DMITRY G. MELNIK AND TERRY A. MILLERThe Ohio State University, Dept. of Chemistry, Laser Spectroscopy Facility,

120 W. 18th Avenue, Columbus, Ohio 43210JINJUN LIU, Department of Chemistry, University of Louisville, 2320 South

Brook Street, Louisville, Kentucky 40292.

ANALYSIS OF THE ROTATIONAL STRUCTURE OF THE TRANSITION OF ISOPROPOXY RADICAL: ISOLATED vs. COUPLED STATE MODEL

2 2A AB X

Jahn Teller Effect

Pseudo Jahn Teller Effect

Pseudo Jahn Teller Effect

355(10) cm-1

60.7(7) cm-1

b Ramond et. al. J. Chem. Phys. 112, 1158 (2000)c Rabi Chhantyal-Pun, Jinjun Liu and Terry A. Miller , TI14 ,MSS 2012 Columbus d Jin et. al. J. Chem. Phys. 121, 11781 (2004)

CH3O

C2H5O

i-C3H7O

a Foster et. al. J. Phys. Chem. 90 6766 (1986)

2X E

2A A

2X A

2A A2X A

Background

(a)

(b)

(c,d)

Background

1. Rotationally resolved spectrum of isopropoxy radical has been has been quantitatively fit to a simple isolated asymmetric rotor model with spin rotation a

2. Experimentally observed rotational constants are consistent with the quantum chemistry calculations.

3. Experimentally observed spin-rotational parameters are inconsistent with

(i) quantum chemistry calculations (ii) predictions based on the previously obtained values for

other alkoxy radicals. (iii) multimode vibronic calculations

4. Despite the expected strong Coriolis and spin-orbit mixing with the closely lying electronic state, which would expect to produce characteristic a-type transitions, none are observed.

The physics behind pp. 3 and 4 needs to be understood.

2 2A AB X

2AA

a D. G. Melnik, T. A. Miller and J. Liu, TI15, 67th MSS, Columbus OH 2012

THz

814.30 814.35 814.40 814.45

Experimental and predicted spectra: simple asymmetric rotor

Exp

c-type

c-typeb-type

c

b

c

c

b

c

b

Parameters of the effective rotational Hamiltonian

Parameter Experimental “Isotopic”predict.

ab initio1 ab initio2 vibronic calc.3,4,5

9.338(3) 9.187 9.23

8.064(3) 8.008 8.15

4.893(3) 4.825 4.90

+4.26(2) -0.11 -0.11 -0.13

-4.59(2) -13.94 -0.76 -2.85

+1.72(1) -0.47 -0.03 -0.15

1.96(3) +2.55 +0.17 -0.48

state parameters (GHz)X̃� a:

/ 2

aa

bb

cc

bc cb

A

B

C

[1] B3LYP/6-31G(d)[2] CCSD/cc-pVTZ – Gyorgy Tarczay, private communication.[3] We assumed the value for an unquenched spin-orbit coupling constant -145 cm -1, and the angle between the CO bond and z-axis 72 degrees.

[4] [5]

22.52 20.51 21.175

2.9 0.94a aac abB B

0a

a

a q

BB

q

( ) ( )ev x evX a L A a

a D. G. Melnik, T. A. Miller and J. Liu, TI15, 67th MSS, Columbus OH 2012

Traditional treatment of spin-rotation

,

( ) ( ) ( ) ( ). .

( ) ( ) ( ) ( ) 1 .

2

ev SO ev ev COR eviSR

k i i k

ev ev ev ev

k i i k

i H k k H iH h c

E E

i aL k k B i N Sh c N S N S

E E

Second order PT treatment

For the lowest vibronic state the expected sign for ab is that of the spin orbit couplingconstant (i.e., negative) .

2 ( 0)X A v

2 ( 0)A A v

all other vibronic states

Second order PT:

Vibronic calculations a + experiment:

0,

( ) ( )

( ) ( )ev SO ev

i k ikev COR ev

i H kE E E

k H i

-

-10

-2 20

1

1

38.4 cm vibronic calcula

60.7 cm experiment

47.1

tion

m

s

ce

E

E

a d E E

a D. G. Melnik, T. A. Miller and J. Liu, TI15, 67th MSS, Columbus OH 2012

( )ROTH X

( )SRH X

Isolated and twofold coupled Hamiltonian

Isolated state model

2A ( 0)X v 2A ( 0)X v 2A ( 0)A v 2A ( 0)A v

Twofold (coupled state) model

( )SRH A

( )SRH X

( )ROTH A

( )SRH A

1. Van-Vleck transformation (usually 2nd order PT)

( )ROTH X

( )SRH X

( )ROTH A

( )SRH A

Van-Vleck transformation within the twofold

SO CORH H

SO CORH H

SO CORH H

SO CORH H

X state rotation levels are treated as partsof “compound” twofold state constraintson X and A state parameters need to be imposed

Hamiltonian and the basis set.

Vibronic basis set (basis functions are real): -- eigenfunctions of the vibronic Hamiltonian.

Rotational Hund’s case “b” basis

Effective rotational Hamiltonian:

(0) ( ) ,

(1) ( )

ev ev

ev ev

X a

A a

JSNK

ROT SR SO CORH H H H H

0

22

1

1(0)

2

1 + (1)

2

ROT

SR N S

N

H

H

S

I B N

2

0 1

2

1 0

0 1

1 0 0;

0 1 0

1 0 0 0;

0 0 0 1

c bCOR y t c t b

SO y e c c e b b

z y

H C N B N

H a d S a d S

I

i

i

Transition intensities.

2

*, , ,,

, ,

( )( )B J SN K B J SN K X J SN KB J SN K J SN K ev evX J SN K

N KN

kK

S F T C C J SN K B J SNk K

Spin-rovibronic eigenvectors for the twofold and the B state:

,

,

,

,

, ( )

,

X JSNKJSNK ev

NK k

B JSNKev JSNK

NK k

X JSNK C k J SN K

B JSNK B C J SN K

Rotational transition intensity:

Isolated state model:No explicit summation over componentswith different rovibronic symmetry onlyin-plane transitions are allowed

Twofold model:Explicit summation is performed over components with different rovibronic symmetry both in-plane and out-of-planetransitions are allowed.

Molecular constants for the coupled twofold.

Parameter GHz value (twofold) value (isolated)

A 9.350 (5) 9.338 (3)

B 8.070 (4) 8.064 (4)

C 4.903 (4) 4.893 (3)

azed (cm-1) -38.84 (10) ---

zt 0.264(6) ---

DE0 (cm-1) 46.6 (15) ---

q 19.2(7) ---

eaa 0 +4.26 (2)

ebb 0 -4.59 (1)

ecc 0 1.72 (1)

ebc 0 1.96 (3)

Constraints for the twofoldHamiltonian:

Spin-rotation parameters for the X state are restricted to 0 due to 100% correlation to spin-orbit and Coriolis parameters.

220

sin

cos

sin

cos

0

e c e

e b e

ct t

bt t

e

a d a d

a d a d

E E a d

Experimental spectra and simulation.

THz

814.30 814.35 814.40 814.45

Experimental.

Twofold model,all transition types.

Isolated model,c-type + b-type.

THz

814.30 814.35 814.40 814.45

Component contribution to transition intensities.

Full simulation,a,b, and c-type

c-type

b-type

a-type

Correlation of isolated state and twofold models.

SROT RR SO COH HHH H

Twofold Hamiltonian Isolated state Hamiltonian

ROT SRH H H

1. Van-Vleck transformation within the twofold (i.e. transition from twofold to isolated model) does not introduce new rotational operators, but affects the parameters of the existing ones (spin-rotation).

2. On the other hand, second order PT fails to predict parameters of SR tensor even qualitatively (specifically, second order contribution to ).

3. Two types contribution to the spin-rotation parameters in the isolated state model:

0aa

(2 2) 2 1n nCOR SOH H

0 0

0

, ,. .

k m

k i i m

i i

H H

X H H Xh c

E E

-- even order VVT (the second order, n=0 is already discussed)

-- odd order VVT, independent of Coriolis coupling (dominated by spin-orbit terms)

(2 1) 2

(2 1) (2 1)

n nROT SO

n n

n

H H

2 2

20

2

220

2

2

2

20

0

cos

2

sin

sin 2

4

0

eaa

ecc

ebb

ebc

cb

a dC

E

a dB

E

a dB

a dA

E

E

Third order contribution to spin-rotation parameters.

sin

cos

e c e

e b e

a d a d

a d a d

“Geometric” approximation forthe components of the spin-orbit coupling:

0aa ; A rot. constant is usuallywell-determined and unaffectedby the third order spin-orbit effects.

Therefore it provides the direct measure of

2

20

ea d

E

Summary.

1. Rotationally resolved spectra of the is analyzed using two models, isolated state and twofold (coupled states). Both analyses adequately predict spectra to the experimental error.

2. Parameters of the two models are related to each other, but have more transparent physical meaning.

3. Application of the twofold model for the analysis of the rotational structure of isopropoxy radical provides a good opportunity to test multifold approach for the analysis of the spectra involving strongly coupled vibronic states.

2 2B A X A

Acknowledgements

• Colleagues:

Dr. Mourad RoudjaneDr. Rabi Chhantyal Pun Terrance Codd,Neal Kline

• OSU

• NSF

•UoL

Spin-Rotation: third order and beyond.

0.0 0.5 1.0 1.5 2.0

0

2

4

6

8

10

12

14

eyy

, GH

z

0

ea d

E

Simulations A = 9.338 GHz.DE0 = 47.4 cm-1

2

20

eaa

a dA

E

2

220

2

2

eaa

e

e

a dAE a d

a dA

E

Third order VVT is clearlyinsufficient for qualitative prediction of spin-rotationalparameters in the isolated model.

Application of the twofold modeleliminates the need of cumbersomecalculations.

Isopropoxy

0

0.83ea d

E