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THz vibration-rotation-tunneling (VRT) spectroscopy of the water (D2O)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

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• 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 ?

...

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• 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

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• 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%

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-- 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

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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)

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• D2O trimer torsional vibrations

-10

-20

30

00

31

-21

+10

+20

+21+kn -kn

Index n = 0, 1, 2, …

Pseudorotation number k = 0, ±1, ±2, 3, 3, ±2, ±1, 0…

(K’-K”) = -1, 0, +1

l, u

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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 D2O trimer and ~ 300 MHz for H2O trimer

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• A typical D2O trimer transition with a 5MHz quartet splitting

76 :108 :54 :11

Nuclear spin weights:

Representative

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Observed water trimer vibrations

D2O trimer H2O trimer

142cm-1

Translational

Torsinal

~ 525cm-1

Librational

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Experimental System

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Data signal acquisition diagram

Lock-in

Microwave

FM 29KHz

Diodemixer

THzLaser

2~118 GHzmm

Absorption

MW

Det Oscilloscopemonitor

Gate

Computer

CO2

Laser

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• The stick spectrum of the (D2O)3 ±21←00 torsional perpendicular band

• Spacings of B (6 GHz) indicate a planar average structure

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• Effective Hamiltonians

• For non-degenerate states |k,n> with k = 0 or 3 (modulo 6)

Heff (k,n) = B(k,n)(Jx2+Jy

2) + C(k,n)Jz2

• For degenerate states |k,n> with k = ±1 or ±2 (modulo 6), Heff (k,k’,n) =δk’,k[B(|k|,n)(Jx

2+Jy2) + C(|k|,n)Jz

2] ±δk’,k(-2ζk’,kC(|k|,n))Jz +δk’,k-2 (modulo 6)μ(|k|,n)

- - J-J-

+δk’,k+2 (modulo 6)μ(|k|,n)++ J+J+

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kn

00 +10 -10 +20 -20 30 31 +21 -21

E0 0.0a 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)

C 3087.71(1) 3090.47(2) 3095.82(2) 3099.55(3) 3089.84(3) 3088.61(1)

DJ 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)

DJK -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)

DK 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 D2O trimer molecular constants (MHz)

• Standard deviation of 1.7 MHz better than 2 MHz experimental uncertainty

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Results and analysis

• 149 new transitions were observed and assigned up to (J,K) =(16,16) with help of 69 old transitions; • All strong D2O trimer transitions were assigned in 2779 to 3047GHz & the torsional band ±21←00 has been completed;

• A total of 218 transitions are included in a new global fitting for all six D2O 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.

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• The calculated and experimental energy levels of (D2O)3

torsional vibrations (cm-1).

| kn > DDa BGLKa 3Db Exp.

00 0.0 0.0 0.0 0.0

±10 7.68 5.15 4.966 8.53848

±20 25.18 17.15 16.597 27.99227

30 36.61 24.73 23.970 41.09974

31 96.14 88.92 87.438 90.38082

±21 107.50 98.26 96.914 98.09912

±11 129.74 117.76 116.566 --

01 132.47 130.06 129.020 --

02 143.22 151.60 151.367 --