Water Molecule Structure by suchenfz

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									Water Molecule Structure




                                                                     a
Water is a tiny V-shaped molecule with the molecular formula H2O . Its molecular diameter is about
       g
2.75 Å. In the liquid state, in spite of 80% of the electrons being concerned with bonding, the three
atoms do not stay together as the hydrogen atoms are constantly exchanging between water molecules
due to protonation/deprotonation processes. Both acids and bases catalyze this exchange and even
when at its slowest (at pH 7), the average time for the atoms in an H2O molecule to stay together is
only about a millisecond. As this brief period is, however, much longer than the timescales
encountered during investigations into water's hydrogen bonding or hydration properties, water is
usually treated as a permanent structure.
Water molecules (H2O) are symmetric (point group C2ν) with two mirror planes of symmetry and a
                                                                                           h
2-fold rotation axis. The hydrogen atoms may possess parallel or antiparallel nuclear spin. The water
molecule consists of two light atoms (H) and a relatively heavy atom (O). The approximately 16-fold
difference in mass gives rise to its ease of rotation and the significant relative movements of the
hydrogen nuclei, which are in constant and significant relative movement.

Water's lone pairs?

The water molecule is often described in school and
undergraduate textbooks of as having four,
approximately        tetrahedrally        arranged,
  3
sp -hybridized electron pairs, two of which are
associated with hydrogen atoms leaving the two
remaining lone pairs. In a perfect tetrahedral
arrangement the bond-bond, bond-lone pair and
lone pair-lone pair angles would all be 109.47° and
such tetrahedral bonding patterns are found in
condensed phases such as hexagonal ice.Ab initio
calculations on isolated molecules, however, do not
confirm the presence of significant directed electron   Note. This cartoon of water does not represent
density where lone pairs are expected.                   its actual outline, which is more rotund (see
                                                                             below).

Early 5-point molecular models, with explicit negative charge where the lone pairs are purported to be,
faired poorly in describing hydrogen bonding, but a recent TIP5P model shows some promise.
Although there is no apparent consensus of opinion [116], such descriptions of substantial
  3
sp -hybridized lone pairs in the isolated water molecule should perhaps be avoided [117], as an
  2
sp -hybridized structure (plus a pz orbital) is indicated. This rationalizes the formation of (almost

planar) trigonal hydrogen bonding that can be found around some restricted sites in the hydration of
proteins and where the numbers of hydrogen bond donors and acceptors are unequal.




                                                   Note that the average electron density around the
                                                   oxygen atom is about 10x that around the hydrogen
 The approximate shape and charge distribution     atoms.
                   of water.
The electron density distribution for water is shown above right with some higher density contours
around the oxygen atom omitted for clarity. The polarizability of the molecule is centered around the
                       3                                                                  3
O-atom (1.4146 Å ) with only small polarizabilities centered on the H-atoms (0.0836 Å ) [736]. For
              16           17       18
an isolated H2 O, H2 O or H2 O molecule, the calculated O-H length is 0.957854 Å and the H-O-H

                           16
angle is 104.500° (D2 O, 0.957835 Å, 104.490°) [836]. The charge distribution depends significantly

on the atomic geometry and the method for its calculation but is likely to be about -0.7e on the O-atom
(with the equal but opposite positive charge equally divided between the H-atoms) for the isolated
                   d
molecule [778]. The experimental values for gaseous water molecule are O-H length 0.95718 Å,
                          e
H-O-H angle 104.474° [64]. These values are not maintained in liquid water, where ab initio (O-H
length 0.991 Å, H-O-H angle 105.5° [90]) and neutron diffraction studies (O-D length 0.970 Å,
                                f
D-O-D angle 106° [91]) suggest slightly greater values, which are caused by the hydrogen bonding
weakening the covalent bonding. These bond lengths and angles are likely to change, due to
polarization shifts, in different hydrogen-bonded environments and when the water molecules are
bound to solutes and ions. Commonly used molecular models use O-H lengths of between 0.957 Å
and 1.00 Å and H-O-H angles of 104.52° to 109.5°.

Water electronic structure
                                                                             2.00         1.82
 The electronic structure has been proposed as 1sO                                  2sO

       1.50          1.12          2.00         0.78       0.78
2pxO          2pzO          2pyO          1sH1         1sH2       [71], however it now

appears that the 2s orbital may be effectively unhybridized with
the bond angle expanded from the (then) expected angle of 90°
due to the steric and ionic repulsion between the
partially-positively charged hydrogen atoms (as proposed by
Pauling over 50 years ago [99]). The molecular orbitals of
                2           2       2       2          2
water, (1a1) (2a1) (1b2) (3a1) (1b1) , are shown on another page

(24 KB).Shown opposite is the electrostatic potential associated
with the water structure. Although the lone pairs of electrons do
not appear to give distinct directed electron density in isolated
molecules, there are minima in the electrostatic potential in
approximately the expected positions.
The mean van der Waals diameter of water has been reported as
identical with that of isoelectronic neon (2.82 Å) [112].
Molecular model values and intermediate peak radial
distribution data indicates however that it is somewhat greater
(~3.2Å). The molecule is clearly not spherical, however, with
about a ±5% variation in van der Waals diameter dependent on
the axis chosen; approximately tetrahedrally placed slight
indentations being apparent opposite the (putative) electron                                     Van der Waals radii [206]
pairs.

Water dimer

Much effort has been expended on the structure of small isolated water clusters. The most
energetically favorable water dimer is shown below with a section through the electron density
distribution (high densities around the oxygen atoms have been omitted for clarity). This shows the
                    b
tetrahedrality of the bonding in spite of the lack of clearly seen lone pair electrons; although a small
amount of distortion along the hydrogen bond can be seen. This tetrahedrality is primarily caused by
electrostatic effects (that is, repulsion between the positively charged non-bonded hydrogen atoms)
rather than the presence of tetrahedrally placed lone pair electrons. The hydrogen-bonded proton has
reduced electron density relative to the other protons [222]. Note that, even at temperatures as low as a
few kelvin, there are considerable oscillations (< ps) in the hydrogen bond length and angles [591].
The molecular orbitals of the water dimer are shown on another page (50 KB)




                                                             R = 2.976 (+0.000, -0.030) Å, α = 6 ±
                                                             20°, β = 57 ± 10° [648]; α is the donor
                                                             angle and β is the acceptor angle. The
                                                             dimer (with slightly different geometry)
                                                             dipole moment is 2.6 D [704]. Although
                                                             β is close to as expected if the lone pair
                                                             electrons were tetrahedrallly placed (=
                                                             109.47°/2), the energy minimum (~21 kJ
                                                                 -1
                                                             mol ) is broad and extends towards β =
                                                             0°.



Water models

Simplified models for the water molecule have been developed to agree with particular physical
properties (for example, agreement with the critical parameters) but they are not robust and resultant
data are often very sensitive to the precise model parameters [206]. Models are still being developed
and are generally more complex than earlier but they still generally have poor predictive value outside
the conditions and physical parameters for which they were developed.

Reactivity

Although not often perceived as such, water is a very reactive molecule available at a high
concentration. This reactivity, however, is greatly moderated at ambient temperatures due to the
extensive hydrogen bonding. Water molecules each possess a strongly nucleophilic oxygen atom that
enables many of life‘s reactions, as well as ionizing to produce reactive hydrogen and hydroxide ions.
Reduction of the hydrogen bonding at high temperatures, or due to electromagnetic fields, results in
greater reactivity of the water molecules.




Footnotes
    a
   Water's composition (two parts hydrogen to one part oxygen) was discovered by the London
scientist Henry Cavendish (1731-1810) in about 1781. He reported his findings in terms of
phlogiston (later the gas he made was proven to be hydrogen) and dephlogisticated air (later this
was proven to be oxygen). Cavendish died (1810) in his Laboratory just 30 minutes walk from
the present site of London South Bank University.

It has recently been suggested that H1.5O may better reflect the formula at very small (attosecond)
timescales when some of the H-atoms appear invisible to neutron and electron interaction [515]. The
experimental results have since been questioned [630] and described as erroneous [796], but have
been recently confirmed and thought due to a failure of the Born-Oppenheimer approximation (this
assumes that the electronic motion and the nuclear motion in molecules can be separated) [1134].
Thus the formula H1.5O is incorrect but such suggestions do, however, add support to the view that
observations concerning the structure of water should be tempered by the timescale used. [Back]
b                                      -1(
        The tetrahedral angle is 180-cos 1/3)°; 109.47122° = 109° 28' 16.39". Tetrahedrality (q, the



orientational order parameter) may be defined as                                     , where φjk is the
angle formed by lines drawn between the oxygen atoms of the four nearest and hydrogen-bonded
water molecules [169]. It equals unity for perfectly tetrahedral bonding (where cos(φjk) = -1/3) and
averages zero (±0.5 SD) for random arrangements, with a minimum value of -3. The density order
parameter is described elsewhere. [Back]
c                                                            -1
    ortho-H2O rotates in its ground state with energy 23.79 cm [1150]. Due to deuterium's nuclear spin

of 1 (compare 1/2 for H's spin), the lowest energy form of D2O is ortho. D2O converts to a 2:1
ortho:para ratio at higher temperatures. HDO, having non-equivalent hydrogen atoms, does not
possess an ortho/para distinction. T2O behaves similarly to H2O as tritium also possesses a nuclear
spin of 1/2. [Back]
d
  The charge on the hydrogen atoms across the periodic
table are shown opposite [820]. The hydrogen atom
charges are blue and the charges on the other atoms are
indicated red. [Back]
e
  The actual values depend on the vibrational state of the molecule with even values of 180° being
attainable during high order bend vibrations (v2 >= 7, λ < 900 nm) for the H-O-H angle [860].
Vibrations are asymmetric around the mean positions. In the ground state, the bond angle (104.5°) is
much closer to the tetrahedral angle than that of the other Group VI hydrides, H2S (92.1°), H2Se (91°)
or H2Te (89°). [Back]
f
 The H-O-H angle in ice Ih is reported as 106.6°±1.5° [717], whereas recent modeling gives values of
108.4°±0.2° for ice Ih and 106.3°±4.9° for water [1028]. [Back]
g
    The atomic diameter can be determined from interpolation of the effective ionic radii of the
                                              2-               -                     +
isoelectronic ions (from crystal data) of O        (2.80 Å), OH (2.74 Å) and H3O (2.76 Å) [1167].

Coincidentally, this diameter is similar to the length of a hydrogen bond. The water molecule is
smaller than ammonia or methane, with only H2 and HF being smaller molecules. [Back]

h
    As is found in molecular hydrogen (H2), the hydrogen atoms in water (H2O) may possess parallel

(paramagnetic ortho-H2O, magnetic moment = 1) or antiparallel (nonmagnetic para-H2O, magnetic
moment = 0) nuclear spin. The equilibrium ratio in H2O is all para at zero Kelvin, where the
molecules have no rotational spin in their ground state, shifting to 3:1 ortho:para at less cold
                       c
temperatures (>50 K); the equilibrium taking months to establish itself in ice (or gas) and nearly an
hour in ambient water [410]. This means that liquid H2O effectively consists of a mixture of
non-identical molecules and the properties of pure liquid ortho-H2O or para-H2O are unknown. The
differences in the properties of these two forms of water are expected to be greater in an electric field
[1186], which may be imposed externally, from surfaces or from water clustering itself. Many
materials preferentially adsorb para-H2O due to its non-rotation ground state [410, 835]. The apparent
                                                                       -1
difference in energy between the two states is a significant 1-2 kJ mol , far greater than expected from
                                 -1
spin-spin interactions (< μJ mol ) [835]. It is possible that ortho-H2O and para-H2O form separate

hydrogen bonded clusters [1150]. [Back]


Details of water's molecular vibrations and absorptions are given on another page.

Water Hydrogen Bonding




Hydrogen bonding occurs when an atom of hydrogen is attracted by rather strong forces to two atoms
                                                                                             h
instead of only one, so that it may be considered to be acting as a bond between them [99]. Typically
this occurs where the partially positively charged hydrogen atom lies between partially negatively
charged oxygen and nitrogen atoms, but is also found elsewhere, such as between fluorine atoms in
    -                                                  -   -       -                               -
HF2 and between water and the smaller halide ions F , Cl and Br (for example, HO-H····Br , [178,

1190]; the strength of hydrogen bonding reducing as the halide radius increases), and to a much
                     -
smaller extent to I [190] and even xenon [941]. In theoretical studies, strong hydrogen bonds even
occur to the hydrogen atoms in metal hydrides (for example, LiH····HF; [217]).

Hydrogen bond strength

In water the hydrogen atom is covalently attached to the oxygen of a water molecule (492.2148 kJ
   -1                                                                        -1a1
mol [350]) but has (optimally) an additional attraction (about 23.3 kJ mol        [168]; almost 5 x the
                                                 a2
average thermal collision fluctuation at 25°C) to a neighboring oxygen atom of another water
                                                                        i
molecule that is far greater than any included van der Waals interaction . Formation of hydrogen bonds
between water molecules gives rise to large, but mostly compensating, energetic changes in enthalpy
(becoming more negative) and entropy (becoming less positive). Both changes are particularly large,
based by per-mass or per-volume basis, due to the small size of the water molecule. This
enthalpy-entropy compensation is almost complete, however, with the consequence that very small
imposed enthalpic or entropic effects may exert a considerable influence on aqueous systems. It is
possible that hydrogen bonds between para-H2O, possessing no ground state spin, are stronger and
last longer than hydrogen bonds between orth-H2O [1150].
                                                                                                       d
The hydrogen bond in water is part (about 90%) electrostatic and part (about 10%) covalent [96] and
                                                                                    δ-   δ+   δ-
may be approximated by bonds made up of covalent HO-H····OH2, ionic HO -H ····O H2, and

                              -    +
long-bonded covalent HO ··H––O H2 parts with HO-H····OH2 being very much more in evidence

         -       +
than HO ··H––O H2, where there would be expected to be much extra non-bonded repulsion.

Hydrogen bonding effects all the molecular orbitals even including the inner O1s (1a1) orbital which
                         -1
is bound 318 kJ mol (3.3 eV) less strongly in a tetrahedrally hydrogen bonded bulk liquid phase
compared to the gas phase [1227]. X-ray spectroscopic probing indicates that the electron transitions
between molecular orbitals (changing with the local hydrogen bonding topology) with differing such
contributions may shift on a time scale of less than a femtosecond. Contributing to the strength of
water's hydrogen bonding are nuclear quantum effects (zero point vibrational energy) which bias the
length of the O-H covalent bond longer than its 'equilibrium' position length (as the shorter
HO-H····OH2 hydrogen bonds are stronger), so also increasing the average dipole moment [554]. On
forming the hydrogen bond, the donor hydrogen atom stretches away from its oxygen atom and the
acceptor lone-pair stretches away from its oxygen atom and towards the donor hydrogen atom [585],
both oxygen atoms being pulled towards each other.
An important feature of the hydrogen bond is that it possesses direction; by convention this direction
is that of the shorter O-H (   ) covalent bond (the O-H hydrogen atom being donated to the O-atom
                                                 1
acceptor atom on another H2O molecule). In H-NMR studies, the chemical shift of the proton
                                                         -1
involved in the hydrogen bond moves about 0.01 ppm K upfield to lower frequency (plus about 5.5
ppm further upfield to vapor at 100°C); that is, becomes more shielded with reducing strength of
                                                                                            17
hydrogen bonding [222] as the temperature is raised; a similar effect may be seen in water's O NMR,
                            -1                                                              b
moving about 0.05 ppm K upfield plus 36-38 ppm further upfield to vapor at 100°C. Increased
extent of hydrogen bonding within clusters results in a similar effect; that is, higher NMR chemical
shifts with greater cooperativity [436]. The bond strength depends on its length and angle, with the
                                                                                        +
strongest hydrogen bonding in water existing in the short linear proton-centered H5O2 ion at about
           -1
120 kJ mol . However, small deviations from linearity in the bond angle (up to 20°) possibly have a
relatively minor effect [100]. The dependency on bond length is very important and has been shown to
                                                                                                      c
exponentially decay with distance [101]. Some researchers consider the hydrogen bond to be broken
                                                                                 c2
if the bond length is greater than 3.10 A or the bond angle less than 146° [173], although ab initio
calculations indicate that most of the bonding energy still remains and more bent but shorter bonds
may be relatively strong; for example, one of the hydrogen bonds in ice-four (143°). Similarly
                                                -1
O····H-O interaction energies below 10 kJ mol have been taken as indicative of broken hydrogen
bonds although they are almost 50% as strong as 'perfect' hydrogen bonds and there is no reason to
presuppose that it is solely the hydrogen bond that has been affected with no contributions from other
interactions. Also, the strength of bonding must depend on the orientation and positions of the other
bonded and non-bonded atoms and 'lone pair' electrons [525]. There is a trade-off between the
covalent and hydrogen bond strengths; the stronger is the H····O bond, the weaker the O-H covalent
bond, and the shorter the O····O distance. The weakening of the O-H covalent bond gives rise to a
good indicator of hydrogen bonding energy; the fractional increase in its length determined by the
increasing strength of the hydrogen bonding [217]; for example, when the pressure is substantially
increased (~ GPa) the remaining hydrogen bonds (H····O) are forced shorter [655] causing the O-H
covalent bonds to be elongated. Hydrogen bond strength can be affected by electromagnetic and
magnetic effects. Dissociation is a rare event, occurring only twice a day that is, only once for every
  16
10 times the hydrogen bond breaks.

Hydrogen bond cooperativity

When a hydrogen bond forms between two water molecules, the redistribution of electrons changes
the ability for further hydrogen bonding. The water molecule donating the hydrogen atom has
increased electron density in its 'lone pair' region [577], which encourages hydrogen bond acceptance,
and the accepting water molecule has reduced electron density centered on its hydrogen atoms and its
remaining 'lone pair' region [577], which encourages further donation but discourages further
acceptance of hydrogen bonds. This electron redistribution thus results in both the cooperativity (e.g.
accepting one hydrogen bond encourages the donation of another) and anticooperativity (for example,
accepting one hydrogen bond discourages acceptance of another) in hydrogen bond formation in water
networks. Cooperative hydrogen bonding increases the O-H bond length whilst causing a 20-fold
greater reduction in the H····O and O····O distances [436]. Thus O····O distances within clusters are
likely to be shorter than those at the periphery, in agreement with the icosahedral cluster model. If the
hydrogen bond is substantially bent then it follows that the bond strength is weaker. The main criteria
to determine the strength of hydrogen bonds are their (relatively inaccurately determined)
intermolecular distances and the (more precise) wavenumbers of their stretching vibrational modes
                                                  e
and those of the donor hydrogen covalent bond. Any factors, such as polarization, that reduces the
hydrogen bond length, is expected to increase its covalency. There is still some dispute over the size of
                d
this covalency, however any covalency will increase the network stability relative to purely
electrostatic effects. The hydrogen bond in water dimers is sufficiently strong to result in the dimers
persisting within the gas state at significant concentrations (for example, ~0.1% H2O at 25°C and 85%
humidity) to contribute significantly to the absorption of sunlight and atmospheric reaction kinetics
[266]. The molecular orbitals involved in the hydrogen bonding between two water molecules (50 KB)
and five water molecules (29 KB) in a cyclic pentamer are given on other pages.
Although the hydrogen atoms are often shown along lines connecting the oxygen atoms, this is now
thought to be indicative of time-averaged direction only and unlikely to be found to a significant
extent even in ice.
Liquid water consists of a mixture of short, straight and strong hydrogen bonds and long, weak and
bent hydrogen bonds with many intermediate between these extremes. Short hydrogen bonds in
water are strongly correlated with them being straighter [1083]. Proton magnetic shielding studies
give the following average parameters for the instantaneous structure of liquid water at 4°C;
non-linearity, distances and variance; all increasing with temperature [458]. Note that the two water
molecules below are not restricted to perpendicular planes and only a small proportion of hydrogen
bonds             are           likely            to          have            this           averaged




structure.

The hydrogen bond length of water varies with temperature and pressure. As the covalent bond
lengths vary much less with temperature and pressure, most of the densification of ice 1h due to
reduced temperature or increased pressure must be due to reduction in the hydrogen bond length. This
hydrogen bond length variation can be shown from the changes in volume of ice 1h [818]. As
hydrogen bond strength depends almost linearly on its length (shorter length giving stronger hydrogen
bonding), it also depends almost linearly (outside extreme values) on the temperature and pressure
[818]. The latest molecular parameters for water are given elsewhere. At 0 K the O····O distance in
ice Ih is 2.75 A. The energy of a linear hydrogen bond depends on the orientation of the water
                                         j
molecules relative to the hydrogen bond.
Note that in liquid water, the instantaneous hydrogen bonded arrangement of most molecules is not as
symmetrical as shown here. In particular, the positioning of the water molecules donating hydrogen
bonds to the accepting positions on a water molecule (that is, the water molecules behind in the
diagram above, labeled 'd') are likely to be less tetrahedrally placed, due to the lack of substantial
tetrahedrally positioned 'lone pair' electrons, than those water molecules that are being donated to
from that water molecule (that is, the water molecules top and front in the diagram above, labeled 'a'
[1224]. Also, the arrangement may well consist of one pair of more tetrahedrally arranged strong
hydrogen bonds (one donor and one acceptor) with the remaining hydrogen bond pair (one donor and
                                             -1
one acceptor) being either about 6 kJ mol weaker [573], less tetrahedrally arranged [373, 396] or
bifurcated [573]; perhaps mainly due to the anticooperativity effects mentioned below. X-ray
absorption spectroscopy confirms that, at room temperature, 80% of the molecules of liquid water
have one (cooperatively strengthened) strong hydrogen bonded O-H group and one non-, or only
weakly, bonded O-H group at any instant (sub-femtosecond averaged and such as may occur in
pentagonally hydrogen bonded clusters), the remaining 20% of the molecules being
four-hydrogen-bonded tetrahedrally coordinated [613]. Such 'instantaneous' structuring is not now
                                                                                                g
thought to represent the more time-averaged structure, which is basically tetrahedral [1024].
Liquid water contains by far the densest hydrogen bonding of any solvent with almost as many
hydrogen bonds as there are covalent bonds. These hydrogen bonds can rapidly rearrange in response
to changing conditions and environments (for example, solutes). The hydrogen bonding patterns are
random in water (and ice Ih); for any water molecule chosen at random, there is equal probability
(50%) that the four hydrogen bonds (that is, the two hydrogen donors and the two hydrogen acceptors)
are located at any of the four sites around the oxygen. Water molecules surrounded by four hydrogen
bonds tend to clump together, forming clusters, for both statistical [11] and energetic reasons.
Hydrogen bonded chains (that is, O-H····O-H····O) are cooperative [379]; the breakage of the first
bond is the hardest, then the next one is weakened, and so on (see the cyclic water pentamer). Thus
unzipping may occur with complex macromolecules held together by hydrogen bonding, for example,
nucleic acids. Such cooperativity is a fundamental property of liquid water where hydrogen bonds are
up to 250% stronger than the single hydrogen bond in the dimer [77]. A strong base at the end of a
chain may strengthen the bonding further. The cooperative nature of the hydrogen bond means that
acting as an acceptor strengthens the water molecule acting as a donor [76]. However, there is an
anticooperative aspect in so far as acting as a donor weakens the capability to act as another donor, for
example, O····H-O-H····O [77]. It is clear therefore that a water molecule with two hydrogen bonds
where it acts as both donor and acceptor is somewhat stabilized relative to one where it is either the
donor or acceptor of two. This is the reason why it is suspected that the first two hydrogen bonds
(donor and acceptor) give rise to the strongest hydrogen bonds [79]. An interesting way of describing
the cooperative/anticooperative nature of the water dimer hydrogen bond is to use the nomenclature
d'a'DAd''a'' where DA represents the donor-acceptor nature of the hydrogen bond, the d'a' represents
the remaining donor-acceptor status of the donating water molecule and d''a'' represents the remaining
donor-acceptor status of the accepting water molecule [852]. Individually, the most energetically
favored donating water molecules have the structures 02D, 12D, 01D and 11D with 00D and 10D
disfavored whereas the most energetically favored accepting water molecules have the structures A20,
A21, A10 and A11 with A00 and A01 disfavored.
                   increasing hydrogen bond
                strength




anticooperat
     ive
           c
 ooperative
(= -d'+a'+d''
     -a'')


     -2             -1            0              1              2             3              4


 10DA01          10DA00        10DA10         10DA20


                 10DA11        10DA21


                 00DA01        00DA00         00DA10        00DA20


                               00DA11         00DA21


                 11DA01        11DA00         11DA10        11DA20
                                  11DA11        11DA21


                 01DA01           01DA00        01DA10         01DA20


                                  01DA11        01DA21


                 12DA01           12DA00        12DA10         12DA20


                                  12DA11        12DA21


                 02DA01           02DA00        02DA10         02DA20


                                  02DA11        02DA21




Cations may induce strong cooperative hydrogen-bonding around them due to the polarization of
                                                      +
water O-H by cation-lone pair interactions (Cation ····O-H····O-H). Luck et al [78] introduced a
                                                                                   +            2+
cooperativity factor for this effect, which varied as the Hofmeister series from K (1.08) to Zn (2.5).
Total hydrogen bonding around ions may be disrupted however as if the electron pair acceptance
increases (for example, in water around cations) so the electron pair donating power of these water
molecules is reduced; with opposite effects in the hydration water around anions. These changes in the
relative hydration ability of salt solutions are responsible for the swelling and deswelling behavior of
hydrophilic polymer gels [317].
The substantial cooperative strengthening of hydrogen bond in water is dependent on long range
                                                           f
interactions [98]. Breaking one bond generally weakens those around whereas making one bond
generally strengthens those around and this, therefore, encourages larger clusters, for the same average
bond density. The hydrogen-bonded cluster size in water at 0°C has been estimated to be 400 [77].
Weakly hydrogen-bonding surface restricts the hydrogen-bonding potential of adjacent water so that
these make fewer and weaker hydrogen bonds. As hydrogen bonds strengthen each other in a
cooperative manner, such weak bonding also persists over several layers and may cause locally
changed solvation. Conversely, strong hydrogen bonding will be evident at distance. The weakening
                                           -1                    -1
of hydrogen bonds, from about 23 kJ mol to about 17 kJ mol , is observed when many bonds are
broken at superheating temperatures (> 100°C) so reducing the cooperativity [173]. The breakage of
these bonds is not only due to the more energetic conditions at high temperature but also results from a
related reduction in the hydrogen bond donating ability by about 10% for each 100°C increase [218].
The loss of these hydrogen bonds results in a small increase in the hydrogen bond accepting ability of
water, due possibly to increased accessibility [218].
Every hydrogen bond formed increases the hydrogen bond status of two water molecules and every
hydrogen bond broken reduces the hydrogen bond status of two water molecules. The network is
essentially complete at ambient temperatures; that is, (almost) all molecules are linked by at least one
unbroken hydrogen bonded pathway. Hydrogen bond lifetimes are 1 - 20 ps [255] whereas broken
bond lifetimes are about 0.1 ps with the proportion of 'dangling' hydrogen bonds persisting for longer
than a picosecond being insignificant [849]. Broken bonds are basically unstable [849] and will
probably reform to give same hydrogen bond (as shown by the slow ortho-water/para-water
equilibrium process [410]), particularly if the other three hydrogen bonds are in place; hydrogen bond
breakage being more dependent on the local structuring rather than the instantaneous hydrogen bond
strength [833]. If not, breakage usually leads to rotation around one of the remaining hydrogen bond(s)
[673] and not to translation away, as the resultant 'free' hydroxyl group and 'lone pair' are both quite
reactive. Also important, if seldom recognized, is the possibility of the hydrogen bond breaking, as
evidenced by physical techniques such as IR, Raman or NMR and caused by loss of hydrogen bond
'covalency' due to electron rearrangement, without any angular change in the O-H····O atomic
positions. Thus, clusters may persist for much longer times [329] than common interpretation of data
from these methods indicates. Evidence for this may be drawn from the high degree of hydrogen bond
breakage seen in the IR spectrum of ice [699], where the clustering is taken as lasting essentially
forever.

Rearranging hydrogen bonds

The molecular orbitals of water indicate that the two 'lone pairs' of electrons do not give distinct
directed electron density in isolated molecules, with tetrahedral nature of water's hydrogen bonding
due to four-coordination involving two donor and two acceptor hydrogen bonds. However trigonal
(approximately planar) hydrogen bonding is also possible with two donor and one acceptor hydrogen
bonds associated with individual water molecules. The lack of substantial tetrahedrally positioned
'lone pair' electrons may ease this process, at a cost of one hydrogen bond energy. Also the acceptor
hydrogen bond in three coordinated but tetrahedral arrangements (two donor and one acceptor
hydrogen bonds with one vacant acceptor site) can slide through a planar arrangement to the vacant
tetrahedral site without breaking. This flexibility in the hydrogen bonding topology facilitates
hydrogen-bonding rearrangements.

Bifurcated hydrogen bonds

Bifurcated hydrogen bonds (where both hydrogen atoms from one water molecule are hydrogen
bonding to the same other water molecule, or one hydrogen atom simultaneously forms hydrogen
bonds to two other water molecules) have just under half the strength of a normal hydrogen bond (per
half the bifurcated bond) and present a low-energy route for hydrogen-bonding rearrangements [255].
They allow the constant randomization of the hydrogen bonding within the network. However, it
should be noted that they require the breakage of two hydrogen bonds; one hydrogen bond to form the
bifurcated arrangement and another to make way for a different hydrogen bond to form. Any
necessary rotation may also involve bending or stretching other hydrogen bonds. Bifurcation of
hydrogen bonds cannot cause their net breakage and only occur when a broken hydrogen bond
releases a lone pair to accept the incoming hydrogen bond donor [1135]. Trifurcated hydrogen bonds
(where one hydrogen atom simultaneously forms hydrogen bonds to three other water molecules,
forming a tetrahedral face) may also form but only have about one sixth the strength of a normal
hydrogen bond per third of the bifurcated bond [573], require free lone pairs on all three bound water
molecules and the rest of local cluster must also be poorly hydrogen bonded.

Information transfer

Hydrogen bonding carries information about
solutes and surfaces over significant distances in
liquid water. The effect is synergistic, directive and
extensive. Thus, in the diagram opposite, strong
hydrogen-bonding in molecule (1), caused by
solutes or surfaces, will be transmitted to
molecules 2 and 3, then to 5 and 6 and then as
combined power to 8.The effect is reinforced by
additional polarization effects and the resonant
intermolecular transfer of O-H vibrational energy,
mediated by dipole-dipole interactions and the
hydrogen bonds [142]. Reorientation of one
molecule induces corresponding motions in the
neighbors.



Thus solute molecules can 'sense' (for example, effect each others solubility) each other at distances of
several nanometers and surfaces may have effects extending to tens of nanometers. This long range
correlation of molecular orientation has recently been confirmed using hyper-Rayleigh light scattering
[152] and is a reason for the high dielectric constant of water and the consequential reduction in this
dielectric constant as the temperature is raised and the number of hydrogen bonds is reduced [239].
Where water molecules are next to flat hydrophobic surfaces, and unable to form extensive clathrate
structuring, some hydrogen bonds must be broken and the water molecules will tend to change
orientation, from one hydrogen bond directed orthogonally away from the surface (as in clathrates) to
one hydrogen bond directed orthogonally towards the surface, in order to minimize the energy
requirement. Also the water molecules tend to collapse into their shallow energy minima due to
increased non-bonded interactions. Although there may be a consequentially increased density in the
first water layer, the second and subsequent water shells compensate by forming stronger hydrogen
bonds and a less dense structure. Consequences of this include differential solvation properties
affecting surface absorption.
Hydrogen bonding rearrangement offers a
low energy pathway for the transfer of
hydrogen atoms during tautomerism, in a
way similar to Grotthuss mechanism for
hydrogen ion transport. Shown opposite is
adenine tautomerism that can give rise to
Adenine - Cytosine (mutation producing)
pairing, which uses the rare tautomer on the
left.




Footnotes

a1
  This is the energy (ΔH) required for breaking and completely separating the bond, and should equal
                                                                           -1   -1
about half the enthalpy of vaporization. On the same basis ΔS = 37 J deg mol [168]. Just breaking
the hydrogen bond in liquid water leaving the molecules essentially in the same position requires only
                                                              -1
about 25% of this energy; recently estimated at 6.3 kJ mol [690]. If the hydrogen bond energy is
determined from the excess heat capacity of the liquid over that of steam (assuming that this excess
                                                                                -1
heat capacity is attributable to the breaking of the bonds) ΔH = 9.80 kJ mol [274]. A number of
                                                     -1
estimates give the equivalent ΔG at about 2 kJ mol at 25°C [344]; however from the equilibrium
                                     -1                -1
content of hydrogen bonds (1.7 mol ) it is -5.7 kJ mol . The hydrogen bonding in ice Ih is about 3 kJ
    -1                                          -1
mol stronger than liquid water (= 28 kJ mol at 0 K, from lattice energy including non-bonded
interactions) and evidenced by an about 4 pm longer, and hence weaker, O-H covalent bond.
Hydrogen bonds in D2O are more linear, shorter [554] and stronger than in H2O and those in T2O are
expected to be stronger still. Thus given the choice, hydrogen bonds form with the preference
O-T····O > O-D····O > O-H····O. [Back]
a2
  The average molecular linear translational energy is RT/2. The average collision energy is RT (2.479
       -1
kJ mol ). 2% of collisions have energy greater than the energy required to break the bonds (9.80 kJ
   -1
mol , [274]) as determined by excess heat capacity. [Back]
b
  Unfortunately this is difficult to use as a tool, however, due to the averaging of the shift and the
complexity of the system. The spin-lattice relaxation times (T1, ~3.6 s, 25°C) of the water protons is
also a function of the hydrogen bonding, being shorter for stronger bonding. The effect of solutes,
however, shows the chemical shift and spin-lattice relaxation time are not correlated, as solutes may
reduce the extent of hydrogen bonding at the same time as increasing its strength [281]. [Back]
c
    Whether a hydrogen bond is considered broken or just stretched and/or bent should be defined by its
strength but, as the isolated bond strength may be difficult to determine, this often remains a matter of
definition based on distances and angles. An arrangement with strained geometry is very unlikely to
last long. It may, however, occur during the breakage, formation or partner-switching (that is,
bifurcation) of a hydrogen bond or arise transiently, due to thermal effects or other molecular
                                                                                                    -13
interactions, in a long-lived hydrogen bond. The lifetime of a hydrogen bond (if more than 10 s)
presents another measure of hydrogen bond formation but this also suffers from uncertainties in the
definition of its geometry. [Back]
c2
  Other workers use more generous parameters; for example, in [848], the hydrogen bond length must
be less than 3.50 A and the bond angle greater than 120°. The importance of choosing a correct
definition for the hydrogen bonds has been examined [1240]. The simple distance criterion of 2.50 A
for the H····O distance was found very useful and cheapest in computational terms whereas methods
based on energy proved poor. Adding further criteria, such as the bond angles, proved of marginal use
[1240]. [Back]
d
 There is still some controversy surrounding this partial covalency with both for (for example, [411]
gives the 3a1 orbital as most responsible for the hydrogen bonding via orbital mixing), against (for
example, [437] favors 'antibonding' rather than bonding due to the charge transfer) and neutral [438]
in the recent literature. If the water hydrogen bond is considered within the context of the complete
range of molecular hydrogen bonding then it appears most probable that it is not solely electrostatic
[447]; indeed the continuous transformation of ice VII to ice X would seem to indicate a continuity of
electron sharing between water molecules. Although N-H····N and N-H····O hydrogen bonds are
known to be weaker than the O-H····O hydrogen bonds in water, there is clear evidence for the bonds'
                                                                                        2            15
covalent natures from NMR. In nucleic acids, inter-nucleotide N-H····N coupling ( JNN, using              N

                                                                                                    3
nuclei) confirms some covalent nature in the N-H····N hydrogen bond [779]. Also, 3-bond NMR ( JNC)

splitting has been found through peptide N-H····O=C hydrogen bonds in proteins, confirming some
covalent nature in the N-H····O hydrogen bond [780]. [Back]
e
  The O-H vibrational frequency does not follow the O····O hydrogen bond length exactly due to
dispersion of the hydrogen bond O-H····O angle [439]. [Back]
f
 However note that some hydrogen bonds may distort a hydrogen bonded cluster such that when such
a bond breaks the detached cluster may form a more optimum tetrahedrally bonded arrangement with
lower energy and thus reclaiming some or most of the energy lost by bond breakage. [Back]
g
  The interpretation of the structure of water in terms of strands and rings of doubly-linked
hydrogen-bonded molecules [613] was not confirmed by a Compton scattering study [1083] where the
data was consistent with 3.9 hydrogen bonds (Roo≤3.2A) around each water molecule, and has been
disputed by another X-ray absorption spectroscopic study [690a], which presents a case for the 'non-,
or only weakly, bonded O-H groups' to form the majority of O-H groups present and that these groups
are more strongly bonded. Also, Bowron challenges the above interpretation (that is, [613]) in the
Discussion included in [746] and a Raman study supports the fully tetrahedrally hydrogen bonded
model [875]. This dispute was thought to have been resolved by an ab initio molecular dynamics
study [832] that shows 170 fs fluctuations of 2.2-fold strength between the two donor hydrogen bonds
from each water molecule whilst the overall geometric connectivity is retained, in line with the
hypothesis first presented above. However this study [832] has attracted serious criticism [1159],
leaving its conclusions seemingly unproven. Recent ab initio calculations of the x-ray cross section of
liquid water shows only 20% broken hydrogen bonds are present [1059] and a novel force field for
water, developed from first principles, gives 3.8 shared tetrahedrally coordinated hydrogen bonds per
water molecule [1189]. Also, an ab initio quantum mechanical/molecular mechanics molecular
dynamics simulation study shows that although the time averaged hydrogen bonding is about four
shared hydrogen bonds per water molecule, the instantaneous value is significantly lower at about 2.8
shared hydrogen bonds per water molecule [922]. [Back]
h
    The hydrogen bond in water was first suggested by Latimer and Rodebush in 1920 [789]. [Back]
i                                                                                     -1
  The van der Waals attraction has been estimated as high as about 5.5 kJ mol [548] based on
isoelectronic molecules at optimal separation, but is likely to be repulsive within a hydrogen bond due
to the close contact (see for example, [736]). Separating the hydrogen bond components, as below,
helps our understanding, although in reality these components are combined.
    Attraction/repulsion


++ electrostatic        long range interaction (< 30 A) based on point charges, or on dipoles plus
                                                                                                  -1
attraction              quadrupoles, and so on. They may be considered as varying with distance .
++ polarization         due to net attractive effects between charges and electron clouds (< 8 A), which
attraction              may increase cooperatively dependent on the local environment. They may be
                                                             -4
                        considered as varying with distance . This net attractive effect may contain a
                        small repulsive element due to slightly increased electron cloud overlap.
+ covalency             highly directional and increases on hydrogen bonded cyclic cluster formation.
attraction              It is very dependent on the spatial arrangement of the molecules within the
                        local environment (< 6 A)
+ dispersive            interaction (< 6 A) due to coordinated effects of neighboring electron clouds.
                                                                            -6
attraction              They may be considered as varying with distance .
-- electron             very short range interaction (< 4 A) due to electron cloud overlap. They may be
                                                            -12
repulsion               considered as varying with distance .


                                                                                              [Back]
j
  In an unstrained tetrahedral network (such as ice Ih) only the six structures below can arise with no
structures at intermediate angles. The hydrogen bond energy depends particularly on the angle of
rotation around the hydrogen bond, as below, due to the interaction between the molecular dipoles.
Note that the hydrogen bonds in the structure pairs (a) and (e), and (b) and (d) have identical energies.
In ice Ih with no net dipole moment, the configurations with extreme cis/trans ratios have 56.3% cis
(i.e. a+e+f) or 64.7% trans (that is, b+c+d) but the calculated difference in energies was only 0.12%
               -1                                                      -1
(0.06 kJ mol ) [858]; much lower than the expected (several kJ mol ) difference in energy between
trans and cis structures c and f. As a, c and e involve protons in hydrogen bonds parallel to the c-axis,
their increased strength relative to b, d and f may be causative to the (0.3%) shortened c-axis in the ice
Ih unit cell.




Water Phase Diagram

A phase diagram shows the preferred physical states of matter at different temperatures and pressure.
Within each phase the material is uniform with respect to its chemical composition and physical state.
At typical temperatures and pressure (marked by an 'E' below) water is a liquid, but it becomes solid
(that is, ice) if its temperature is lowered below 273 K and gaseous (that is, steam) if its temperature is
raised above 373 K, at the same pressure. Each line represents a phase boundary and gives the
conditions when two phases coexist. Here, a change in temperature or pressure may cause the phases
to abruptly change from one to the other. Where three lines join, there is a 'triple point' when three
phases coexist but may abruptly and totally change into each other given a change in temperature or
pressure. Four lines cannot meet at a single point. A 'critical point' is where the properties of two
                                                                                                g
phases become indistinguishable from each other. The phase diagram of water is complex, having a
number of triple points and one or possibly two critical points. Many of the crystalline forms may
remain metastable in much of the low-temperature phase space at lower pressures.
The mean surface conditions on Earth, Mars and Venus
are indicated. The complex central part of the phase
diagram is expanded opposite. The critical point and the
orange line in the ice-one phase space refer to the
low-density (LDA) and high-density (HDA) forms of
amorphous water (ice) [16]. Although generally
accepted and supported by diverse experimental
evidence [754a, 861], the existence of this second, if
metastable, critical point is impossible to prove
absolutely at the present time and is disputed by some
[200, 618, 628, 754b, 1115]. The transition between
LDA and HDA is due to the increased entropy and
attractive van der Waals contacts in HDA compensating
for the reduced strength of its hydrogen bonding.


The high-pressure phase lines of ice-ten (X) and ice-eleven (XI) [81] are still subject to experimental
verification and the boundary between supercritical water and ice-seven (VII) (see [691]) is still to be
firmly established.
Both the critical points are shown as red circles in the phase diagram, above. Beyond the critical point
in the liquid-vapor space (towards the top right, above), water is supercritical existing as small but
liquid-like hydrogen-bonded clusters dispersed within a gas-like phase [456, 894], where physical
properties, such as gas-like or liquid-like behavior, vary in response to changing density. The critical
                           -3
isochor (density 322 kg m ) is shown as the thin dashed line extension; this may be thought of as
dividing more-liquid-like and more-gas-like properties [540]. The properties of supercritical water are
very different from ambient water. For example, supercritical water is a poor solvent for electrolytes,
which tend to form ion pairs. However, it is such an excellent solvent for non-polar molecules, due to
its low dielectric constant and poor hydrogen bonding, that many are completely miscible. Viscosity
and dielectric both decrease substantially whereas auto-ionization increases substantially. The physical
properties of water close to the critical point (near-critical) are particularly strongly affected [677],
Extreme density fluctuations around the critical point causes opalescent turbidity. Many properties of
cold liquid water change above about 200 MPa (for example, viscosity, self-diffusion, compressibility,
Raman spectra and molecular separation), which may be explained by the presence of a high density
liquid phase containing interpenetrating hydrogen bonds. The chemical properties of water are also
greatly changed at high temperatures and pressures due to the changes in ionization, solubility,
diffusivity and reactivity due to decreasing hydrogen-bonding [1116].
As pressure increases, the ice phases become denser. They
achieve this by initially bending bonds, forming tighter ring
or helical networks, and finally including greater amounts of
network inter-penetration. This is particularly evident when
comparing ice-five with the metastable ices (ice-four and
ice-twelve) that may exist in its phase space.




                                              The liquid-vapor density data for the graphs above,
                                              opposite and below were obtained from the IAPWS-95
                                              equations [540]. Other phase diagrams for water are
                                              presented elsewhere [681].
The density of liquid water increases with increase
in pressure. Seen opposite is the density of liquid
and solid (that is the ices) water along the
liquid-solid phase line. Note that temperature
varies along this phase line (as shown dashed).
Hexagonal ice is less dense than liquid water
whereas the other ices found in equilibrium with
water are all denser with phase changes occurring
on the approach of the liquid and solid densities.




Triple points

Triple points occur where three phase lines join and the three phases may coexist at equilibrium.
Thermodynamic data for the triple points of water
                                                                   -1            3
 Triple points             MPa                   °C     ΔS, J mol       ΔV cm        Ref.     D2O [711]
                                                              -1            -1
                                                            K            mol
gas    liquid    Ih    0.000611657               0.01                                536    661 Pa, 3.82°C
                                                   0                                             [70]
                                    gas        liquid     -132.5        -22050


                             gas          Ih                                -154.5             -22048


                           liquid         Ih                             -22.0       1.63         8
                                                                                       4
 gas     Ih    XI       0         -201                              711   0 MPa, -197°C
                                   .0
liquid   Ih    III   207.5        -22.                              537     220 MPa,
                                    0                                        -18.8°C
                           liquid    Ih         -14.9   2.434       838


                     liquid        III                      -13.9            -0.839


                        Ih         III                       1.0             -3.273


 Ih      II    III   212.9              -34.                        537     225 MPa,
                                         7                                   -31.0°C
                                     Ih    II   -2.1    -3.919      838


                        Ih         III                       1.0             -3.532


                         II        III                       3.2              0.387


  II     III   V     344.3              -24.                        537     347 MPa,
                                         3                                   -21.5°C
                                     II   III    3.1    0.261       838


                            II      V                        3.3             -0.721


                         III        V                        0.1             -0.982


liquid   III   V     346.3              -17.                        537     348 MPa.
                                         0                                   -14.5°C
                                 liquid   III   -13.2   -0.434      838


                     liquid         V                       -13.1            -1.419
                               III     V                                0.1               -0.985


  II      V     VI          ~620              ~-5                              539
                                                5
liquid    V     VI          625.9             0.16                             537      629 MPa,
                                                                                          2.4°C
                                     liquid     V        -15.7    -0.949       838


                           liquid     VI                               -16.2              -1.649


                               V      VI                               -0.5               -0.700


 VI      VII    VI          2,100             ~5                                8       1950 MPa,
                II                                                                        ~0°C
liquid   VI     VI          2,200             81.6                              8       2060 MPa,
                 I                                                                        78°C
  VII    VIII   X          62,000             -173                             538
liquid   VII    X          43,000             >70                              612
                                                0



 Ice phases

 All the crystalline phases of ice involve the water molecules being hydrogen bonded to four
 neighboring water molecules. In all cases the two hydrogen atoms are equivalent, with the water
 molecules retaining their symmetry, and they all obey the 'ice' rules: two hydrogen atoms near each
                                                     j
 oxygen, one hydrogen atom on each O····O bond. The H-O-H angle in the ice phases is expected to
 be a little less than the tetrahedral angle (109.47°), at about 107°.
 Two different forms of ice-eleven have been described by different research groups: the high-pressure
 form (also known as ice-thirteen) involves hydrogen atoms equally-spaced between the oxygen atoms
 [84] (like ice-ten) whereas the lower pressure low temperature form uses the incorporation of
                                               +
 hydroxide defect doping (and interstitial K ions) to order the hydrogen bonding of ice Ih [207], that
 otherwise occurs too slowly. Another ice-ten has been described, being the proton ordered form of
 ice-six (VI) occurring below about 110 K. Only hexagonal ice-one (Ih), ice-three (III), ice-five (V),
 ice-six (VI) and ice-seven (VII) can be in equilibrium with liquid water, whereas all the others ices,
 including ice-two (II, [273]), are not stable in its presence under any conditions of temperature and
 pressure. The low-temperature ices, ice-two, ice-eight (VIII), ice-nine (IX), ice-eleven (low pressure
form), ice-thirteen (XIII) [1002] and ice-fourteen (XIV) [1002] all possess (ice-nine and ice-fourteen
incompletely) low entropy ordered hydrogen-bonding whereas in the other ices (except ice-ten [80]
and ice-eleven where the hydrogen atoms are symmetrically placed) the hydrogen-bonding is
disordered even down to 0 K, where reachable. Ice-four (IV) and ice-twelve (XII) [82] are both
metastable within the ice-five phase space. Cubic ice (Ic) is metastable with respect to hexagonal ice
(Ih). It is worth emphasizing that liquid water is stable throughout its phase space above. Kurt
Vonnegut's highly entertaining story concerning an (imaginary) ice-nine, which was capable of
crystallizing all the water in the world [83], fortunately has no scientific basis (see alsoIE) as ice-nine,
in reality, is a proton ordered form of ice-three, only exists at very low temperatures and high
pressures and cannot exist alongside liquid water under any conditions. Ice Ih may be metastable with
respect to empty clathrate structures of lower density under negative pressure conditions (that is,
stretched) at very low temperatures [520].
Structural data on the ice polymorphs
                                                        h
    Ice        Density,     Protons        Crystal              Sym      Dielectric            Notes
                     -3 a       f
polymorph       g cm                                            metry                 i
                                                                        constant, εS

Hexagonal         0.92      disorder      Hexagonal              one        97.5
ice, Ih                        ed                                C6
Cubic ice,        0.92      disorder        Cubic               four
Ic                             ed                                C3
      b
LDA               0.94      disorder    Non-crystallin                                    As prepared, may
                               ed            e                                            be mixtures of
                                                                                          several types
      c
HDA               1.17      disorder    Non-crystallin                                    As prepared, may
                               ed            e                                            be mixtures of
                                                                                          several types
          d
VHDA              1.25      disorder    Non-crystallin
                               ed            e
II, Ice-two       1.17      ordered     Rhombohedral             one        3.66
                                                                 C3
III,              1.14      disorder      Tetragonal             one        117           protons may be
Ice-three                      ed                                C4                       partially ordered
IV, Ice-four      1.27      disorder    Rhombohedral             one                      metastable in ice
                               ed                                C3                       V phase space
V, Ice-five       1.23      disorder     Monoclinic              one        144           protons may be
                               ed                                C2                       partially ordered
                                                            e
VI, Ice-six       1.31      disorder     Tetragonal              one        193           protons can be
                               ed                                C4                       partly ordered
                                                    e
VII,              1.50      disorder        Cubic               four        150           two
Ice-seven                      ed                                C3                       interpenetrating
                                                                                          ice Ic frameworks
                                                       e
VIII,             1.46      ordered      Tetragonal               one                4    low temperature
Ice-eight                                                         C4                      form of ice VII
IX, Ice-nine      1.16      ordered      Tetragonal               one              3.74   low temperature
                                                                  C4                      form of ice III,
                                                                                          metastable in ice
                                                                                          II space
                                                   e
X, Ice-ten        2.51      symmet         Cubic                 four                     symmetric proton
                              ric                                 C3                      form of ice VII
XI,               0.92      ordered     Orthorhombic             three                    low temperature
Ice-eleven                                                        C2                      form of ice Ih
XI,               >2.51     symmet       Hexagonal              distort                   Found            in
             k                                             e
Ice-eleven                     ric      close packed              ed                      simulations only
XII,              1.29      disorder      Tetragonal             one                      metastable in ice
Ice-twelve                     ed                                 C4                      V phase space
XIII,             1.23      ordered      Monoclinic               one                     ordered form of
Ice-thirteen                                                      C2                      ice V phase
XIV,              1.29      mostly      Orthorhombic              one                     ordered form of
Ice-fourtee                 ordered                               C4                      ice XII phase
n
XV,              1.31 (?)   ordered           ?                    ?                      ordered form of
             n
Ice-fifteen                                                                               ice VI phase

More structural data on the ice polymorphs
   Ice      Molecular        Small    He               Approximate O-O-O angles, °                Ring
polymorp environment          ring     lix                                                     penetration
    h            s           size(s)                                                            hole size


Hexagona             1            6        No                     All 109.47±0.16                 None
l ice, Ih                                  ne


Cubic ice,           1            6        No                             109.47                  None
Ic                                         ne


      b
LDA                 3+           5, 6      No                  mainly 108, 109 and 111            None
                                           ne


      c
HDA                 6+           5, 6      No                          broad range                None
                                         ne


          d
VHDA              6+          5, 6       No               broad range      None [747]
                                         ne


II, Ice-two     2 (1:1)         6        No    80,100,107,118,124,128;       None
                                         ne    86,87,114,116,128,130


III,            2 (1:2)       5, 7        4    (1) 91,95,112,112,125,125     None
Ice-three                                —f    (2) 98,98,102,106,114,135
                                         old


IV,             2 (1:3)         6        No    (1) 92,92,92,124,124,124     some 6
Ice-four                                 ne    (3) 88,90,113,119,123,128


V, Ice-five   4 (1:2:2:2)   4, 5, 6, 8   No    (1) 82,82,102,131,131,131   8 (1 bond)
                                         ne    (2) 88,91,109,114,118,128
                                               (3) 85,91,101,103,130,135
                                               (4) 84,93,95,123,125,126


VI,             2 (1:4)       4, 8       No    (1) 77,77,128,128,128,128   8 (2 bond)
Ice-six                                  ne    (2) 78,89,89,128,128,128


VII,              1             6        No                  109.47         every 6
Ice-seven                                ne


VIII,             1             6        No                  109.47         every 6
Ice-eight                                ne


IX,             2 (1:2)       5, 7        4    (1) 91,95,112,112,125,125     None
Ice-nine                                 —f    (2) 98,98,102,106,114,135
                                         old


X, Ice-ten        1             6        No                  109.47         every 6
                                         ne
XI,                1               6        No                  109.47                       None
Ice-eleven                                  ne


XI,           undetermined         6        No              undetermined                    every 6
Ice-eleven                                  ne
k



XII,             2 (1:2)         7, 8        5    (1) 107,107,107,107,115,115                None
Ice-twelve                                  —f    (2) 67,83,93,106,117,132
                                            old


XIII,         7 (all equal)    4, 5, 6, 8   No    (1) 82,82,102,131,131,131               8 (1 bond)
Ice-thirtee                                 ne    (2) 88,91,109,114,118,128
n                                                 (3) 85,91,101,103,130,135
                                                  (4) 84,93,95,123,125,126


XIV,             2 (1:2)         7, 8        5    (1) 107,107,107,107,115,115                None
Ice-fourte                                  —f    (2) 67,83,93,106,117,132
en                                          old




The thermal conductivities properties of crystalline and amorphous ices have been reviewed [1202].
Other stable or metastable phases of ice have been proposed (for example, Ice XIII and ice XIV [958])
and may exist but their structures have not been established. Such new phases are thought particularly
likely to be found within the phase space of ice II and ice V. Several new phases (for example ice i)
have only been found (so far) in modeling studies. 'Metallic' water, where electrons are freed to move
extensively throughout the material and the atoms of water exist as ions, probably exists as an
                           m
antifluorite type structure above 1.76 TPa [1138]. It is not thought that any other phases are stable at
higher pressures than this.
The proposed topology of the transformations between ice XI                ice II        ice IX and ice
VIII           ice X has been described [1237].




Footnotes
a
    density at atmospheric pressure. [Back]
b
  Low-density amorphous ice (LDA). The structural data in the Table is given assuming LDA has the
structure of ES. [Back]
c
  High-density amorphous ice (HDA). The structural data in the Table is given assuming HDA has the
structure of crushed CS. [Back]
d
  Very high-density amorphous ice (VHDA). The structural data in the Table assumes no hydrogen
bond rearrangements from LDA or HDA. As VHDA is likely to be a a relaxed form of HDA, this
assumption seems unlikely [935]. [Back]
e
    Structure consists of two interpenetrating frameworks. [Back]
f
 Although primarily ordered or disordered, ordered arrangements of hydrogen bonding may not be
perfect and disordered arrangements of hydrogen bonding are not totally random as there are
correlated and non-bonded preferential effects. [Back]
    g
        If water behaved more typically as a low molecular weight material, its phase diagram may have
                          looked rather like this (where 'x' marks ambient conditions on earth): [Back]


h
    Crystal cell parameters have been collated [711]. [Back]
i
  Dielectric constants fall into two categories dependent on whether the hydrogen bonds are ordered
(low values) or disordered (high values). [Back]
j
 Weaknesses (Bjerrum defects) in the ice crystal are apparent where the ice rules are disobeyed. Both
O····O contacts, without an intervening proton (L defect) and O-H····H-O contacts (D defect) may
occur due to molecular rotations where neighboring water molecules fail to adjust their hydrogen
                                                                  +        -
bonding. Other defects may be caused by the presence of H3O and OH ions. [Back]

k
    Also known as ice XIII. [Back]
m
   The antifluorite structure consists of an face centered cubic (FCC) unit cell with oxygen anions
occupying the FCC lattice points (corners and faces) and hydrogen cations occupy the eight
tetrahedral sites within the FCC lattice. [Back]
n
    This ice has not yet been prepared. [Back]

								
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