Quantum behaviour of hydrogen and muonium in solid-state and biological systems
For hydrogen-like nuclei (HLN) such as the proton or muon, the quantum zero point energy cannot be ignored. The main objectives of this thesis were to identify practical ways to model this quantatively, and hence i) to gain an understanding of interactions between the HLN and its environment, and ii) to use this understanding to evaluate the wavefunction of such a nucleus within an electronic structure calculation. Several features of the HLN-electron interactions were studied analytically by assuming their interaction to be harmonic in nature. It was shown that the accurate modelling of the HLN-electron correlation was extremely important in the evaluation of the HLN wavefunction. A parametrised correlation model (PCM) was developed, and was shown to accurately reproduce the effective potential energy surface experienced by the HLN when HLN-electron correlation was included. The required parameters showed a simple HLN mass dependence. The PCM was used to study DNA base molecule adducts formed by addition of a single HLN. The relative stability of these adducts was shown to be dependent on the mass of the HLN, and the inclusion of HLN-electron correlation was shown to lead to a stabilisation of the C-X bonds relative to the N-X and O-X bonds. The PCM was used to study the interaction of H and Mu with the diamond dopants sulphur and phosphorus. The PCM correctly predicted differences between the HLN wavefunctions in crystalline and molecular environments. The HLN-electron correlation energy was shown to be large enough to cause the phosphorus-muonium defect complex formation energy to become positive. HLN-impurity-vacancy complexes in diamond were studied using the PCM, and it was found that the lowest energy state was obtained by the HLN saturating a carbon dangling bond, irrespective of the impurity species. It was concluded that the HLN would be effectively localised at a single site.