1. 1 THz vibration-rotation-tunneling (VRT) spectroscopy of the water (D 2 O) 3 trimer : --- the 2.94THz torsional band L. K. Takahashi, W. Lin, E. Lee, F. N. Keutsch R. J. Saykally by Jia-xiang Han & Department of Chemistry, University of California, Berkeley, California 94720 Chem. Phys. Lett. 423 (2006) 344-351

2. 2 Characterize structure changes from dimer to bulk -- Tremendous progress has been made with THz laser spectroscopy at Berkeley Motivation for water cluster studies Heptamer ? Octamer ?...

3. 3 Exploit the H-bond dynamics -- Water properties are determined by H-bond network and its dynamics -- The translational and librational motions are directly involved Motivation for water cluster studies

4. 4 Determine the Intermolecular Potential Surface (IPS) -- Provide extensive experimental data to determine the IPS -- Test the water models Motivation for water cluster studies Studies have indicated the hydrogen binding energy of liquid water: two body interaction accounts for 75% three body … 20 % all higher … 5%

5. 5 -- detailed VRT data of water trimer are desirable Pair IPSs have been developed for water from the THz VRT spectroscopic data of water dimer -- more dimer data would be useful to refine the pair IPS Determine the three body interaction

6. 6 Theoretical background A. Torsion tunneling Flipping motion is equivalent to rotation around the symmetry axis, called a “pseudorotaion”, quantum number k to specify torsional energy levels, which causes a severe Coriolis perturbation. Selection rule: (k”-K”) – (k’-K’) = 3 (modulo)

7. 7 D 2 O trimer torsional vibrations -1 0 -2 0 3030 0 3131 -2 1 +1 0 +2 0 +2 1 +kn+kn -k n Index n = 0, 1, 2, … Pseudorotation number k = 0, ±1, ±2, 3, 3, ±2, ±1, 0… (K’-K”) = -1, 0, +1 l, u

8. 8 B. Bifurcation tunneling This motion has an important role in determining water properties, governs the breaking and reforming of H-bonds splits the torsional energy levels (the quartet splitting) The splitting is a few MHz for D 2 O trimer and ~ 300 MHz for H 2 O trimer

9. 9 A typical D 2 O trimer transition with a 5MHz quartet splitting 76 :108 :54 :11 Nuclear spin weights: Representative

10. 10 Observed water trimer vibrations D 2 O trimerH 2 O trimer 142cm -1 Translational Torsinal ~ 525cm -1 Librational

11. 11 Experimental System

12. 12 Data signal acquisition diagram Lock-in Microwave FM 29KHz Diode mixer THz Laser 2~118 GHz  m  m Absorption    MW Det Oscilloscope monitor Gate Computer CO 2 Laser

13. 13 The stick spectrum of the (D 2 O) 3 ±2 1 ←0 0 torsional perpendicular band Spacings of B (6 GHz) indicate a planar average structure

14. 14 Effective Hamiltonians For non-degenerate states |k,n> with k = 0 or 3 (modulo 6) H eff (k,n) = B (k,n) (J x 2 +J y 2 ) + C (k,n) J z 2 For degenerate states |k,n> with k = ±1 or ±2 (modulo 6), H eff (k,k’,n) =δ k’,k [B (|k|,n) (J x 2 +J y 2 ) + C (|k|,n) J z 2 ] ±δ k’,k (-2ζ k’,k C (|k|,n) )J z +δ k’,k-2 (modulo 6) μ (|k|,n) - - J - J - +δ k’,k+2 (modulo 6) μ (|k|,n) ++ J + J +

15. 15 knkn0 +1 0 -1 0 +2 0 -2 0 3030 3131 +2 1 -2 1 E0E0 0.0 a 255977.3(4)839187.2(4)1232139.3(5)2709548.8(6)2940937.6(3) B(=A)5796.35(2)5795.97(2)5794.66(3)5792.89(4)5788.68(3)5786.32(2) C3087.71(1)3090.47(2)3095.82(2)3099.55(3)3089.84(3)3088.61(1) DJDJ 0.0296(2)0.0282(2)0.0278(2)0.0276(3)0.0273(3)0.0268(6)0.0274(4)0.0279(3)0.0292(3) D JK -0.0405(5)-0.0469(6)-0.0459(6)-0.0430(7)-0.0421(8)-0.043(1)-0.0397(9)-0.0460(7)-0.0438(6) DKDK 0.0121(8)0.0198(7)0.0188(9)0.0173(8)0.015(1)0.017(1)0.0129(9)0.019(1)0.0158(8) ζ ---0.04388(1)-0.04822(1)-- 0.00029(1) |µ ++ |--26.68(1)13.73(2)-- 3.599(9) Improved D 2 O trimer molecular constants (MHz) Standard deviation of 1.7 MHz better than 2 MHz experimental uncertainty

16. 16 Results and analysis 149 new transitions were observed and assigned up to (J,K) =(16,16) with help of 69 old transitions; All strong D 2 O trimer transitions were assigned in 2779 to 3047GHz & the torsional band ±2 1 ←0 0 has been completed; A total of 218 transitions are included in a new global fitting for all six D 2 O trimer torsional bands with 823 transitions; New improved 50 molecular constants are obtained with a standard deviation of 1.7 MHz better than 2 MHz experimental uncertainty.

17. 17 The calculated and experimental energy levels of (D 2 O) 3 torsional vibrations (cm -1 ). | k n >DD a BGLK a 3D b Exp. 0 0.0 ±1 0 7.685.154.9668.53848 ±2 0 25.1817.1516.59727.99227 3030 36.6124.7323.97041.09974 3131 96.1488.9287.43890.38082 ±2 1 107.5098.2696.91498.09912 ±1 1 129.74117.76116.566-- 0101 132.47130.06129.020-- 0202 143.22151.60151.367--