1 B. RAM PRASAD, MANGALA SUNDER KRISHNAN Department of Chemistry, Indian Institute of Technology Madras, Chennai , India. AND E. ARUNAN Department of Inorganic and Physical Chemistry Indian Institute of Science, Bangalore , 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.

3 Spectral assignment of benzene – water dimer Stick diagram of the J = 3 → 4 progression observed for the C 6 H 6 - H 2 O 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= Debye and m= 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).

4 Original and revised Assignments Is this progression really arising from three different states, attributed to the three J = 1 states of H 2 O ? 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 C 6 H 6 - H 2 O dimer.  Revised assignment based on Stark effect, divides the m=1 progression into three different states, in blue, red and black.

5 13 CC 5 H 6 -H 2 O and C 6 H 5 D-H 2 O 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 C 6 H 6 -H 2 O ) 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. 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: Yun-Bo Duan, Hui-Min Zhang, and Kojiro Takagi, J. Chem. Phys. 104, 3914 (1996).

8 Assuming the internal rotation is periodic: the dipole moment operator is, The transformed dipole moment operator is, Yun-Bo Duan, and Kojiro Takagi, J. Chem. Phys. 104, 7395 (1996).

9 The effective dipole moment operator for the ground vibrational state is, Therefore, Stark Hamiltonian in our calculations: Calculating all the required matrix elements like,

10 First order Stark correction: Second order Stark correction:

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13 Numerical 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