J. Chem. Sci., Vol. 121, No. 5, September 2009, pp. 839–848. © Indian Academy of Sciences.
839

Dedicated to the memory of the late Professor S K Rangarajan 

Structure and stability of spiro-cyclic water clusters 

Chemical Laboratory, Central Leather Research Institute, Council of Scientific and Industrial Research,
Adyar, Chennai 600 020 

Indian Institute of Science Education and Research (IISER), Mohali, Sector 26, Chandigarh 160 019 

Honorary Professor, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560 064 

e-mail: subuchem@hotmail.com; nsath@iitk.ac.in

Структура и стабильность спирально-циклических кластеров воды

Abstract. The structure and stability of spiro-cyclic water clusters containing up to 32 water molecules
have been investigated at different levels of theory. Although there exist minima lower in energy than
these spiro-cyclic clusters, calculations at the Hartree–Fock level, density functional theory using B3LYP
parametrization and second order Møller–Plesset perturbation theory using 6-31G and 6-311++G
basis sets show that they are stable in their own right. Vibrational frequency calculations and atoms-in-
molecules analysis of the electron density map confirm the robustness of these hydrogen bonded clusters.

Keywords. Hydrogen bonding; water clusters; spiro-cyclic; atoms-in-molecules. 

1. Introduction 

H-bonding in water clusters has been the subject of
several experimental and theoretical investigations
due to its importance in various real life systems.

High level ab initio calculations predict the structure
and stability of small water clusters with near quan-
titative accuracy.

These studies have been found to
be extremely useful in interpreting the high-resolu-
tion spectral data obtained from size and mass selec-
tive beam techniques.

These calculations
provide valuable information on H-bonding and also
take us beyond what is easily obtained experimen-
tally. The 12-mer, 16-mer and 20-mer of the water
molecule seem to prefer stacked cube and stacked
pentagonal geometries.

The much anticipated
buckyball structure is not the most stable geometry
for the water 20-mer!

It is well-known from the crystal structure data-
base that the water molecule plays different roles in
the stabilization of crystal structures and displays a
variety of structural topologies in crystal structures
and in confined environments.

The surge in activity in the area of supramolecular chemistry ex-
emplifies the importance of water mediated crystalli-
zation and H-bonding interaction. 

Most of the structural arrangements and shapes
exhibited by water clusters in various environments
are already known in organic chemistry. For exam-
ple, water hexamer exists in boat and chair forms
and these structural motifs are known for cyclohex-
ane. Similarly, water octamer assumes the shape of a
cubane. In all these organic moieties, every carbon
atom is invariably sp

hybridized and forms a maxi-
mum of four covalent bonds in a tetrahedral fashion.
The oxygen atom in water also exhibits ~sp

hybridization and can form a maximum of four hydrogen
bonds as illustrated in scheme 1. In classical organic
chemistry, spiro-cyclic molecules are also interest-
ing from structure and reactivity point of view.
Hence, it is interesting to probe the possibility of the
existence of analogous spiro-cyclic motifs in water
clusters. In the present study, the structure and sta-
bility of spiro-cyclic water clusters have been inves-
tigated and compared with the most stable water
clusters using ab initio and density functional theo-
retic methods. 

2. Computational details 

Geometries of all the water clusters under investiga-
tion have been optimized without any constraint at
different levels of theory using the G98W suite of
programs. 

Stabilization energies (SEs) of all the
clusters have been calculated using the supermo-
lecule approach and corrected for basis set superpo-
sition error (BSSE) following the procedure adopted
by Boys and Bernardi: 

where Ecluster is the energy of the cluster, n the total
number of molecules in the cluster and Ei the energy
of the ith monomer in its specific location computed
using the basis set for the n-mer. The relative popu-
lation of various conformers for each (H2O)n cluster
as a function of temperature is computed using the
Boltzmann distribution formula:

where kB is the Boltzmann constant, En is the rela-
tive energy of the conformer with respect to the
most stable geometry and T is the temperature. To
ensure that the optimized geometries obtained corre-
spond to true minima in the energy space, vibra-
tional frequencies were calculated at HF/6-31G and
HF/6-311++G levels. They were scaled by a fac-
tor of 0 8929 and 0 9070, respectively. The theory of
atoms-in-molecules (AIM) 

was used to character-
ize the hydrogen-bonding interaction using the topo-
logical properties of the electron density at the
hydrogen bond critical point (HBCP) using the
AIM2000 package. 

3. Results and discussion 

3.1 Geometries 

Various spiro-cyclic water clusters considered in
this study are represented schematically in scheme 1.
The size of the rings formed in each cluster is used
in the nomenclature. For example, the cluster 3–3
has two trimer rings arranged in a spiro-cyclic fash-
ion. The optimized geometries of different spiro-
cyclic water clusters are shown in figures 1 and 2.
Of all the water clusters considered, 3–3, 3–4, 3–5,
3–6 and 4–4 retain their spiro-cyclic structures at all
levels of calculation. However the clusters, 4-5, 4-6,
5-5, 5-6 and 6-6 rearrange from the initial spiro-
cyclic structure during optimization. The increase in
the cluster size in each ring decreases the donor–
acceptor interaction between the nearby water mole-
cules and as a consequence the spiro-cyclic structure
collapses. 

In all the spiro-cyclic water clusters, the central
water molecule, which is shared by both the rings, is
tetra-coordinated. In this mode of interaction, the
central water molecule accepts two protons and also
donates two protons, resulting in an overall stabili-
zation of the spiro-cyclic structure. A close scrutiny


Figure 1. Optimized geometries of different spiro-
cyclic water clusters obtained using HF/6-311++G cal-
culation. These clusters are found to be stable without
any reorganization during energy minimization at DFT
and MP2 levels of theory. 

Scheme 1. Schematic representation of spirocyclic models (organic and water
cluster) considered in this study.

of the structures reveals that the two rings are or-
thogonal to each other, similar to their organic
counter parts. A comparison of the geometries ob-
tained from ab initio calculations for 3–6, 4–6, 5–6
and 6–6 clusters shows that the hexamer ring adopts
a chair form in all the cases. The pentamer ring
found in 3–5, 4–5, 5–5 and 6–5 clusters deviates
slightly from the planar arrangement. The trimer and
tetramer rings are planar as observed in the most
stable water clusters. Some of these clusters are not
stable at higher level calculations. However, these
spiro-cyclic structures (for example 6–6 and 4–4)
are observed in certain crystals
suggesting that
the stabilization of these structural motifs must be
arising from additional interaction with the host
molecules and crystal packing. In contrast, the 3–3,
3–4, 3–5, 3–6 and 4–4 spiro clusters seem to be sta-
ble even in the absence of any host lattice and asso-
ciated packing effect.