Water's molecular vibrations
and absorptions
Water's lone pairs
Water electronic structure
Water dimer
Water models
Water reactivity
Water molecules i are tiny and V-shaped with molecular formula H2O a and molecular diameter about 2.75 Å.g 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 2-fold rotation
axis. The hydrogen atoms may possess parallel
or antiparallel nuclear
spin.h 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. [Back to Top 
]
Note. This cartoon of water does not represent its actual outline, which is more rotund (see below).
The water molecule is often described in school and undergraduate textbooks of as having four, approximately tetrahedrally arranged, sp3-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 density where lone pairs are expected. The negative charge is more evenly concentrated along the line between where these lone pairs would have been expected, and lies closer to the center of the O-atom than the centers of positive charge on the hydrogen atoms.
Early 5-point molecular models, with explicit negative charge where the lone pairs are purported to be, fared 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 sp3-hybridized lone pairs in the isolated water molecule should perhaps be avoided [117], as an sp2-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 atoms.
The approximate shape and charge distribution 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 almost isotropic, centered around the O-atom (1.4146 Å3) with only small polarizabilities centered on the H-atoms
(0.0836 Å3) [736]. Parameters using ab initio calculations with the 6-31G**
basis set are shown right.j For an isolated H216O,
H217O or H218O
molecule, the more exact calculated O-H length is 0.957854 Å
and the H-O-H angle is 104.500° (D216O,
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 molecule [778].d The experimental values for gaseous water molecule are O-H
length 0.95718 Å, H-O-H angle 104.474° [64].e
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 diffraction
studies (O-H length 1.01 Å, O-D length 0.98 Å [1485]; O-D length 0.970 Å, D-O-D angle 106°
[91])f suggest slightly
greater values, which are caused by the hydrogen bonding
weakening the covalent bonding and reducing the repulsion between the electron orbitals. 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°. [Back to Top ]
The electronic structure has been proposed as 1sO2.00 2sO1.82 2pxO1.50 2pzO1.12 2pyO2.00 1sH10.78 1sH20.78 [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 water, (1a1)2(2a1)2(1b2)2(3a1)2(1b1)2, 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.
Van der Waals radii [206]
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 pairs. [Back to Top ]
Much effort has been expended on the structure of small isolated water clusters. Typically, in the atmosphere there is about one water dimer for every thousand free water molecules. The most energetically favorable water dimer is shown right using ab initio calculations with the 6-31G** basis set.j It is also shown below with a section through the electron density distribution (high densities around the oxygen atoms have been omitted for clarity). This shows the tetrahedralityb 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 potential energy surface [1668] and wagging vibration [1743] of the water dimer have been described and 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 tetrahedrally
placed (= 109.47°/2), the energy minimum (~21 kJ
mol-1) is broad and extends towards β = 0°. [Back to Top ]
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 appear to have poor predictive
value outside the conditions and physical parameters for which
they were developed. [Back to Top ]
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. [Back to Top ]
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 more 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 The tetrahedral
angle is 180-cos-1(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 ortho-H2O rotates in its ground state with energy 23.79 cm-1 [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 isoelectronic ions (from crystal data) of O2- (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 (bond length 0.96 Å) is smaller than ammonia (bond length 1.01 Å) or methane (bond length 1.09 Å), with only H2 (bond length 0.74 Å) and HF (bond length 0.92 Å) 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 of these nuclear spin states in H2O is all para at zero Kelvin, where the molecules have no rotational spin in their ground state, shifting to the most stable ratio [1694] of 3:1 ortho:para at less cold temperatures (>50 K);c 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 difference in energy between the two states is a significant 1-2 kJ mol-1, far greater than expected from spin-spin interactions (< μJ mol-1) [835]. It has been suggested that structural rearrangements may be induced by ortho-H2O : para-H2O conversion [1430], as it is possible that hydrogen bonds between para-H2O, possessing no ground state spin, are stronger and last longer than hydrogen bonds between ortho-H2O [1150]. It is thus possible that ortho-H2O and para-H2O form separate hydrogen bonded clusters [1150]. [Back]
i Liquid water consists of a mixture of molecules [1377] and ions, including H2O, HDO, H3O+ and OH-. A 'standard' water (Vienna Standard Mean Ocean Water) has been proposed. 'Pure liquid water', meaning consisting of just H2O molecules, only exists in computer simulations. Even 'just H2O' consists of a mixture of 'ortho' and 'para' forms. Avoiding this complexity, 'water' is normally taken to mean H2O molecules, without consideration over its magnetic state. [Back]
j More exact parameters are given in the text. These parameters are given mainly for comparison with the hydrogen and hydroxide ions.. [Back]
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This page was last updated by Martin Chaplin on 5 September, 2011
