Water structure: Methods
Why different methods give different water structures?
Nuclear Magnetic Resonance (NMR)
Several independent methods have been used to investigate
the structure of liquid water and aqueous solutions. Although
each method is often promoted as producing accurate results,
the different methods produce conflicting conclusions. This
not only generates academic disputes but also, and more importantly,
causes general confusion and bewilderment leading to scientific
Why different methods give different water structures?
Each method produces data but this data does not directly
give the structure of water. It has to be interpreted. Any
analysis depends on a theoretical base to interpret the data.
More importantly, the results are only as good as this theoretical
base, however excellent the quality of the data collected.
In addition, different methods give information at particular
time-, or size-scales and so may naturally differ.a Here I show the principles behind the most important analytical
methods (Dielectric spectroscopy, Diffraction
methods, Models, Nuclear
magnetic resonance, Physical properties, Vibrational spectra, X-Ray
spectroscopy) and the main assumptions made to interpret
their resulting data.
The size and time scales for the different techniques are
Timescales for different methods
Time and size
|Pump-probe laser, X-ray absorption
||~10-15s, single molecule
|Infrared, Raman, models
||~10-12s, single molecule - local cluster
|Neutron scattering, NMR shift
||~10-9-10-6s, local cluster
|X-ray diffraction, thermodynamics
||> s, local cluster
Instantaneous structures show the actual positions and orientations of molecules, but these will be disordered relative to each other due to vibrational and linear and rotational diffusional motions; thus they will not show, or will show only poorly, any long term or extensive order in the system. Diffraction data shows long term order but cannot determine whether the order is due to the same molecules being present in the same positions throughout or whether there are simply 'favored' positions with the molecules exchanging rapidly between them. [Back to Top ]
Dielectric spectroscopy 
measures water tumbling and can detect water quantitatively
in different clusters if they are held by different average
hydrogen bond strengths. The dielectric loss is determined
over a wide frequency range (kHz-GHz). Slow tumbling (~
ns) is due to tightly bound water whereas fast tumbling
(~ ps) is due to loosely bound water. Opposite is shown
an example spectrum of a protein solution ,
where the non-bulk water dielectric loss spectrum (red)
can be divided into three underlying Gaussian peaks.c Difficulty remains in unambiguously assigning the molecular
structures that produce these peaks. Dielectric spectroscopy does seem to show that long range interactions (~0.1 mm) are present in water . [Back to Top ]
Diffraction methods measure the time-averaged distances between the atoms
of water molecules but cannot directly determine the cluster
geometry. X-ray diffraction is sensitive to the concentration
of electrons. Even though there are twice as many hydrogen atoms as oxygen atoms in water, these electron-poor
atoms contribute little with 85% of the data being provided by the gOO(r) radial
distribution function and the remainder from the gOH(r) radial
distribution function . Neutron diffraction is sensitive
to nuclei but needs mixtures of D2O, HDO and
H2O and so produces less precision and accuracy
as such mixtures structure water differently from pure H2O.
It gives gOO(r), gOD(r)
and gDD(r) radial distribution data, which does
allow some, if incomplete, orientation information to be
extracted for neighboring water molecules. Electron diffraction can only be used on thin films due to its strong scattering. Recent wide-angle X-ray diffraction has confirmed the existence of two distinctly different hydrogen-bonded environments in liquid water .
The use of diffraction methods for studying the hydration structure of alkali ions has been reviewed . Diffraction data
may be refined by fitting water model simulations . The resulting fit, however, is insensitive
to the model chosen  such that optimizing the model to the fit does not, perforce, produce a better model.
Diffraction results are discussed further elsewhere. Diffraction methods give data little different from bulk water beyond the first hydration shell where other methods indicate changed structure .
Diffraction methods are excellent for testing models of
water structure but less good for delivering the real structure
of water due to the difficulty in obtaining orientation
information and correlations at intermediate distances. [Back to Top ]
Many molecular models for water are described on another
page of this site. An underlying assumption for these
models is that the structure of liquid water may be modeled
using just two-body effects (that is, molecule A affects
molecule B independently of molecule C affecting molecule
B) and do not include any contribution from any covalency in their interaction. Models for liquid water have, so far,
proved to be poor predictors for physical and molecular
properties outside those used in their development and parameterization.
Modeling studies may result in a picture of an 'average'
liquid water molecule, which may be misleading as such 'average'
structures do not exist in most ice phases and may not be
relevant to liquid water. [Back to Top ]
Nuclear Magnetic Resonance (NMR)
Water contains three isotopes of use in NMR.d
Properties of hydrogen nuclei
NMR, H2O atoms
1, 0, -1
5/2, 3/2, 1/2, -1/2, -3/2, -5/2
Relative sensitivity at natural abundance
1.4 x 10-6
1.1 x 10-5
Gyromagnetic ratio, rad T-1 s-1 *
26.7522 x 107
4.1066 x 107
-3.6281 x 107
Frequency at 2.3488 T (MHz) *
The 1H and 2H NMR spectra can be used to quantify the deuterium atom content of H2O, HDO, D2O mixtures from the natural abundance to nearly 100%
. As it has been reported that magnetic
fields may alter the clustering of water ([192, 485, 647]),
then the results of NMR must be considered with this possibility
in mind. Another weakness to the use of NMR is that only ortho-water is NMR-active, para-water having no intrinsic magnetic moment
NMR analysis generally gives reduced information due to
proton exchange and movement of water between environments.
The average proton residence time on a water molecule is
about a millisecond at 25 °C and pH 7, being less than
that at other pHs or higher temperatures. Therefore, only
single, population weighted averaged, 1H, 2H
or 17O NMR peaks are generally seen in aqueous
solutions. The exception to this is where separate non-
(or very slowly) exchanging pools of water molecules are
Water's NMR chemical shifts (17O and 1H)
are affected by ions in solution with increasing ionic radius
generally causing an increased deshielding effect on the
water oxygen atoms but a decreased deshielding effect on
the water's protons .
The effects are linearly concentration dependent with a
change in slope above the concentration that causes a minimum
in the specific heat (~ 2-3 M) .
Here, the charge density effect (greater charge density
causing greater deshielding), as seen in the division of
ions into kosmotropes and chaotropes is less important than the ionic size effect .
As larger ionic size results in an increased number of first
shell water molecules interacting with the ion's field within
the clathrate surroundings, the apparent shielding change
may be due to an increased effect on the average shift.
Both 1H and 17O NMR peaks shift to
downfield (greater ppm) with increasing hydrogen bond strength;
in the case of 17O, the donor O shift increasing
greater than the acceptor O reduces. However, only ‘averaged’
water environments may be obtained. Where several aqueous
environments exist, the 1H NMR spectrum (mainly
just one broad peak) may be deconvoluted into Gaussian sub-bands
due to differing degrees of hydrogen-bonded water with greater
chemical shift (that is, ppm) indicating stronger hydrogen
bonding and greater tetrahedrality of the water clustering
NMR has been used to estimate changes in water's hydrogen
bond lengths and strengths .
Such investigation makes use ab initio calculations
to interpret changes in the longitudinal relaxation T1 (see below) of HDO in D2O solution by assuming
(somewhat incorrectly) that this mixture has a similar structure
to pure H2O.
The NMR signal undergoes two relaxation processes; spin-lattice
(longitudinal) relaxation resulting in the decay of the
spin distribution (T1) and spin-spin (transverse)
relaxation (T2) resulting in the loss of the
spin coherence. T2 is inversely proportional
to the width (at half height) of the NMR peak. T1 is 3.6 s at 25 °C due mostly to dipole-dipole couplings
T1 reduces with increasing dissolved molecular
oxygen concentration (due to its paramagnetic nature) 
and dissolved oxygen concentrations are expected to be greater
in more hydrophobic environments near hydrophobic surfaces,
dissolved oxygen is capable of giving rise to artifacts
in the NMR spectra of water. Such affects may change over
a period of several days .
Shorter T2 values indicate less molecular mobility;
the 1H T2 of water at 25 °C, viscous
water and ice at 0 °C are about 3 s, ~1 ms and ~5 μs
respectively. However, the T2 relaxation times
are also reduced by exchange reactions, with for example, proteins carboxyl, hydroxyl and amine groups. Generally
only single, population weighted averaged, 1H, 2H or 17O relaxation rates are seen
in aqueous solutions. The exception to this is where separate
non- (or very slowly) exchanging pools of water molecules
exist such as occur in porous media including biological
tissue and many foodstuffs. T1 and T2 are approximately equal for liquid water, both dropping
with increased hydrogen-bonded clustering (for example, increased viscosity) under normal conditions. However, as
the degree of tetrahedral clustering increases further,
T1 increases as T2 decreases .
T1 thus shows a minimum at intermediate viscosity, at the NMR resonant frequency,
whereas T2 decreases continuously with increasing
viscosity. Note that NMR relaxation is a non-equilibrium
kinetic event and cannot give thermodynamic quantities such
as water activity.
17O has been used to estimate water
means of NMR line-width measurement where
strongly clustered water gives broader peaks.
However this reasoning is faulty and the data is often
imprecise and probably affected by dissolved O2 and pH; see also Paul
Shin's critique of this method.
Shown opposite are the 17O NMR peaks for
water at widely different temperatures, showing how
little the width changes even under so different conditions
Nuclear Overhauser effects (NOEs) may be used to identify
relatively static water molecules within the first hydration
shell (<~0.5 nm) around biological molecules .
Apparent diffusion rates of water are measured using magnetic
field gradients and may be incorporated into magnetic resonance
images (MRI). As diffusion is restricted in more extensive
aqueous clusters, this method can differentiate different
pools of water by their mean diffusion rates. [Back to Top ]
Physical properties such as viscosity, compressibility, speed
of sound, heat capacity, refractive index, thermal
conductivity and surface tension can all be used to gather information concerning the structure
of water. The interpretation of this data is not clear-cut,
however. Note that only the surface properties, not the
bulk properties, are discovered using surface tension. The
surface structure of water is very different from the bulk
structure and may mislead. [Back to Top ]
Water gives complex infrared and
Raman spectra . Analysis of these, together with changes
caused by variations in temperature and/or pressure, or
the presence of solutes, is thought capable of providing
detailed information concerning liquid water structuring. Liquid water spectra reportedly corresponds to linear mixtures of just two contributing forms .b Due to peak broadening caused by the
varying interactions between neighboring molecules,
the spectra may be analyzed by supposing a number
of Gaussian-shapedc vibrational absorptions underlying the complex peaks.
Difficulties in the analysis concern determining how
many absorption peaks are present and what are the molecular
origins for these vibrations. Clearly the more vibrations
that are thought to contribute to a complex absorption
peak, the better may be any produced fit.
The peak at about 3400 cm-1, mainly due
to symmetric and asymmetric stretching, has received
considerable attention. It appears to consist of a
small number of overlapping peaks but may be far more
complex. The assignment of symmetric, asymmetric stretch
and bending overtone is usually discarded in favor
of the assumption of combined stretch absorptions
shifted due to local hydrogen bonding arrangements.
However and importantly, there is no consensus as
to the number of underlying absorptions with different
researchers using three, four or five absorptions,
as are shown indicatively opposite.
in the analysis is due to the lack of a consensus
view as to what these underlying absorptions represent.
It is unclear whether the number of hydrogen bonds
are important ,
or is it the type of hydrogen bond (single, bifurcated
or trifurcated) ,
or is it the hydrogen bond bending angles ,
or perhaps the nature of the formed or broken donor
and acceptor hydrogen bonds [699b], or the length of the hydrogen bonds .
Each of these has been clearly argued (for example, see below) but the contributing vibrational peaks
must contain all of these (and other) contributions. It is now believed that analysis involving individual water molecules and gaussian peaks may be inherently flawed as the absorption bands also reflect coherent vibrational transfer involving several to many water molecules .
Further confusion of the Raman spectroscopy is that the peaks in the 3000-3700 cm-1 range are affected by the Raman excitation wavelength . In particular, the component at ~3200 cm-1 is in resonance with visible red light from a vibrational overtone.
Assignments from different authors
hydrogen bond molecular linkages
||2 H-bond, donors broken
||3636 cm-1, unlinked
||2 H-bond, acceptors broken
||3572 cm-1, 3 H-bond, acceptor broken
||1 O-H H-bonded, 1 bifurcated
||3 H-bond, donor broken
||3430 cm-1,2 H-bond, acceptor and donor broken
||Both O-H are weakly H-bonded
||3 H-bond, acceptor broken
||3220 cm-1, 4 H-bond
||Both O-H are strongly H-bonded
||3014 cm-1, 3 H-bond, donor broken
From high to low wavenumber;
0 = greatest wavenumber.
The O-H hydrogen bond is shared between two accepting
O-H hydrogen bond is shared between three accepting
A thorough and careful analysis of the combination band
centered at about 5260 cm-1 failed to distinguish
the substructures that correlate with the vibrational sub-bands
The use of a pump-probe laser using 70-fs pulses at 3350
cm-1 (O-H stretch) and detecting the resultant
molecular vibrations within the hydrogen-bonded clusters
over a range of frequencies with time shows efficient energy
However, this method is not yet able to show structuring
Two-dimensional Raman spectroscopy has been shown to provide information concerning water's intermolecular dynamics and may eventually provide data on the hydrogen bond network rearrangements responsible for water's anomalies .
Terahertz spectroscopy (1 - 6 THz = 33 - 200 cm-1) may be used to investigate water dynamics on the picosecond timescale, such that hydration layers around biomolecules may be determined [1196, 1427]. It is a powerful technique for examining changes in water mobility and shows changes in the water structuring at greater distances from biomolecules than those found using NMR or neutron scattering . The terahertz region is expected to be a very important region for cluster and biomolecule vibrations  and provides information about the water further from the surface than NMR or diffraction methods . The hydration state of solutions may be examined using terahertz time-domain attenuated total reflection spectroscopy, which makes use of the complete complex dielectric function; both the dielectric loss, due to relaxation motion of water, and the changes in the real part of the dielectric constant . [Back to Top ]
X-ray-based techniques can be used to study the hydrogen-bond network of liquid water . As the techniques have an attosecond timescale, they reflect the instantaneous molecular configuration of the water molecules.
X-Ray absorption spectroscopy (XAS) involves the absorption
of high-energy photons to excite core (1s, 2s) electrons
to unoccupied p-character valence levels. The energies required
are sensitive to the local environment mostly providing information
concerning the hydrogen bond donating orbitals of the absorbing molecule at very
short timescales (~ 10-18s) [373, 690a, 1757]. At high photon energy, expelled electrons have sufficient
energy to escape from their atom (to the continuum)
and at higher energies these escaped electrons may produce
signals due to backscattering. Care must be taken to avoid artifacts at the water-air surface due to desorption . X-ray Raman scattering (XRS) gives similar results to XAS and involves the inelastic scattering of x-rays from the core electrons.
Above left is shown the O K-edge (1s) XAS of liquid water
(red) with possible underlying
Gaussian (blue) and continuum
first peak at about 535 eV is due to excitation from the
1s orbital to the vacant O-H 4a1 antibonding orbital. Assignment of these gaussian peaks
to electron transitions depends heavily on the underlying
theory (for example, see the current
dispute) as there is little structure in the experimental
spectrum, this spectrum varies from run to run [690c],
between methods and between different energies of the X-rays.
Thus, data fitting is error-prone. An interesting discussion
of these differences has been recently published .
Related to XAS is the X-ray emission spectra (XES, ) involving
transitions from the three outermost occupied molecular
orbitals 1b1, 3a1 and 1b2 to fill the vacancy (produced as above) in the 1a1 (1s) orbital ;
peaks occurring in the 520-528 eV range and corresponding to instantaneous local structuring (~ 10-15s). Recent X-ray emission spectroscopy shows the presence in liquid water of two well-separated peaks (split from the lone-pair non-bonding 1b1 peak) that interconvert but do not broaden with changes in temperature . This strongly supports a two-state
network model such as presented here. [Back to Top ]
Another recently improved X-ray technique is small-angle X-ray scattering (SAXS, ) which is sensitive to density inhomogeneities in the nm-range has confirmed the existence of two distinctly different hydrogen-bonded environments in liquid water .
aConsider, for example, the very
different photographs obtained at night of cars on the road
between the use of fast flash and a natural light long exposure.
b There is evidence, however, that
the spectra may be due to a continuous variation in the hydrogen
bonding and not due to discrete but overlapping populations
c A Gaussian curve (normal
distribution curve) may be represented by the relationship:
where A is the amplitude, Amax is the peak height, λ is the wave
number , λmax is the
wavenumber at the peak and W is the width of the
peak at half height. [Back, 2]
d 16O and 18O have no nuclear spin. [Back]