1. Water clusters observed by chirped-pulse rotational spectroscopy: Structures and hydrogen bonding Cristobal Perez, Matt T. Muckle, Daniel P. Zaleski, Nathan Seifert, Brooks H. Pate Department of Chemistry, University of Virginia, Charlottesville, Virginia, USA Zbigniew Kisiel Institute of Physics, Polish Academy of Sciences, Warszawa, Poland Berhane Temelso, George C. Shields Bucknell University, Lewisburg, Pennsylvania, USA 67th OSU International Symposium on Molecular Spectroscopy RH03

2. Comparison of chirped pulse and Balle-Flygare type spectra:  Transitions for the cage water hexamer (frequencies/MHz)  Chirped pulse spectrum = 8 GHz width recorded overnight  Balle-Flygare spectrum = 1 MHz width recorded in 10 minutes IFPAN BF, cavity IFPAN BF, cavity VIRGINIA chirped

3. Hexamer structure determination I: Kraitchman equations Substitution oxygen atom coordinates (Å) :

4. Hexamer structure determination II: least squares r 0 geometry  Oxygen framework geometry requires determination of 3N - 6=12 internal structural parameters  21 experimental moments of inertia are available (parent+six 18 O species)  Fit made with the STRFIT program from PROSPE website B obs -B calc < 0.31 MHz

5. Evolution of assumptions concerning the indeterminable structural parameters of the hydrogens: Assessed by the value of the total deviation of the least squares fit (in uÅ 2 units)

6. Comparison of experiment (dark red) and calculation (semi-transparent): calculation (semi-transparent): Experiment = r 0 Experiment = r s Calculation = vibrationally averaged MP2/aug-cc-pVDZ Try out the rotatable 3D models in Fig.3 of Perez et al., Science 336, 897 (2012)

7. expt., r 0 calc., vibrationally averaged MP2/aug-cc-pVDZ 9 hydrogen bonds all 6 H 2 O’s with 3 H-bonds  E = + 0.0 kJ/mol ?! Water detachment energy (kJ/mol)

8. 8 hydrogen bonds 2 H 2 O’s with 2 H-bonds 4 H 2 O’s with 3 H-bonds uu{1}  E = + 0.9 kJ/mol ?!

9. 7 hydrogen bonds 4 H 2 O’s with 2 H-bonds 2 H 2 O’s with 3 H-bonds  E = + 2.7 kJ/mol

10. The smallest water clusters and O...O distances: 2.98 Å 2.84 Å 2.80 Å 2.76 Å Saykally + Wales, Science 336, 814 (2012)

11. O...O distances in clusters and bulk water: Liu, Brown, Cruzan, Saykally, J.Phys.Chem. A 101, 9011 (1997) ?

12. A.K.Soper, Chem.Phys. 258,121 (2000) neutron diffraction revised to 2.8 Å Hexamer O...O distances and the radial distribution function for liquid water: Book: 2.886 Å Prism: 2.802 Å Cage: 2.852 Å Cage + Prism + Book, r 0 distances Uwe Bergmann et al. JCP 127,174504 (2007) X-ray Raman: liquid = 2.81 Å ice Ih = 2.76 Å Long standing OO distance in liquid water = 2.84 Å (neutron diffraction)

13. There is remarkable agreement between experiment and computation concerning the variation in O... O bond distances... allowing more confident, detailed insight into the hydrogen bonding network for each isomer.

14. The O... O distance is a known measure of hydrogen bond strength and in the hexamer isomers these span the range 2.70 to 3.01 Å. This is a departure from the more uniform picture for (global minimum) clusters up to the water pentamer in which symmetry enforces a single O... O distance, systematically decreasing with cluster size. The shortest O... O distance in the hexamers is shorter than 2.76 Å in the pentamer, whereas the longest hexamer O... O distance exceeds 2.98 Å for the water dimer.

15. The water detachment energies show large variation but correlate with the O... O distances and with the number of hydrogen bonds to each water monomer.

16. The water heptamer, (H 2 O) 7 :  All seven single 18 O species assigned  r s analysis without imaginary coordinates (unlike in the hexamers)  Least squares r 0 fit possible but r m (1) geometry is even better: very low deviation of fit of 0.0069 uA 2  The r m (1) geometry probably accounts for hydrogen indeterminacies and compares well with ab initio equilibrium  Average nearest neighbour OO distances: r 0 = 2.848 Åliquid = 2.81 Å r s = 2.835 Å r m (1) = 2.823 Å r m (1) compared with equilibrium ab initio

17. Similarity between the (H 2 O) 7 and the prism (H 2 O) 6 structures: r 0 compared with vibrationally averaged ab initio E disp  E es All other H-bonds: E disp  E es /2

18. This (work) provides a consistent picture of the diversity of hydrogen bonding appearing at the hexamer cluster level...... which is a small scale prelude to the known diversity in the structure of liquid water. C.Perez et al., et al., Science 336, 897 (2012)