Water cluster

Short description: Cluster of water molecules held together through hydrogen bonding

Hypothetical (H2O)100 icosahedral water cluster and the underlying structure.

In chemistry, a water cluster is a discrete hydrogen bonded assembly or cluster of molecules of water.[1][2] Many such clusters have been predicted by theoretical models (in silico), and some have been detected experimentally in various contexts such as ice, bulk liquid water, in the gas phase, in dilute mixtures with non-polar solvents, and as water of hydration in crystal lattices. The simplest example is the water dimer (H2O)2.

Water clusters have been proposed as an explanation for some anomalous properties of liquid water, such as its unusual variation of density with temperature. Water clusters are also implicated in the stabilization of certain supramolecular structures.[3] They are expected to play a role also in the hydration of molecules and ions dissolved in water.[4][5]

## Contents

* 1 Theoretical predictions
* 2 Experimental observations
* 3 Cluster models of bulk liquid water
* 4 See also
* 5 References
* 6 External links

## Theoretical predictions

Detailed water models predict the occurrence of water clusters, as configurations of water molecules whose total energy is a local minimum.[6][7][8]

Of particular interest are the cyclic clusters (H2O)n; these have been predicted to exist for n = 3 to 60.[9][10][11] At low temperatures, nearly 50% of water molecules are included in clusters.[12] With increasing cluster size the oxygen to oxygen distance is found to decrease which is attributed to so-called cooperative many-body interactions: due to a change in charge distribution the H-acceptor molecule becomes a better H-donor molecule with each expansion of the water assembly. Many isomeric forms seem to exist for the hexamer (H2O)6: from ring, book, bag, cage, to prism shape with nearly identical energy. Two cage-like isomers exist for heptamers (H2O)7, and octamers (H2O)8 are found either cyclic or in the shape of a cube.

Other theoretical studies predict clusters with more complex three-dimensional structures.[13] Examples include the fullerene-like cluster (H2O)28, named the water buckyball, and the 280-water-molecule monster icosahedral network (with each water molecule coordinate to 4 others). The latter, which is 3 nm in diameter, consists of nested icosahedral shells with 280 and 100 molecules.[14][15] There is also an augmented version with another shell of 320 molecules. There is increased stability with the addition of each shell.[16] There are theoretical models of water clusters of more than 700 water molecules,[17][18] but they have not been observed experimentally. One line of research uses graph invariants for generating hydrogen bond topologies and predicting physical properties of water clusters and ice. The utility of graph invariants was shown in a study considering the (H2O)6 cage and (H2O)20 dodecahedron, which are associated with roughly the same oxygen atom arrangements as in the solid and liquid phases of water.[19]

## Experimental observations

Experimental study of any supramolecular structures in bulk water is difficult because of their short lifetime: the hydrogen bonds are continually breaking and reforming at timescales faster than 200 femtoseconds.[20]

Nevertheless, water clusters have been observed in the gas phase and in dilute mixtures of water and non-polar solvents like benzene and liquid helium.[21][22] The experimental detection and characterization of the clusters has been achieved by spectroscopy - far-infrared (FIR)[23] and vibration-rotation-tunneling (VRT)[24] \- and by H-NMR[25][26] and neutron diffraction.[27] The hexamer is found to have planar geometry in liquid helium, a chair conformation in organic solvents, and a cage structure in the gas phase. Experiments combining IR spectroscopy with mass spectrometry reveal cubic configurations for clusters in the range n=(8-10).

When the water is part of a crystal structure as in a hydrate, x-ray diffraction can be used. Conformation of a water heptamer was determined (cyclic twisted nonplanar) using this method.[28][29] Further, multi-layered water clusters with formulae (H2O)100 trapped inside cavities of several polyoxometalate clusters were also reported by Mueller et al.[30][31]

## Cluster models of bulk liquid water

Several models attempt to account for the bulk properties of water by assuming that they are dominated by cluster formation within the liquid.[32] According to the quantum cluster equilibrium (QCE) theory of liquids, n=8 clusters dominate the liquid water bulk phase, followed by n=5 and n=6 clusters. Near the triple point, the presence of an n=24 cluster is invoked.[33] In another model, bulk water is built up from a mixture of hexamer and pentamer rings containing cavities capable of enclosing small solutes. In yet another model an equilibrium exists between a cubic water octamer and two cyclic tetramers.[34] However, none of these models yet have reproduced the experimentally-observed density maximum of water as a function of temperature.

## See also

* Hydrogen bond
* Mpemba effect
* Properties of water
* Richard J. Saykally

## References

1. ↑ Xantheas, Sotiris; Dunning Jr., Thorn (1993). "Ab initio studies of cyclic water clusters (H2O)n, n=1–6. I. Optimal structures and vibrational spectra". The Journal of Chemical Physics 99 (11): 8774–8792. doi:10.1063/1.465599. Bibcode: 1993JChPh..99.8774X.
2. ↑ Ralf Ludwig (2001). "Water: From Clusters to the Bulk". Angew. Chem. Int. Ed. 40 (10): 1808–1827. doi:10.1002/1521-3773(20010518)40:10<1808::AID-ANIE1808>3.0.CO;2-1. PMID 11385651.
3. ↑ Ghosh, Sujit; Bhardwaj, Parimal (2004). "A Dodecameric Water Cluster Built around a Cyclic Quasiplanar Hexameric Core in an Organic Supramolecular Complex of a Cryptand". Angewandte Chemie 116 (27): 3661–3664. doi:10.1002/ange.200454002. Bibcode: 2004AngCh.116.3661G.
4. ↑ A. D. Kulkarni; S. R. Gadre; S. Nagase (2008). "Quantum chemical and electrostatic studies of anionic water clusters(H2O)n−". Journal of Molecular Structure: THEOCHEM 851 (1–3): 213. doi:10.1016/j.theochem.2007.11.019.
5. ↑ A. D. Kulkarni; K. Babu; L. J. Bartolotti; S. R. Gadre. (2004). "Exploring Hydration Patterns of Aldehydes and Amides: Ab Initio Investigations". J. Phys. Chem. A 108 (13): 2492. doi:10.1021/jp0368886. Bibcode: 2004JPCA..108.2492K.
6. ↑ Fowler, P. W., Quinn, C. M., Redmond, D. B. (1991) Decorated fullerenes and model structures for water clusters, The Journal of Chemical Physics, Vol. 95, No 10, p. 7678.
7. ↑ Keutsch, F. N. and Saykally, R. J. (2001) Water clusters: Untangling the mysteries of the liquid, one molecule at a time, PNAS, Vol. 98, № 19, pp. 10533–10540.
8. ↑ Maheshwary, Shruti; Patel, Nitin; Sathyamurthy, Narayanasami; Kulkarni, Anand (2001). "Structure and Stability of Water Clusters (H2O)n, n = 8-20". Journal of Physical Chemistry A 105: 10525–10537. doi:10.1021/jp013141b.
9. ↑ A. D. Kulkarni; R. K. Pathak; L. J. Bartolotti. (2005). "Structures, Energetics, and Vibrational Spectra of H2O2···(H2O)n, n = 1−6 Clusters: Ab Initio Quantum Chemical Investigations". J. Phys. Chem. A 109 (20): 4583–90. doi:10.1021/jp044545h. PMID 16833795. Bibcode: 2005JPCA..109.4583K.
10. ↑ S. Maheshwary; N. Patel; N Sathyamurthy; A. D. Kulkarni; S. R. Gadre (2001). "Structure and Stability of Water Clusters (H2O)n, n = 8-20: An Ab Initio Investigation". J. Phys. Chem. A 105 (46): 10525. doi:10.1021/jp013141b. Bibcode: 2001JPCA..10510525M.
11. ↑ Ignatov, Ignat; Gluhchev, Georgi; Neshev, Nikolai; Mehandjiev, Dimitar (2021). "Structuring of Water Clusters Depending on the Energy of Hydrogen Bonds in Electrochemically Activated Waters Anolyte and Catholyte". Bulgarian Chemical Communications 53 (2): 234–239.
12. ↑ Gao, Yitian; Fang, Hongwei; Ni, Ke (2021). "A hierarchical clustering method of hydrogen bond networks in liquid water undergoing shear flow". Scientific Reports 11 (1): 9542. doi:10.1038/s41598-021-88810-7. PMID 33953246. Bibcode: 2021NatSR..11.9542G.
13. ↑ G. S. Fanourgakis; E. Aprà; W. A. de Jong; S. S. Xantheas (2005). "High-level ab initio calculations for the four low-lying families of minima of (H2O)20. II. Spectroscopic signatures of the dodecahedron, fused cubes, face-sharinbucky water g pentagonal prisms, and edge-sharing pentagonal prisms hydrogen bonding networks". J. Chem. Phys. 122 (13): 134304. doi:10.1063/1.1864892. PMID 15847462. Bibcode: 2005JChPh.122m4304F.
14. ↑ Tokmachev, A.M., Tchougreeff, A.L., Dronskowski, R. (2010) Hydrogen-Bond Networks in Water Clusters (H2O)20: An Exhaustive Quantum-Chemical Analysis, ChemPhysChem, Vol. 11, №2, pp. 384–388.
15. ↑ Sykes, М. (2007) Simulations of RNA Base Pairs in a Nanodroplet Reveal Solvation-Dependent Stability, PNAS, Vol. 104, № 30, pp. 12336–12340.
16. ↑ Loboda, Oleksandr; Goncharuk, Vladyslav (2010). "Theoretical study on icosahedral water clusters". Chemical Physics Letters 484 (4–6): 144–147. doi:10.1016/j.cplett.2009.11.025. Bibcode: 2010CPL...484..144L. https://zenodo.org/record/896134.
17. ↑ Chaplin, M. F. (2013) What is liquid water, Science in Society, Iss. 58, 41-45.
18. ↑ Zenin, S. V.(2002)Water, Federal Center for Traditional Methods for Diagnostics and Treatment, Moscow
19. ↑ Kuo, Jer-Lai; Coe, James; Singer, Sherwin (2001). "On the use of graph invariants for efficiently generating hydrogen bond topologies and predicting physical properties of water clusters and ice". Journal of Chemical Physics 114 (6): 2527–2540. doi:10.1063/1.1336804. Bibcode: 2001JChPh.114.2527K.
20. ↑ Smith, Jared D.; Christopher D. Cappa; Kevin R. Wilson; Ronald C. Cohen; Phillip L. Geissler; Richard J. Saykally (2005). "Unified description of temperature-dependent hydrogen-bond rearrangements in liquid water". Proc. Natl. Acad. Sci. USA 102 (40): 14171–14174. doi:10.1073/pnas.0506899102. PMID 16179387. PMC 1242322. Bibcode: 2005PNAS..10214171S. http://www.lbl.gov/Science-Articles/Archive/sabl/2005/October/Hydrogen-bonds-in-liquid-water.pdf. Retrieved 2009-06-11.
21. ↑ C. J. Gruenloh; J. R. Carney; C. A. Arrington; T. S. Zwier; S. Y. Fredericks; K. D. Jordan (1997). "Infrared Spectrum of a Molecular Ice Cube: The S4 and D2d Water Octamers in Benzene-(Water)8". Science 276 (5319): 1678. doi:10.1126/science.276.5319.1678.
22. ↑ M. R. Viant; J. D. Cruzan; D. D. Lucas; M. G. Brown; K. Liu; R. J. Saykally (1997). "Pseudorotation in Water Trimer Isotopomers Using Terahertz Laser Spectroscopy". J. Phys. Chem. A 101 (48): 9032. doi:10.1021/jp970783j. Bibcode: 1997JPCA..101.9032V.
23. ↑ Liu, Kun; Fellers, Raymond; Viant, Mark; McLaughlin, Ryan; Brown, Mac; Saykally, Richard (1996). "A long path length pulsed slit valve appropriate for high temperature operation: Infrared spectroscopy of jet-cooled large water clusters and nucleotide bases". Review of Scientific Instruments 67 (2): 410–416. doi:10.1063/1.1146605. Bibcode: 1996RScI...67..410L.
24. ↑ Liu, Kun; Cruzan, Jeffery; Saykally, Richard (1996). "Water Clusters". Science 271 (5251): 929–933. doi:10.1126/science.271.5251.929. Bibcode: 1996Sci...271..929L.
25. ↑ Turov, Volodymyr; Krupskaya, Tetiana; Barvinchenko, Valentina; Lipkovska, Natalia; Kartel, Mykola; Suvorova, Liudmyla (2016). "Peculiarities of water cluster formation on the surface of dispersed KCl: The influence of hydrophobic silica and organic media". Colloids and Surfaces A 499: 97–102. doi:10.1016/j.colsurfa.2016.03.069.
26. ↑ Oka, Kouki; Shibue, Natsuhiko; Sugimuka, Natsuhiko; Watabe, Yuki; Winther-Jensen, Bjorn; Hiroyuki, Wishide (2019). "Long-lived water clusters in hydrophobic solvents investigated by standard NMR techniques". Scientific Reports 223 (1): 223. doi:10.1038/s41598-018-36787-1. PMID 30659206. Bibcode: 2019NatSR...9..223O.
27. ↑ Yoshida, Koji; Ishuda, Shigeru; Yamaguchi, Toshio (2019). "Hydrogen bonding and clusters in supercritical methanol–water mixture by neutron diffraction with H/D substitution combined with empirical potential structure refinement modelling". Molecular Physics 117 (22): 3297–3310. doi:10.1080/00268976.2019.1633481. Bibcode: 2019MolPh.117.3297Y.
28. ↑ M. H. Mir; J. J. Vittal (2007). "Phase Transition Accompanied by Transformation of an Elusive Discrete Cyclic Water Heptamer to a Bicyclic (H2O)7 Cluster". Angew. Chem. Int. Ed. 46 (31): 5925–5928. doi:10.1002/anie.200701779. PMID 17577896.
29. ↑ He, W.J.; Luo, G.-G.; Wu, D.-L.; Liu, L.; Xia, J.-X.; Li, D.-X.; Dai, J.-C.; Xiao, Z.-J. (2012). "An odd-numbered heptameric water cluster containing a puckered pentamer self-assembled in a Ag(I) polymeric solid". Inorganic Chemistry Communications 18: 4–7. doi:10.1016/j.inoche.2011.12.036. https://www.sciencedirect.com/science/article/abs/pii/S1387700311006423. Retrieved 31 July 2022.
30. ↑ T. Mitra; P. Miró; A.-R. Tomsa; A. Merca; H. Bögge; J. B. Ávalos; J. M. Poblet; C. Bo et al. (2009). "Gated and Differently Functionalized (kNew) Porous Capsules Direct Encapsulates' Structures: Higher and Lower Density Water". Chem. Eur. J. 15 (8): 1844–1852. doi:10.1002/chem.200801602. PMID 19130528.
31. ↑ A. Müller; E. Krickemeyer; H. Bögge; M. Schmidtmann; S. Roy; A. Berkle (2002). "Changeable Pore Sizes Allowing Effective and Specific Recognition by a Molybdenum-Oxide Based "Nanosponge": En Route to Sphere-Surface and Nanoporous-Cluster Chemistry". Angew. Chem. Int. Ed. 41 (19): 3604–3609. doi:10.1002/1521-3773(20021004)41:19<3604::aid-anie3604>3.0.co;2-t. PMID 12370905.3.0.co;2-t&rft_id=info:pmid/12370905&rfr_id=info:sid/en.wikibooks.org:Chemistry:Water_cluster">
32. ↑ L Shu, L Jegatheesan, V Jegatheesan, CQ Li (2020) The structure of water, Fluid Phase Equilibria 511, 112514
33. ↑ Lehmann, S. B. C.; Spickermann, C.; Kirchner, B. (2009). "Quantum Cluster Equilibrium Theory Applied in Hydrogen Bond Number Studies of Water. 1. Assessment of the Quantum Cluster Equilibrium Model for Liquid Water". Journal of Chemical Theory and Computation 5 (6): 1640–9. doi:10.1021/ct800310a. PMID 26609856.
34. ↑ Borowski, Piotr; Jaroniec, Justyna; Janowski, Tomasz; Woliński, Krzysztof (2003). "Quantum cluster equilibrium theory treatment of hydrogen-bonded liquids: Water, methanol and ethanol". Molecular Physics 101 (10): 1413. doi:10.1080/0026897031000085083. Bibcode: 2003MolPh.101.1413B.

## External links

* Water clusters at London South Bank University Link
* The Cambridge Cluster Database \- Includes water clusters calculated with various water models and the water clusters explored with ab initio methods.

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