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 Chem. Phys. Lett. 423 (2006)

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

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

11 Experimental System

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 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 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 knkn E0E0 0.0 a (4) (4) (5) (6) (3) B(=A) (2) (2) (3) (4) (3) (2) C (1) (2) (2) (3) (3) (1) DJDJ (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 (5) (6) (6) (7) (8)-0.043(1) (9) (7) (6) DKDK (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 (1) (1) (1) |µ ++ | (1)13.73(2) (9) Improved D 2 O trimer molecular constants (MHz) Standard deviation of 1.7 MHz better than 2 MHz experimental uncertainty

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 The calculated and experimental energy levels of (D 2 O) 3 torsional vibrations (cm -1 ). | k n >DD a BGLK a 3D b Exp ± ± ± ±