This thesis describes the development of a scheme for applying wavefunction-based quantum chemistry techniques to crystalline solids: the hierarchical method. The hierarchical method was first proposed by Manby, Gillan and Alfe [1] for cubic crystals. The contribution of electron correlation to the cohesive energy of a crystal is found from calculations on finite clusters of atoms. These clusters are chosen to mimic the structure of the crystal and the edge-effects are subtracted using the hierarchical equation. The quantum chemistry techniques used offer advantages in accuracy over existing solid-state methodologies, such as density functional theory, as they are ab initio and systematically improvable. The hierarchical method was applied to three crystalline solids: lithium hydride, lithium fluoride and neon. For lithium hydride and lithium fluoride, results of high accuracy are reported and comparisons are made with experimental extrapolations as well as contemporary theoretical techniques. In the case of neon, a new hierarchical equation was derived, one that was general to any crystal structure. The assumptions made in the hierarchical method, regarding cluster sizes and the use of symmetry, were successfully tested against a many-body expansion [2]. The systematic improvability of the quantum chemistry techniques employed in the hierarchical method allowed chemical accuracy (±l kcal/mol or ±1.6 mEh) to be approached. For example, the cohesive energy of lithium hydride at the zero point Eok coh was calculated to be -175.3 mEh [3], within 0.4 mEh of the value extrapolated from experimental measurements -174.9 mEh [4]. As well as the cohesive energy Eok coh the hierarchical method can also be used to calculate the equilibrium lattice parameter ao, bulk modulus Bo and surface formation energy a at the zero point. The predicted values for lithium hydride are ao = 4.062 A, Bo = 33.2 GPa, Eok coh = -175.3 mEh [3] and a = 0.43 J m-2 [5]; and for lithium fluoride ao = 4.011 A, Bo = 70.9 GPa, Eok coh = -325.5 mEh and σ = 0.53 J m-2.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:557944 |
| Date | January 2011 |
| Creators | Nolan, Stephen James |
| Publisher | University of Bristol |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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