd,Neal Kline

•OSU

•NSF

Calculation of the asymmetry-induced HJT terms

• Electronic PES is insensitive to isotopic substitution• h1, h2 etc. terms characterize the geometry of the molecule in JT minimum (Watson)

Structural parameters from fit of () to experimentalvalues of A,B,h1 and h2of C3v species:

r

1 1 2

1 1 2

2 2

cos sin cos

sin cos sin

cos sin

xx xz

yy

xz

B h h B h

h B h h

B h h A

3

2

1.36039(8)

1.10697(9)

3.67(6) 10

107.76(1)

3.13(40) 10

3.26(20)

4.44(11)

o

o

CO

CH

CH CD

Parameter Value

R A

R A

R R A

HCH

r

Substitute to the expressionof for asymmetric species,calculate assymetry-inducedterms in HJT

Rotational Hamiltonian HROT and HJT

A’ A’’

“O”

Qa

“A”z

xx

y y

zz

y

x

“B”“O”

,

,

1( )

1( )

( )2

0

( )2

ROT JTROT JT

A BJT R A R A

R

JT ROT

J

OT R A R A

a

T

H H

H HH

H H

ev

ev H

H H ev H ev

e

e

v

i

Q

H

v

Undistorted configuration at

conical intersection