Water Clusters: Introduction
G. Rossetti 1830-1894
has seen the wind?
Neither you nor I;
But when the trees bow down their heads
The wind is passing by.
Water (H2O) is the
third most common molecule in the Universe (after H2 and CO), the most abundant substance on earth and the
only naturally occurring inorganic liquid, a billion cubic
kilometers of which reside in our oceans and 50 tons of which
pass through our bodies in our lifetimes. It has been very
well studied with a number of model
structures having been proposed and refined. a Notwithstanding this, extensively hydrogen-bonded liquid water is unique with a number of anomalous
properties. It has commonly been stated that no single
model is able to explain all of its properties [1, 53a, 54].
In particular, successful models for water must encompass
the radial distribution function,
the pressure-viscosity and temperature-density behavior
and the effects of solutes. Much
work has been invested in developing models for individual water molecules for use in molecular dynamics simulations [2, 3]. These models are very
useful, particularly for investigating short-range order,
but have difficulty addressing the totality of the unusual
nature of water including the long-range ordering that has
been described around macromolecules [4, 5, 6].
In particular, they only show approximate agreement with the
radial distribution functions and most have difficulty explaining
the position and size of the peak
at about 3.7 Å [3, 7].
A number of interstitial models have been described based on dodecahedra [8,
8b], the ice Ih structure [9, 10]
or from computer simulation .
These involve the presence of water molecules within cavities
in the hydrogen-bonded network. A percolation model, where
the degree of hydrogen-bonding decreases as temperature increases,
has also been developed .
Although good at explaining some, but not all, of the properties
of water, its nature is still unclear.
More recently, explanations
of the properties of water have been in terms of non-bonded
interactions in a fully bonded network ,
significant bending in the hydrogen bonds , competition between bonded and
non-bonded interactions [14, 311] or equilibrium
between structural components containing hexagonal, pentagonal
and dodecahedral water arrays .
The unusual properties of water at mixed hydrophilic/hydrophobic
surfaces has been explained in terms of the presence of both
high-density water and strongly associated (low-density) water
outlining the relationship between liquid, supercooled and low-density amorphous ice (LDA)  and the relationship
between the bulk structure of water and calculated and experimental
data on small water clusters 
have appeared recently. The present review has its roots in
a recent paper  that
includes elements of several of these approaches. A brief
history of the development of the water clustering concept b is given on another page.
Whilst the molecular movements within liquid
water require the constant breaking and reorganization
of individual hydrogen bonds on a picosecond timescale, it
is thought by some that the instantaneous degree of hydrogen-bonding is very high (>95%, [13, 168]
at about 0 °C to about 85% at 100 °C )
and gives rise to extensive networks, aided by bonding cooperativity.
It has been suggested that there will be a temperature-dependent
competition between the ordering effects of hydrogen-bonding
and the disordering kinetic effects .
There are many
pieces of evidence indicating that the time-averaged hydrogen-bonded
network possesses a large extent of order. These include the fine structure in the diffraction
data , microwave dielectric relaxation
measurements on glucose solutions ,
vibrational spectra that have indicated the presence of large
clusters , collective dipole orientation fluctuations with time scales 50,000 times slower that expected , and the
formation and properties of low-density water in gels .
There is some evidence that water is self-organizing  and can exist as macro-scale (10-120 µm) clusters .
A random network model has been described for LDA , liquid 
and supercooled water .
However, although this model is simple, requiring no 'fitting'
parameters, and has proven to be useful ,
it fails to describe some of water's properties unless made
inhomogeneous; for example the entropy of LDA is much lower than can be explained by this model .
A variation of this model concentrates on pentagonal rings
and cavities .
Several workers suggest that the structure of liquid water
should be related to crystalline ice structures [6, 22], although this structuring
must be significantly different due to the ease with which
water supercools and its high heat of fusion. It has similarly
been proposed to be a mixture of almost equal quantities of
and high-density amorphous ice (HDA)
 or related, if
less well defined, clusters .
Recently, a two-state network model including ice Ih (hexagonal ice)
and ice-two (ice II) substructures,
locally rearranging on a picosecond timescale, has been used
to explain many of the properties of water [23, 56, 57, 268]. Although attractive,
the inclusion of explicit ice-two clusters in this model leads
to some difficulties, such as the pressure requirement for
the extensive ice-two cluster formation necessary to achieve
the density of water, the ordered nature of the hydrogen bonding
in ice-two and consequent extremely low relative permittivity (dielectric constant)
(3.7 ) which is not
apparent in liquid water, and the number of unit cells (at
12 molecules per unit cell) required per cluster for the experimental
non-bonded close contacts; indeed recently less emphasis has
been placed on the explicit inclusion of ice-two in this model
by its proposers [60, 409]. In many
respects the outer-structure two-state mixture model 
is, however, not inconsistent with the model described here
with mutual agreement concerning both the 'key features' 
of O···O next
near-neighbor distances and O···O···O
hydrogen bond angle distribution. A related two-state model
including ice Ih and ice-three (ice III) substructures has been used to explain hydration
Other workers have used less explicit two-state models possessing
high and low-density components to explain the properties
of supercooled water [24, 790], the pressure-dependent
growth of the peak at about 3.7 Å in the radial distribution function 
and many other anomalies .
Water dodecahedra have been found in aqueous solutions [26, 27], crystals , and in the gas
phase . Dodecahedral
water clusters have also been reported at hydrophobic and protein surfaces ,
where low-density water with stronger hydrogen bonds and lower entropy
has been found . Similar
dodecahedral cavities have been found in LDA  and form relatively easily
in water during molecular simulations .
In these pages a dynamic structural model for water
is proposed that both builds on, and is consistent with, many
of these different approaches. The basis of this model is a network
that can convert between lower and higher density forms without
breaking hydrogen bonds. It contains a mixture of hexamer and pentamer
substructures and contains cavities capable of enclosing small solutes.
The model was developed by arranging alternating
sheets of boat-form and chair-form water hexamers from the lattices
of hexagonal and cubic
ice respectively. This structure was folded to form an icosahedral
three-dimensional network with capacious pores capable of partial
collapse due to competition between bonded and non-bonded interactions.
In order to develop the (icosahedral water
clusters) model described, molecular model building and dynamics
were performed using the HyperChem (Hypercube
Inc., Ontario, Canada) molecular modeling package. To obtain
the co-ordinates, the network was optimized using the AMBER force field with special parameters (O···O
stretch 28 kJ mol-1 Å-1, O···O
distance 2.84 Å; O···O···O
bend (kθ) varying about 4
kJ mol-1 rad-2, from 109.47°; van der
Waals σ = 3.536 Å, ε = 0.636 kJ mol-1). These parameters were chosen as reasonable
to create the model but were not critical. All data reported is
derived from structures with average O···O
and O-H nearest neighbor distances of 2.82 Å and 0.96 Å
respectively. Hydrogen atoms were not treated explicitly, being
placed such that each oxygen has two near and two far hydrogen neighbors
after model building was completed.
a Small clusters of liquid, but
structured, water molecules within molecular 'test tubes"
(carbon nanotubes) have been visualized using a transmission
electron microscope .
The pictures however still need much interpretation. [Back]
b Some authors prefer the terms 'dynamic heterogeneities' or 'density fluctuations' to 'clusters', but this site does not. The same type of structuring is meant in most of these cases. [Back]