Water in liberal space expresses bond formation exclusively directed by orbital interaction of oxygen and independent dual hydrogen atoms. But, within the proximity of Vander Waals fields encapsulating the liberty of water molecules as in the case of Fullerene, its behavior tends to change forming Dimers, Trimers or Polymers. This is a matter of great interest. There were few successful attempts in the recent past, in which C70 Buckminster Fullerenes was injected with dual water molecules and observed its features. Those Water molecules expressed exceptional properties in bond alignment and formations into a dimer inside a distance of 3.7 Å × 4.6 Å, a prolate C70 Fullerene. The endohedral C70 structure offered an opportunity to review the properties of embedded monomeric and dimeric water molecules with hydrogen bonding. X-ray diffraction provided insight into this formation. The property of the individual atoms and molecules tends to change when confined to a cage of atomic dimension. Some of the recent endohedral fullerene works show lots of promising in science and technology      .
Fullerene C60 is truncated icosahedrons which resembles like football with 20 hexagons and 12 pentagons having the diameter of Van der Waals and nucleus to nucleus is 1.1 nm and 0.71 nm respectively. The discovery of fullerenes opened up by ways of constructing large atomic cluster of various shapes and sizes and research has been going on for the last three decades in discovering similar cage structure and modifying the known cage structures to yield materials with different characteristics. Fullerenes that have additional atoms, ions, or charges enclosed within their inner spheres are called as endohedral fullerene. The arrangement of water molecules in a cluster is known to depend on the environment.
Having studied fullerenes and water clusters one wonders about the shape of water cluster inside the confines of a fullerene cage. The fullerene cage is so stable and the space within is so limited, water cluster inside the fullerene cage forming unusual geometries. In this paper, the situation of embedding triple water molecule in fullerene C60 is presented. This pursuit was to increase the total charge available in the modulated fullerene with water and to achieve dipole movement of much higher than 0.5 Debye  realized through one water molecule encapsulation.
2. Methods of Calculation
Computations of ab-initio calculations at the levels of STO-3G, 3-21G and 6-31G of Restricted Hartree-Fock (RHF) method by using the quantum computations package, Firefly   and Avogadro  , have been carried out at RajaRajeswari Collage of Engineering (RRCE), Bangalore-560074, India.
The structure of endohedral fullerene in which three water molecules encapsulated in Carbon 60 is shown in Figure 1. The structure of different views and orientations of three encapsulated water molecules inside the fullerene is shown in Figure 2. The view of the three encapsulated water molecules and the end to end distance between two six memberring is as shown in Figure 3(a) and Figure 3(b). All the ab-initio calculations were optimized at STO-3G, 3-21G and 6-31G levels by RHF method. Total energy inatomic units for the water trimer, bucky ball (C60) and endohedral fullerene encapsulating three water molecules are given in Table 1. It is noteworthy to identify that the trimer molecule of water orients inside C60 differently compared to free water trimer  molecules. The
Figure 1. Structure of endohedral fullerene with 3 encapsulated water molecules.
Figure 2. Orientations of water molecules in the endohedral fullerene. Bond length in Å and Bond angles in degrees.
Figure 3. (a) Encapsulated water molecules and (b) End to end distance between two six member carbon ring.
Table 1. Total energy of the molecules in atomic units.
hydrogen bond length between the oxygen atoms of the water molecules in the trimer of the endohedral fullerene is found to be 2.21 Å at STO-3G and 2.28 Å at 3-21G and 6-31G optimized structures, which is the indication of strong hydrogen bonds in encapsulation against the free water trimer molecules forming cyclic hydrogen bonds of 2.8 Å as reported  . Water trimer in the encapsulated fullerene shows a strange behavior of forming ortho meta stable state which was discussed for one water molecule in C60  . This result is in line with our earlier works on hydrogen bonded dimers involving linear and circular hydrogen bonds     . This study shows the importance of high end computations as we reported  .
Dipole moment values indicate the role of charges in conductivity. This pursuit was to increase the total charge available in the modulated fullerene with water and to achieve dipole movement of much higher than 0.5 Debye  realized through one water molecule encapsulation in C60. Water trimer is actively involved in flipping and circular activities inside the endohedral buckyball. It provides an opportunity to investigate further results in the domain of conductivity and molecular encapsulations. Our ab-initio calculations on the three water molecule embedded in C60 shows the dipole moment of 0.8Debye at STO-3G, 0.9 Debye at 3-21G and 1.0 Debye at 6-31G levels. This is the indication of structural distortion and the starting point of conductivity. Because of ortho meta stable state water trimer inside the endohedral fullerene magnetism may arise.
One hydrogen atom of all the three water molecules (H-O-H) encapsulated in the endohedral fullerene is anchored with respect to H-O- in a triangle among themselves in an angle H-H-H is 57.17˚, 60.94˚ and 61.89˚ respectively. On the other hand, the other hydrogen atom is deflected in all the three water molecules with respect to -O-H and the angle between the deflected hydrogen is 60.26, 59.84 and 59.90 respectively. The bond length of the deflected hydrogen atom of one water molecule and the oxygen of the second water molecule, deflected hydrogen of second water molecule and the oxygen of the third water molecule and deflected hydrogen of third water molecule and the oxygen of the first water molecule have been observed respectively as 1.499 Å, 1.477 Å and 1.510 Å respectively. The ab-initio calculations of Fullerene C60, Water trimer and Water trimer encapsulated fullerene in three different levels of basis sets, STO-3G, 3-21G and 6-31G, using RHF have been taken place and their optimized and the total energy for stabilizing the molecules is presented as shown in the Table 1. Water molecules in the endohedral fullerene adopt an angle is 102.8˚, 102.8˚ and 103.1˚ and their bond length as defined in Figure 4 and Table 2. The angles of each of the water molecules and their bond lengths are having little deviation
Figure 4. Geometry of the trimer water molecule adopted in the endohedral fullerene.
Table 2. Bond angle and bond length.
from their corresponding experimental values for gas phase, O-H length is 0.95718 Å and the H-O-H angle is 104.474˚  and liquid water, O-H length 0.991 Å, H-O-H angle 105.5˚  and 106.0˚  . The final diameter of the fullerene is about 7.12 Å. However, the end to end length of the six member ring is closed to 6.52 Å. The hydrogens and oxygens of all the three water molecules are stabilized by maximally interacting with five member and six member rings of the fullerene molecule. Graphical representations of the molecule are referred by Visual Molecular Dynamics software Package  .
The water molecules in the confined space of Carbon inside fullerene provide the opportunity for conductivity due to the presence of dipole moment. The unusual arrangement of circular hydrogen bonded water trimer molecules with flipping action shows ortho meta stable state is interesting and to be investigated further for applications in the field of conductivity and magnetism.
The authors are acknowledging the support rendered by Central Forensic Science Laboratory, Sector-36A, Chandigarh, India, RRCE management, Bangalore-74, India and KGRCET Management, Telangana, India.