OPEN Size, separation, structural order, and

SUBJECT AREAS:
mass density of molecules packing in
FLUIDS
INFRARED SPECTROSCOPY
water and ice
Yongli Huang1*, Xi Zhang2,3*, Zengsheng Ma1, Wen Li1, Yichun Zhou1, Ji Zhou4, Weitao Zheng5
Received & Chang Q. Sun1,2,3,5
6 September 2013
Accepted 1
Key Laboratory of Low-Dimensional Materials and Application Technologies (Ministry of Education) and Faculty of Materials,
7 October 2013 Optoelectronics and Physics, Xiangtan University, Hunan 411105, China, 2NOVITAS, School of Electrical and Electronic
Engineering, Nanyang Technological University, Singapore 639798, 3Center for Coordination Bond and Electronic Engineering,
Published College of Materials Science and Engineering, China Jiliang University, Hangzhou 310018, China, 4State Key Laboratory of New
21 October 2013 Ceramics and Fine Processing, Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, China,
5
School of Materials Science, Jilin University, Changchun 130012, China.

Correspondence and
The structural symmetry and molecular separation in water and ice remain uncertain. We present herewith
requests for materials
a solution to unifying the density, the structure order and symmetry, the size (H-O length dH), and the
should be addressed to separation (dOO 5 dL 1 dH or the O:H length dL) of molecules packing in water and ice in terms of statistic
C.Q.S. (Ecqsun@ntu. mean. This solution reconciles: i) the dL and the dH symmetrization of the O:H-O bond in compressed ice, ii)
edu.sg) the dOO relaxation of cooling water and ice and, iii) the dOO expansion of a dimer and between molecules at
water surface. With any one of the dOO, the density r(g?cm23), the dL, and the dH, as a known input, one can
resolve the rest quantities using this solution that is probing conditions or methods independent. We
* These authors clarified that: i) liquid water prefers statistically the mono-phase of tetrahedrally-coordinated structure with
contributed equally to fluctuation, ii) the low-density phase (supersolid phase as it is strongly polarized with even lower density)
exists only in regions consisting molecules with fewer than four neighbors and, iii) repulsion between
this work.
electron pairs on adjacent oxygen atoms dictates the cooperative relaxation of the segmented O:H-O bond,
which is responsible for the performance of water and ice.

W
ater and ice has attracted much attention because of its anomalies pertaining to issues from galaxy to
geology, astrophysics, biology, climate, and to our daily lives1–7. However, the structure order, the
geometric symmetry, the size and the separation between molecules packing in water and ice (H2O)
and their correlation remain yet highly disputed, independent issues despite decades-long intensive investigation.
For instances, the separation between adjacent oxygen atoms (dOO) was measured to vary from 2.70 to 3.00 Å8–20
and the molecular size (the H-O bond length dH) changes from 0.970 to 1.001 Å 21. A H2O molecule demonstrates
high instantaneous asymmetry with coordination numbers varying from two22 to four or even greater23. The
geometric structure of the weekly-ordered H2O liquid was interpreted in terms of either the monomial-phase of
tetrahedrally-coordinated structures with thermal fluctuation2,24–26 or the mixed-phase of low- and high-density
fragmentation27–29. However, uncertainties in these seemingly independent issues determine jointly the density of
water and ice that is macroscopically detectable but the correlation among these quantities is often ignored in
consideration. This fact serves as one essential constraint for the solution to the uniqueness of structure order and
molecular separation, in terms of statistic expectation, that water molecules prefer. Therefore, these structural and
dimensional discrepancies can be resolved simultaneously based on the framework reported in this Letter without
needing any assumption or approximation.

Results
Firstly, the sp3-orbital hybridization is the unique choice of oxygen upon reacting with atoms of relatively lower
electronegativity, irrespective of the structural phase30. As shown in Figure 1a, an oxygen atom (2s22p4) catches
two electrons from neighboring atoms such as hydrogen (H) and metals and then hybridizes its sp orbits with
tetrahedrally directional orbits26. In the case of H2O, one O forms two intramolecular H-O bonds with shared
electron pairs and , 4.0 eV binding energy26 and fills up the rest two orbits with its nonbonding electron lone
pairs ‘‘:’’ to form the intermolecular O:H non-covalent bonds of , 0.1 eV binding energy31. The inhomogeneous

SCIENTIFIC REPORTS | 3 : 3005 | DOI: 10.1038/srep03005 1

 www.nature.com/scientificreports

This tetrahedron containing two equivalent H2O molecules and four

identical O:H-O bonds at different orientations forms the basic block
building up the bulk water and ice despite fluctuations.
Thirdly, as illustrated in Figure 1c, four of the eight cubes are
occupied by the basic 2H2O block tetrahedrally and the rest four
cubes are empty, which means that each cube of a3 volume accom-
modates only one H2O molecule on average. With the known mass of
a H2O molecule consisting 8 neutrons, 10 protons, and 10 electrons,
M 5 (10 3 1.672621 1 8 3 1.674927 1 10 3 0.000911) 3 10227 kg
and the known density r 5 M/a3 5 1 (gcm23) at 4uC under the
atmospheric pressure, this structural order defines immediately
and unambiguously the density-dependent molecular separation,
dOO, and the next-nearest neighboring distance !2a (unit in Å),
( pffiffiffi
dOO ~ 3a=2~2:6950r{1=3
pffiffiffi ð1Þ
2a~4:4001r{1=3

Finally, the O:H-O bond, in Figure 1d, consists of the longer-and-

softer part of the O:H van der Waals bond (dL) and the shorter-and-
stiffer part of the H-O polar-covalent bond (dH) rather than either of
them alone. The O:H-O bond approximates a pair of asymmetric and
H-bridged oscillators coupled by Coulomb-repulsion, whose relaxa-
tion in length and energy and the associated local charge distribution
determine the anomalies of water ice under various stimuli such as
Figure 1 | Sampling procedure for the structure of water and the
compression32, coordination number reduction26, and cooling1,7,35.
segmented O:H-O bond. (a) An extension of (a) the sp3-hybridized
Under excitation, oxygen atoms dislocate along the O:H-O bond
oxygen (red) motif with two nonbonding electron lone pairs (blue) and
two bonding electron pairs (yellow) results in (b) an ideal tetrahedron that
in the same direction but by different amounts with H atom as the
contains two equivalent H2O molecules connected by four identical O:H-
coordination origin. The O:H-O interaction in Figure 1d holds stat-
O bonds of different orientations. The packing of the basic building blocks
istically true in any phase including amorphous despite the strong
(b) forms (c) a diamond structure, which ensures the tetrahedral
fluctuations whose extent is subject to the thermal conditions due to
coordination of the central oxygen atom in the coordination origin. the switching on and off the O:H interactions.
Therefore, only four of the eight cubes in (c) are occupied by (b) and the A molecular dynamics (MD) computation has enabled us to
rest four remain empty. (d) The O:H-O bond forms an asymmetric, decompose the measured volume-pressure V(P) profile of com-
coupled, H-bridged oscillators whose relaxation in length and energy and pressed ice36,37 into the dH(P) and the dL(P) cooperative curves32,
the associated local charge distribution determine the physical properties see Figure 2. The dx(P) curves meet at dL 5 dH 5 1.12 Å under ,
of water and ice26,32,35. Small pairing dots on oxygen represent the electron 59 GPa pressure of ice, which is exactly the measured proton sym-
pairs. metrization of hydrogen bond in ice38,39.
This coincidence indicates that the MD derived dx(P) relation
represents the true cooperativity of the dL and the dH bond relaxa-
distribution of charge and energy around the central oxygen atom tion. Plotting the dL(P) against the dH(P) yields immediately the
entitles a H2O molecule only Cv2 group symmetry except for the (projection along the O—O) length cooperativity that is free from
rotation and vibration of the molecule. Therefore, an oxygen atom probing conditions or probing methods,
always tends to find four neighbors to form a stable tetrahedron but dL ~2:5621|½1{0:0055|expðdH =0:2428Þ ð2Þ
the nonequivalent bond angles (/H-O-H , 104.5u and /H:O:H .
109.5u) and the repulsion between electron pairs on oxygen26,32 The dx (x 5 L and H) value approaches the true bond length with ,
refrain the steady tetrahedron from being formed in the liquid phase. 1.5% deviation (1-cos(10u) 5 0.015) as the O:H-O angle remains
The strong fluctuation proceeds more like the motion of a complex 160u in liquid and greater in solid35. Combining eqs (1) and (2),
pendulum surrounded by four non-bonding lone pairs, because of one is able to scale the size dH and the separation dOO of H2O
the O:H bond switching on and off restlessly in a period of sub- molecules with the given packing order in Figure 1c and the mea-
picosecond2,25,28,29. Therefore, it would be more realistic and mean- sured density under various conditions. If the dOO or the dH matches
ingful to consider the statistic expectation of the coordination num- those of direct measurement, the structure order in Figure 1c and eqs
ber, the structure order, and the molecular separation in all phases at (1) and (2) are justified true and unique.
question for a long time span rather than seeking for the instant- Using eq 1, one can convert, as shown Figure 3a for instance, the
aneous accuracy of a certain independent quantity by taking the measured density r(T) profiles of water droplets of different sizes
snapshot at a quick flash25 for the highly correlated and fluctuating (1.4 and 4.4 nm)40,41 as input into the dOO as an output for water at
system. different temperatures. The density transition points change with
Secondly, the packing order of H2O molecules follows Pauling’s water droplet size. For droplet of 1.4 nm, the transition is at
Ice Rule33 in all phases except for water under extremely high tem- 205 K, it is at 242 K for 4.4 nm droplet and 258 K for the bulk
perature and high pressure34. Despite thermal fluctuation in the O:H water35. The droplet size discriminated density transition arises from
non-covalent bond lengths and the /O:H-O bond angles, the aver- the specific heat disparity of the O:H- and the H-O within the O:H-O
age separation and the size of molecules will change when the H2O bond. As the droplet size is reduced, the H-O bond becomes shorter
transits from the strongly-ordered solid phase, to the weakly-ordered and stiffer yet the O:H bond the otherwise26, which shifts the cross
liquid phase, and to the disordered amorphous or vapor phase, as the points of the two specific heat to temperatures outwardly away from
Ice Rule retains. An extension of the Ice Rule results in an ideal that of the bulk (refer to Ref. 35). The dOO in a water droplet expands
tetrahedron, shown in Figure 1b, with higher C3 group symmetry. additionally in the skin region42 but one can only measure its aver-

SCIENTIFIC REPORTS | 3 : 3005 | DOI: 10.1038/srep03005 2

 www.nature.com/scientificreports

Figure 2 | (a) MD calculation reproduction of the V(P) profile of ice36 with derivatives of the O:H and H–O lengths meeting at dH 5 dL 5 1.12 Å under
58.6 GPa compression, which agrees with the measurements of dH 5 dL 5 1.12 Å at 59 GPa38,39.

age26. The dOO values of 2.70 Å measured at 25uC and 2.71 Å at Figure 4 shows the solution consistency to the measured molecular
216.8uC10 match exactly the conversion of 2.6950 Å that is a pro- size dH, molecular separation dL (or dOO), mass density r, and struc-
jection along the O—O at 4uC. This consistency justifies sufficiently tural order of: i) compressed ice36, ii) cooling water and ice40,41, and,
that both eq 1 and the packing order in Figure 1c describe the true iii) water surface and dimer10,19. The dH of 1.0004 Å at unity density is
situations in both water and ice. Furthermore, the data reported in within the measured values ranging from 0.970 to 1.001 Å21. The dOO
Ref. 10 is essentially accurate and correct. values greater than the ideal value of 2.6950 Å at r 5 1 (g?cm23)
correspond to the supersolid phase (low-density, LDP) that exists
indeed27–29 but only presents in the skins of water ice composed of
Discussion
molecules with fewer than four neighbors (Figure 4b)26.
The non-covalent bond length dL, molecular size dH, molecular sepa-
Wilson et al19 have discovered that the surface dOO expands by
ration dOO, and the mass density r can be obtained by solving the
5.9% from 2.801 to 2.965 Å at room temperature. If one considers the
equation with any one of these parameters as a known input,
shortest distance of 2.70 Å10 and the longest 2.965 Å19 of measure-
ments, the surface dOO expands by up to 10%. Furthermore, the
dL {2:5621|½1{0:0055|expððdOO {dL Þ=0:2428Þ~0: volume of water molecules confined in 5.1 and 2.8 nm TiO2 pores
increase by 4 and 7.5%, respectively, with respect to that in the bulk43.
Figure 3b shows the decomposition of the dOO into the dx of water With a 5–10 Å thick air gap existing in between molecules and the
and ice at cooling40,41. The dx(T) profiles follow the rules of O:H-O hydrophobic surface44, water molecules at the interface exhibit skin
bond relaxation26,32,35: i) both oxygen atoms dislocate in the same vibration attributes45 of 3400 cm21 compared to that of 3200 cm21
direction (see inset) along the O:H-O bond by different amounts for the bulk water. The separation dOO 5 2.980 Å for a dimer is even
with respect to the H atom; ii) the longer-and-softer O:H part always greater.
relaxes more than the shorter-and-stiffer H-O part does. The coop- In these supersolid regions, molecular under-coordination short-
erativity of the dx relaxation confirms further that35: i) cooling con- ens the dH and lengthens the dL, resulting in dOO expansion and
traction happens only to the O:H bond in the solid (T , 205 K (Data polarization because of the inter electron-pair repulsion26. The least
1) or 241 K (Data 2)) and in the liquid phase (T . 277 K), which density of ice is 0.92, which corresponds to dOO 5 2.695(0.92)21/3 5
lengthens the H-O bond slightly by inter-electron-pair repulsion, 2.7710 Å. However, the density of the supersolid phase is r 5 (2.695/
resulting volume contraction; ii) in the freezing transition phase, 2.965)3 5 0.7509 g?cm23, which is far lower than the least density of
the process of length relaxation reverses, leading to the O—O length the bulk ice or the maximal density of water (0.75/0.92/1.0), accord-
gain and volume expansion at freezing. ing to eq 1. Considering the limitation of penetration depth in the

Figure 3 | (a) The dOO , r(T) profiles (eq 1) of water droplets of different sizes (1.4 and 4.4 nm)40,41 match the dOO values measured at 25uC and 216.8uC
(Figure S1 and S2 of Supporting Information)10. (b) The dH and the dL (eq 2) agrees with results of MD calculations35. Inset (b) illustrates the cooperative
relaxation of the segmented O:H-O bond. One part becomes longer; the other part will be shorter by different amounts due to the inter-electron pair
repulsion.

SCIENTIFIC REPORTS | 3 : 3005 | DOI: 10.1038/srep03005 3

 www.nature.com/scientificreports

Figure 4 | Accordance of (a) molecular size dH, molecular separation dL(or dOO 5 dH 1 dL), (b) mass density r, and packing order (see Figure 1c) of
H2O molecules in the situations: (i) ice under compression (dH . 1.00 Å)36, (ii) water ice at cooling (0.96 , dH , 1.00 Å)40,41, and (iii) liquid
surface and dimer (dH , 1.00 Å)8–10,14–18. The derived dH 5 1.0004 Å at r 5 1 is within the measurements ranging from 0.970 to 1.001 Å21. The dH
shorter than 0.96 Å corresponds to the supersolid phase in regions of molecules having fewer than four coordination neighbors (CN)19,20,26. In such
regions, a H2O molecule shrinks in size and expands in separation because of inter electron-pair repulsion26.

optical reflection measurements of water and ice, all the reported (vi) The supersolid (low-density) phase indeed exists but only in
data for the skin are reasonably correct. regions consisting water molecules with fewer than four
The molecular separation dOO 5 dL 1 dH grows and molecular size neighbors. The supersolidity phase forms because of the
dH shrinks simultaneously at the skins because of the molecular under- Goldschmidt-Pauling’s rule of H-O bond contraction due
coordination26. The H-O bond contraction follows Goldschmidt- to molecular under-coordination and the inter-electron-pair
Pauling’s rule of ‘‘atomic coordination number-radius’’ correlation46,47; repulsion pertaining to the O:H-O bond.
the dOO expansion results from the Coulomb repulsion between elec-
tron pairs on adjacent oxygen atoms26,32. The skin region, consisting
molecules with fewer than four neighbors, forms such an amazing Methods
The MD calculations were performed using Forcite’s package with ab initio optimized
supersolid phase that possesses the attributes of low-density19, high forcefield Compass2760. The Compass27 has been widely used in dealing with the
elasticity48, polarized49,50, dielectric instability51, thermally stable52 and electronic structures and the hydrogen bond network of water and amorphous ices61
hydrophobic53,54 with densely entrapped bonding electrons55–58. The as well as water chains in hydrophobic crystal channels62.
timescale for hydrogen-bond switching dynamics at the surface is
about three times slower than that in the bulk59 because of the strong 1. Medcraft, C. et al. Water ice nanoparticles: size and temperature effects on the
polarization and high viscosity. mid-infrared spectrum. PCCP 15, 3630–3639 (2013).
The findings apply to any situations including solid-liquid (water- 2. Petkov, V., Ren, Y. & Suchomel, M. Molecular arrangement in water: random but
ice) interface skin as only mass and volume are involved. At the not quite. J. Phys.: Condens. Matter 24, 155102 (2012).
3. Tsai, M. K., Kuo, J. L. & Lu, J. M. The dynamics and spectroscopic fingerprint of
water-hydrophobic surface of different materials, this findings are hydroxyl radical generation through water dimer ionization: ab initio molecular
only valid to the water skin that forms the low-density supersolid dynamic simulation study. PCCP 14, 13402–13408 (2012).
state of polarized, depleted, elastic, and thermally stable26. An air gap 4. Liu, Y. & Wu, J. Communication: Long-range angular correlations in liquid water.
of 0.5 , 1.0 nm thick presents between the superhydrophobic sub- J. Chem. Phys. 139, 041103 (2013).
strate and water44. 5. Ostmeyer, J. et al. Recovery from slow inactivation in K channels is controlled by
water molecules. Nature 501, 121–124 (2013).
The straightforward yet simple solution presented herewith has 6. Gierszal, K. P. et al. p-Hydrogen Bonding in Liquid Water. J. Phys. Chem. Lett. 2,
thus resolved the seemingly independent geometry and dimension 2930–2933 (2011).
uncertainties of water and ice. We may conclude: 7. Medcraft, C. et al. Size and temperature dependence in the far-Ir spectra of water
ice particles. Astrophys. J. 758, 17 (2012).
(i) One should focus on the statistic mean of all the factors and 8. Skinner, L. B. et al. Benchmark oxygen-oxygen pair-distribution function of
their cooperativity involved rather than the instantaneous ambient water from x-ray diffraction measurements with a wide Q-range. J.
Chem. Phys. 138, 074506 (2013).
accuracy of the individual parameter once at a point of time 9. Wikfeldt, K. T. et al. Oxygen-oxygen correlations in liquid water: Addressing the
for the strongly fluctuated water system. discrepancy between diffraction and extended x-ray absorption fine-structure
(ii) The size, separation, structural order, and mass density of using a novel multiple-data set fitting technique. J. Chem. Phys. 132, 104513
molecules packing in water and ice are correlated, which is (2010).
10. Bergmann, U. et al. Nearest-neighbor oxygen distances in liquid water and ice
independent of the structural phases of water and ice or the observed by x-ray Raman based extended x-ray absorption fine structure. J. Chem.
probing conditions. Phys. 127, 174504 (2007).
(iii) Constrained by the Ice Rue, the dH and dL cooperativity, the 11. Morgan, J. & Warren, B. E. X-ray analysis of the structure of water. J. Chem. Phys.
solution has reconciled measurements of hydrogen-bond 6, 666–673 (1938).
length symmetrization of ice under compression, dOO relaxa- 12. Naslund, L. A. et al. X-ray absorption spectroscopy study of the hydrogen bond
network in the bulk water of aqueous solutions. J. Phys. Chem. A 109, 5995–6002
tion of water and ice at cooling, and dOO expansion of a water (2005).
dimer and molecules at water surface. 13. Orgel, L. The hydrogen bond. Rev. Mod. Phys. 31, 100–102 (1959).
(iv) With any one of the molecular separation, mass density, O:H 14. Wilson, K. R. et al. X-ray spectroscopy of liquid water microjets. J. Phys. Chem. B
bond length, and H-O distance as a known input, one can 105, 3346–3349 (2001).
15. Narten, A. H., Thiessen, W. E. & Blum, L. Atom pair distribution functions of
determine using this solution unambiguously the rest three liquid water at 25uC from neutron diffraction. Science 217, 1033–1034 (1982).
parameters and their change with external conditions such as 16. Fu, L., Bienenstock, A. & Brennan, S. X-ray study of the structure of liquid water. J.
pressure, temperature, and coordination environment. Chem. Phys. 131, 234702 (2009).
(v) The tetrahedrally-coordinated structure could be the unique 17. Kuo, J. L., Klein, M. L. & Kuhs, W. F. The effect of proton disorder on the structure
of ice-Ih: A theoretical study. J. Chem. Phys. 123, 134505 (2005).
choice of water and ice despite fluctuations in the dL and 18. Soper, A. K. Joint structure refinement of x-ray and neutron diffraction data on
the /O:H-O angle due to the non-equivalent /H:O:H and disordered materials: application to liquid water. J Phys Condens Matter 19,
/H-O-H bond angles and the inter-electron-pair repulsion. 335206 (2007).

SCIENTIFIC REPORTS | 3 : 3005 | DOI: 10.1038/srep03005 4

 www.nature.com/scientificreports

19. Wilson, K. R. et al. Surface relaxation in liquid water and methanol studied by x- 48. Kahan, T. F., Reid, J. P. & Donaldson, D. J. Spectroscopic probes of the quasi-
ray absorption spectroscopy. J. Chem. Phys. 117, 7738–7744 (2002). liquid layer on ice. J. Phys. Chem. A 111, 11006–11012 (2007).
20. Liu, K., Cruzan, J. D. & Saykally, R. J. Water clusters. Science 271, 929–933 (1996). 49. Siefermann, K. R. et al. Binding energies, lifetimes and implications of bulk and
21. Hakala, M. et al. Intra- and intermolecular effects in the Compton profile of water. interface solvated electrons in water. Nat. Chem. 2, 274–279 (2010).
Phys. Rev. B 73, 035432 (2006). 50. Ishiyama, T., Takahashi, H. & Morita, A. Origin of vibrational spectroscopic
22. Wernet, P. et al. The Structure of the first coordination shell in liquid water. response at ice surface. J. Phys. Chem. Lett. 3, 3001–3006 (2012).
Science 304, 995–999 (2004). 51. Zhang, C., Gygi, F. & Galli, G. Strongly anisotropic dielectric relaxation of water at
23. Soper, A. K. Recent water myths. Pure Appl. Chem. 82, 1855–1867 (2010). the nanoscale. J. Phys. Chem. Lett. 4, 2477–2481 (2013).
24. Head-Gordon, T. & Johnson, M. E. Tetrahedral structure or chains for liquid 52. Qiu, H. & Guo, W. Electromelting of confined monolayer ice. Phys. Rev. Lett. 110,
water. PNAS 103, 7973–7977 (2006). 195701 (2013).
25. Kuhne, T. D. & Khaliullin, R. Z. Electronic signature of the instantaneous 53. Wang, C. et al. Stable liquid water droplet on a water monolayer formed at room
asymmetry in the first coordination shell of liquid water. Nat. commun. 4, 1450 temperature on ionic model substrates. Phys. Rev. Lett. 103, 137801–137804
(2013). (2009).
26. Sun, C. Q. et al. Density, elasticity, and stability anomalies of water molecules with
54. James, M. et al. Nanoscale condensation of water on self-assembled monolayers.
fewer than four neighbors. J. Phys. Chem. Lett. 4, 2565–2570 (2013).
Soft Matter 7, 5309–5318 (2011).
27. Huang, C. et al. The inhomogeneous structure of water at ambient conditions.
55. Winter, B. et al. Hydrogen bonds in liquid water studied by photoelectron
PNAS 106, 15214–15218 (2009).
28. Wernet, P. et al. The structure of the first coordination shell in liquid water. Science spectroscopy. J. Chem. Phys. 126, 124504 (2007).
304, 995–999 (2004). 56. Abu-Samha, M. et al. The local structure of small water clusters: imprints on the
29. Nilsson, A., Huang, C. & Pettersson, L. G. M. Fluctuations in ambient water. J. core-level photoelectron spectrum. J. Phys. B 42, 055201 (2009).
Mol. Liq. 176, 2–16 (2012). 57. Nishizawa, K. et al. High-resolution soft X-ray photoelectron spectroscopy of
30. Sun, C. Q. Oxidation electronics: bond-band-barrier correlation and its liquid water. PCCP 13, 413–417 (2011).
applications. Prog. Mater Sci. 48, 521–685 (2003). 58. Vacha, R. et al. Charge transfer between water molecules as the possible origin of
31. Zhao, M. et al. Atomistic origin, temperature dependence, and responsibilities of the observed charging at the surface of pure water. J. Phys. Chem. Lett. 3, 107–111
surface energetics: An extended broken-bond rule. Phys. Rev. B 75, 085427 (2007). (2012).
32. Sun, C. Q., Zhang, X. & Zheng, W. T. Hidden force opposing ice compression. 59. Ni, Y., Gruenbaum, S. M. & Skinner, J. L. Slow hydrogen-bond switching
Chem. Sci. 3, 1455–1460 (2012). dynamics at the water surface revealed by theoretical two-dimensional sum-
33. Pauling, L. The structure and entropy of ice and of other crystals with some frequency spectroscopy. PNAS 110, 1992–1998 (2013).
randomness of atomic arrangement. J. Am. Chem. Soc. 57, 2680–2684 (1935). 60. Sun, H. COMPASS: An ab initio force-field optimized for condensed-phase
34. Wang, Y. et al. High pressure partially ionic phase of water ice. Nat. Commun 2, applications: Overview with details on alkane and benzene compounds. J. Phys.
563 (2011). Chem. B 102, 7338–7364 (1998).
35. Sun, C. Q. et al. Density and phonon-stiffness anomalies of water and ice in the full 61. He, C., Lian, J. S. & Jiang, Q. Electronic structures and hydrogen bond network of
temperature range. J Phys. Chem. Lett. 4, 3238–3244 (2013). ambient water and amorphous ices. Chem. Phys. Lett. 437, 45–49 (2007).
36. Yoshimura, Y. et al. High-pressure x-ray diffraction and Raman spectroscopy of 62. Natarajan, R., Charmant, J. P. H., Orpen, A. G. & Davis, A. P. Water chains in
ice VIII. J. Chem. Phys. 124, 024502 (2006). hydrophobic crystal channels: Nanoporous materials as supramolecular
37. Sugimura, E. et al. Compression of H2O ice to 126 GPa and implications for analogues of carbon nanotubes. Angew. Chem. Int. Ed. 49, 5125–5129 (2010).
hydrogen-bond symmetrization: Synchrotron x-ray diffraction measurements
and density-functional calculations. Phys. Rev. B 77, 214103 (2008).
38. Benoit, M., Marx, D. & Parrinello, M. Tunnelling and zero-point motion in high-
pressure ice. Nature 392, 258–261 (1998). Acknowledgements
39. Goncharov, A. F., Struzhkin, V. V., Mao, H.-k. & Hemley, R. J. Raman
Critical reading by Yi Sun and financial support received from NSF (Nos.: 21273191,
spectroscopy of dense H2O and the transition to symmetric hydrogen bonds.
1033003, and 90922025) China are gratefully acknowledged.
Phys. Rev. Lett. 83, 1998–2001 (1999).
40. Mallamace, F. et al. The anomalous behavior of the density of water in the range
30 K , T , 373 K. PNAS 104, 18387–18391 (2007). Author contributions
41. Erko, M. et al. Density minimum of confined water at low temperatures: a X.Z. and Y.H. contribute equally in computations. Z.M. and W.L.initiated the topic of
combined study by small-angle scattering of X-rays and neutrons. PCCP 14, research and prepared figures. Y.Z., J.Z. and WZ. involved explanations. C.S. wrote the
3852–3858 (2012). manuscript. All authors reviewed the manuscript.
42. Sulpizi, M., Salanne, M., Sprik, M. & Gaigeot, M.-P. Vibrational sum frequency
generation spectroscopy of the water liquid–vapor interface from density
functional theory-based molecular dynamics simulations. J. Phys. Chem. Lett. 4, Additional information
83–87 (2013). Supplementary information accompanies this paper at http://www.nature.com/
43. Solveyra, E. G. et al. Structure, Dynamics, and Phase Behavior of Water in TiO2 scientificreports
Nanopores. J. Chem. Phys. C 117, 3330–3342 (2013).
Competing financial interests: The authors declare no competing financial interests.
44. Uysal, A. et al. What x rays can tell us about the interfacial profile of water near
hydrophobic surfaces. Phys. Rev. B 88, 035431 (2013). How to cite this article: Huang, Y.L. et al. Size, separation, structural order, and mass
45. Kasuya, M. et al. Characterization of Water confined between Silica surfaces using density of molecules packing in water and ice. Sci. Rep. 3, 3005; DOI:10.1038/srep03005
the resonance shear measurement. J. Phys. Chem. C 117, 13540–13546 (2013). (2013).
46. Goldschmidt, V. M. Crystal structure and chemical correlation. Ber Deut Chem
Ges 60, 1263–1296 (1927). This work is licensed under a Creative Commons Attribution 3.0 Unported license.
47. Pauling, L. Atomic radii and interatomic distances in metals. J. Am. Chem. Soc. 69, To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0
542–553 (1947).

SCIENTIFIC REPORTS | 3 : 3005 | DOI: 10.1038/srep03005 5