Number Water Clusters
A oxonium (H3O+) or ammonium (NH4+) ion may sit
in the tetrahedral cavity of a collapsed water dodecahedron
so forming the magic number cluster H3O+(H2O)20 m/z 379 (as opposite with the oxonium oxygen colored magenta,a or NH4+(H2O)20 m/z 378) as found by electrospray mass spectrometry
studies confirm the dodecahedral clustering by showing
that all the dangling OH groups arise from similarly
situated water molecules [113c].
It should be noted that the extra proton does not need
to be associated with the central water molecule in
the above structure. It could hop to any of the other
20 water molecules, and this would be expected in an
isolated cluster where the poor H-bond donation to H3O+ is avoided. Such a surface protonated structure has
been recently confirmed, and found to be retained at
higher temperatures when two-coordinated water occurs
. Such magic number ions are followed by a reduced mass peak at the next H2O addition, an antimagic number . due to a weak appendaging of an extra H2O to the magic number ion.
H3O+(H2O)20 cluster ions have calculated dipole moments of about 10 D (cf. H2O dipole 1.86 D) and may contribute to the intense terahertz emission of water vapor under optical excitation
Interactive Jmol structures are given.
This symmetric structure was not as found in
an ab initio search ,
but might be expected to be more stable than the one found
there as the bond distortion is less and it has one fewer
non-hydrogen bonding hydrogen atom.b The symmetric clathrate structure, containing a single water
molecule, is found as the (H2O)21 global
minimum energy structure using the TIP5P model . In
contrast the (H2O)21 global minimum
found using the TIP4P model  is
very different and mostly consists of 4-membered rings. Although such low-energy structures (e.g. the structure formed by four fused cubes) are sometimes found as global minima, they have weaker hydrogen bonds and far fewer positions are available for further hydrogen bonding (e.g. the fused cube structure only has 8 such positions compared with 30 on the dodecahedral cluster). Such clusters are therefore thought (by this author) unlikely to be found in real situations. The collapsed clathrate structure (similar to H3O+(H2O)20 above) for (H2O)21 (with ring structure (20,1)8) is preferred over the convex cluster (with ring structure (20,1)10) in contrast to the preferred convex clathrate structure of H2S.(H2O)20, rationalizing the formation of solid H2S but not H2O clathrates .
The clathrate structure
has also been found as a global minimum for H3
using a polarizable model potential [72
where the oxonium ion preferred to sit away from the
center; see opposite (the oxonium ion is towards the
bottom left and colored magenta with the slightly hydrophobic lone pair
pointing outwards). Similar results have been obtained
using an ab initio
approach where surface Zundel
also found [854
Although there is a preference for the
oxonium ion to occupy a cluster surface position in
an isolated cluster this is not likely to be the case
in bulk water; a factor that, if not ignored in such
gas-phase and theoretical studies concerning ionic clusters,
is often understated when results are extrapolated,
directly or by inference, to the bulk water scenario.
The low energy hydroxide cluster ion cluster OH-(H2O)20 behaves differently with the OH- ion centrally placed, accepting four hydrogen bonds and donating one hydrogen bond .
the NH4+ ion sits centrally in the water
dodecahedron with all the hydrogen bonds from the central
ammonium ion equivalent, so helping to explain the apparent
increased structural stability of this ion relative to H3O+(H2O)20.
In agreement with this, an ab initio molecular dynamics
simulation found NH4+ to form four relatively
long-lived hydrogen bondsc to tetrahedrally arranged water molecules 
and such a structure is found to be much more stable than
a cluster with a NH3 in the center and a H3O+ on the surface .
Exchange of hydrogen bond partners by the central NH4+ may explain its faster than expected rotation .
Other hydrogen bonding molecules can substitute
for water in these clusters (for example, methanol, with
its methyl group pointing away from the cluster, H+(H2O)21-n.(CH3OH)n,
n =1, 2, 3...) or add to the outside of the cluster (e.g. acetonitrile, H+(H2O)21.(CH3CN)n,
n =1, 2, 3... ) .
The energy of H2O(H2O)20 clusters with H2O inside a (H2O)20 dodecahedral clathrate cage have been determined . It was found that the puckered cluster (similar to the top structure of the H3O+(H2O)20 magic ion) was 38 kJ mol-1 more stable compared with the convex clathrate containing the H2O molecule . As the puckered structure is more able to undergo rapidly rearrangement, this offers explanation for the reason why no crystalline aqueous clathrate structures contain water molecules in their cavities.
a There are many possible hydrogen-bonding
arrangements. The one shown has been chosen for comparison to the
modeled minimum-energy structure .
the top structure above, a hydrogen bond is shown donating to the
oxonium ion (H3O+). This is expected to be ordinarily very weak (or nonexistent)
but strengthened in the structure shown due to the possibility of
the nuclear delocalization from proton hopping. [Back]
that a single H2O hydrogen-bonded NH4+ forms one of the strongest hydrogen bonds known at 92.5 kJ mol-1 . [Back]