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**68th OSU International Symposium on Molecular Spectroscopy TH08**

Structures of the lowest energy nonamer and decamer water clusters from chirped-pulse rotational spectroscopy Cristobal Perez, 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

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**The genealogy of water nonamer and decamer clusters:**

Assigned + 18O analysis Assigned DE /kcal mol-1

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**The water nonamer clusters, (H2O)9 :**

Praha2008 The water nonamer clusters, (H2O)9 : Complete sets of singly 18O substituted species were assigned for three out of the five assigned nonamer species In the case of the nonamer3 spectroscopic species, which is assigned to cluster 9-D1, there were initially two missing species but effective degeneracy of two pairs of 18O species was eventually resolved out by careful consideration of relative intensities Structural analysis encountered several difficulties: rs analysis was hindered by multiple imaginary coordinates rm(1) analysis only reached satisfactory numerical stability after an ab initio based simplifying assumption of equal length pillars connecting the upper and lower rings

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Structural analysis: The isotopic sets consisting of the parent and all single 18O isotopic species can be treated in several ways: Experiment: Calculation: rs geometry unclear r0 geometry vibrationally averaged geometry rm or reSE geometry equilibrium geometry Programs KRA and EVAL were used for the rs and STRFIT for the rm(1) evaluations, all from the PROSPE website

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**Imaginary coordinates in substitution analysis of water nonamers:**

5 imaginary coordinates for cluster 9-D1 3 for cluster 9-S1 3 for cluster 9-S2 All are c-coordinates rs /Å

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**The underlying reason for nonamer structural difficulties:**

Oxygen atoms O1, O4, O7, O8, O9 are all very close to the ab inertial plane so that their c coordinates are very small. 9-D1 The two degenerate 18O substituted pairs are: O2, O3 O5, O6

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**Comparison of calculation and experiment for the nonamers:**

Praha2008 The complete geometry is for RI-MP2/aug-cc-pVDZ calculation and the blue water units are at the transition point between two alternative minima The smaller spheres are experimental rs coordinates of the oxygen atoms

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**The perplexing misalignment between experimental and calculated inertial coordinates:**

Relative magnitudes of apparent ground state dipole moment components: a b c

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**Misalignment is caused by orientation of just one hydrogen atom:**

The diagrams compare ab initio principal coordinates (complete water molecules) with experimental substitution coordinates (small circles) The responsible hydrogen is in the nonbonded OH belonging to the only water unit bound by two (not three) hydrogen bonds 9-S2 9-S2TS 9-S2A

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**The performance of least-squares geometry fits for the nonamer clusters:**

The fits are to: 30 rotational constants 3N-6 = 21 internal coordinates define the O framework Equal pillars assumption reduces these to 18 for r0 (21 for rm(1))

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**The water nonamers (H2O)9: the pattern of short/long**

OO distances identifies the species

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**The water decamer clusters, (H2O)10 :**

Praha2008 The water decamer clusters, (H2O)10 : Complete sets of singly 18O substituted species were assigned for two out of the four assigned decamer species The structural analysis turned out to be easier than for the nonamers due to lack of imaginary coordinates (although the two blue oxygen atoms are close to the ac plane) rs /Å

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**The water decamers (H2O)10 = stacked pentameric rings**

Identical foreground rings, but co- or contra-rotating background rings

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**? O...O distances in clusters and bulk water:**

Liu, Brown, Cruzan, Saykally, J.Phys.Chem. A 101, 9011 (1997)

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**Water cluster O...O distances and the radial distribution function for liquid water:**

Long standing OO distance in liquid water = 2.84 Å (neutron diffraction) Uwe Bergmann et al. JCP 127, (2007) X-ray Raman: liquid = 2.81 Å ice Ih = 2.76 Å A.K.Soper, Chem.Phys. 258,121 (2000) neutron diffraction revised to 2.80 Å by improved deconvolution of gOO,gOH,gHH Cluster OO distances (9 clusters, 255 values) Nearest neighbour averages (94 values): <r0 > = Å <rm(1) > = Å

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Praha2008 CONCLUSIONS: 18O substitution resulted in determination of oxygen framework geometries for 3 water nonamer clusters, and 2 water decamer clusters Consideration of the patterns of short-long OO distances allowed unambiguous assignment of spectroscopic species to ab initio calculated carriers The oxygen framework geometries all turn out to be for the most stable clusters of a given size: the nonamers are D1, S1 and S2 (E = 0, 1.0, 1.4 kJ/mol resp.) the decamers are PPD1, PPS1 (E = 0, 0.2 kJ/mol resp.) Even at the level of oxygen framework geometries as determined by 18O substitution there are visible effects of ground state averaging of hydrogen atom positions The structures of 9 water clusters determined so far by 18O substitution lead to an average ground state OO distance that is only 0.02Å longer than that in liquid water

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