1 B. RAM PRASAD, MANGALA SUNDER KRISHNAN Department of Chemistry, Indian Institute of Technology Madras, Chennai 600 036, India. AND E. ARUNAN Department.

1

B. RAM PRASAD , MANGALA SUNDER KRISHNAN

Department of Chemistry,

Indian Institute of Technology Madras,

Chennai 600 036, India.

AND

E. ARUNAN

Department of Inorganic and Physical Chemistry

Indian Institute of Science,

Bangalore 560 012, India.

PERTURBATION TREATMENT OF STARK EFFECT ON

TORSIONAL ENERGY LEVELS

2

Acknowledgements

Director IIT Madras,

Dr. S. Karthikeyan,

Dr. Pankaj K Mandal (IISc Bangalore),

Funds:

IIT Madras,

IITM Alumni Association,

Department of Science and Technology India (DST),

Tamilnadu State Council for Science and Technology (TNSCST)

Conference Organizers.

3Spectral assignment of benzene – water dimer

15760 15800 15850 15960

m=1

0'

m=0m=1

0123k210-1-2-3k

320-1-2-30'

121110987654321

Stick diagram of the J = 3 → 4 progression observed for the C6H6 - H2O dimer.

A. Assignment given by Gutowsky et al. for the m=0 and m=1 states.

A

B

B. Assignment given by Emilsson et al. based on the Stark measurements.

Dipole moments obtained by Emilsson through fitting:

m=0 ----- 1.65 Debye and m=1 --- 2.00 Debye.

T. Emilsson, H. S. Gutowsky, G. de Oliveira and C. E. Dykstra, J. Chem. Phys., 112, 1287 (2000).

H. S. Gutowsky, T. Emilsson, and E. Arunan, J. Chem. Phys., 99, 4883 (1993).

4Original and revised Assignments

15760 15800 15850 15960

m=1

0'

m=0m=1

0123k210-1-2-3k

320-1-2-30'

121110987654321

0

Is this progression really arising from three different states, attributed to the three J = 1 states of H2O? or any error in the interpretation of Stark splitting?

Original could be fitted to a VRT Hamiltonian, with most of the lines assigned

to two progressions, that of m = 0 and m = 1 all in blue

Stick diagram of the J = 3 → 4 progression observed for the C6H6 - H2O dimer.

Revised assignment based on Stark effect, divides the m=1 progression into three different states, in blue, red and black.

5

13CC5H6-H2O and C6H5D-H2O spectra

Rotational spectra of these asymmetric tops showed similar m=0 and m=1

progressions.

Both series were split due to asymmetry.

The spectra of the three isotopomers (including parent C6H6-H2O) could be

fit to the same VRT Hamiltonian.

B. Ram Prasad, Mangala Sunder Krishnan and E. Arunan, J. Molec. Spectrosc., 232, 308 (2005).

6

Expressions used by Emilsson et al. for the calculation of dipole moments:

The second order expression:

These expressions are standard symmetric top semi rigid rotor Stark shift expressions.

They do not contain explicitly the effect of the torsional degree of freedom.

22 22 22

20

3 8 16 5 4 1 22.

2 2 1 2 1 2 3 2 5

M J J J J JEv

h v J J J J J J

2 1 2, .

1 2 2 0.50344

E h KM J J Jv and

J J J KME

The first order expression:

7

VRT Hamiltonian in the presence of an electric field can be written as,

and

where,

Stark energy corrections with the effect of torsion:

ˆStark EVRT HH H

Yun-Bo Duan, Hui-Min Zhang, and Kojiro Takagi, J. Chem. Phys. 104, 3914 (1996).

E MH E

1 11 11 1ˆn n n n

n n n ni S i S i S i Si S i SVRT VRTH e e e H e e e

3 7

1

21 1ˆ2 2

ˆ ˆ ˆ ˆˆ ˆN

VRTk

kH J J P V

1 11 11 1ˆn n n n

n n n ni S i S i S i Si S i SM e e e e e e

8

Assuming the internal rotation is periodic: the dipole moment operator is,

The transformed dipole moment operator is,

00 0 01

0k 1

0kl 1

1 cos sin

+ 1 cos sin

+ 1 cos sin

+... .

ˆ

.

ˆ

ˆ

t t tt f f

f

t t tk kf kf

f

t t tkl klf kl

k

k l ff

nf v nf

nf v nf

nf v nf

q

q q

1

2

1 cos sin

,

vv t tt k kt k kk t

t k

t tt

t

t

t

M v C D

n B n

P P

A

Yun-Bo Duan, and Kojiro Takagi, J. Chem. Phys. 104, 7395 (1996).

9The effective dipole moment operator for the ground vibrational state is,

00 ' 1 cos sin, t tt t t t

tt t

t t

P PM A n B n

Therefore, Stark Hamiltonian in our calculations:

ˆStark EVRT HH H

00 00ˆS k Ttar VRH H ME

Calculating all the required matrix elements like,

JKMm JKMm JKM JKM mP

P

and

JKMm JKMm JKM JKMP P P P P P P

10First order Stark correction:

(1)

2

2'

3

1

+ + 2 1

1 cos sin 2 .

+ 1

. 4

z z

xx yy zz yy xxz z z

z

z

z

z

z

zz

EKME

J J

EK MEKM

J

m A n B n m

J

E

m

mK M

J J

' ' ' '

2 2 2*

2 , ', , ', ' , , '

'

'

' '

E E E

J J J m m m

KMm H KMm KM H KM JKM H JKME

E J m E J m E J m E J m

J J J m J m m m

E J m E J m

Second order Stark correction:

11

'

2

'

'

2 '

2

, ,

1

, 1,

2 4

+

E

J J

z z z

zz z

J J

A

m K

KMm H KMm

E J m E J m

E

m

E J m E J m

2 2

2 22 222

2

2 1 .

1 1 +2

1 2 1 2 3

+

xx yyz z

zzz

J J K

J K J MK

J J J

'

2 2 2

1

, 1,

+ .

2 4

z z

x

z

zz

xzz

yyz

E J m E J mA

m Km J K

2 2 2 222

2 +2

2 1 2 1zzz

J K J MK

J J J

12

' '

2*

' '

2 22 2

22'

' '

2'

, ,

1 11

, 1, 1 2 1 2 3

sin cos

E

J m

z z

KM H KM

E J m E J m

J K J

J m J m

m B n A nM

EE J m E J m J J J

m

2 2 2 2

2'

2'

sin cos

+

1

2 1 2 1, 1,

z zm B n A n mJ K J M

J J JE J m E J m

'

'2

*

'

2 2 22

2'

' 2

, ,

1

, , 1

si

n cos

E

m

z z

m m

m

JKM H JKM

E J m

B n A n m

E J m

K ME

E J m E J m J J

13Numerical test case:

H. S. Gutowsky, T. Emilsson, and E. Arunan, J. Chem. Phys., 99, 4883

(1993).

14

Future directions:

The dipole moments and the assignments given by

Emilsson et.al., have to be verified with the torsional

dependent RSPT Stark expressions given here.

Thank you