Theoretical studies of the endohedral fullerene H2O@C60

The endohedral fullerene H2O@C60 is a supramolecule composed of a single water molecule trapped inside a C60 molecule. The large inner cavity of the C60 molecule, together with the absence of bond formation between C60 and H2O, provides a highly symmetrical, nanoscale laboratory for H2O, allowing it to exhibit its single-molecule behaviours in complete isolation from strong interactions. Although strong interactions are absent, weak interactions between H2O and the C60 cage are expected to have some influence on the guest and host molecules. There has been much interest in the dynamics of the confined H2O molecule, which is an asymmetric top rotator, since inelastic neutron scattering measurements depicted a splitting in the lowest rotational state of its ortho spin isomer. Explaining the nature of this splitting will provide a greater understanding of the interesting H2O@C60 system. In this work, a variety of theoretical techniques are used to investigate various properties of the endohedral fullerene H2O@C60. The density functional theory is used to probe the structural properties of H2O@C60 at a number of points on its potential energy surface, using a different theoretical level than currently exists in the literature. Encapsulation of H2O is shown to cause a small perturbation of the molecular orbitals of the C60 cage. Those features of the perturbed frontier orbitals of the C60 cage that can be captured by scanning tunnelling microscopy are predicted analytically using the Hückel molecular orbital theory, the Tersoff-Hamann approach and the technique of projection operators. This thesis reports the first density functional theory simulations of the structural properties of the endohedral fullerenes (H2O)n=2,3,4@C60. The obtained geometries differ from those calculated using the Hartree-Fock method. Encapsulation of these water clusters is found to increase the perturbation of the molecular orbitals of the C60 cage. This thesis represents the first study of the effect of a Jahn-Teller distortion of the C60 cage on the dynamics of the confined H2O molecule. Appropriate extended symmetry groups are developed for the translation-rotation Hamiltonian of H2O when the fullerene cage undergoes a static Jahn-Teller distortion. Matrix representations of these groups are derived from the matrix representation of the icosahedral symmetry group of undistorted C60. An analytical potential function for the symmetry lowering intra-cage interactions is constructed from the quantised translation-rotation symmetry adapted states of the confined H2O molecule. For a C60 cage distorted by Jahn-Teller interactions, the second-order perturbation on the translation-rotation states of H2O can be approximated to that resulting from a spheroidal distortion of the C60 cage along a C5, C3, C2 rotational axis or any radial axis in a plane containing, or perpendicular to, a C-C double bond. The developed function can also be used to model inter-cage interactions with S6 symmetry. It can explain the splitting in the 101 ortho ground state seen in the INS spectra of solid H2O@C60, and gives a prediction of higher translation-rotation states that have not yet been determined experimentally