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The use of spin-pure and non-orthogonal Hilbert spaces in Full Configuration Interaction Quantum Monte-Carlo 10.17863/CAM.16295 Smart, Simon Daniel Full Configuration Interaction Quantum Monte–Carlo (FCIQMC) al- lows for exact results to be obtained for the ground state of a system within a finite-basis approximation of the Schrödinger equation. Work- ing within imposed symmetry constraints permits dramatic reductions in the size and internal connectivity of the Hilbert space considered, with associated reductions in the computational cost involved, as well as permitting exclusion of the natural ground state to extract a se- ries of excited states of the system. As all converged solutions are ˆ eigenfunctions of the square of the total spin operator, S 2 , as well as the Hamiltonian and the projected spin, imposing spin-purity as an additional ‘symmetry’ is a natural extension. In this thesis, the use of various spin-pure spaces is compared to the previously used determinental spaces. Variations on the FCIQMC al- gorithm which work in non-orthogonal (and non-normalised) basis sets, and with the arbitrary discretisation of imaginary time removed, are considered along with the implications of the differences to the normal FCIQMC algorithm. University of Cambridge 2014-02-04 Thesis Doctoral Doctor of Philosophy (PhD) eng https://www.repository.cam.ac.uk/handle/1810/245219 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/7ec916a1-c028-4507-b21b-9a7893d961dc/download 8e46a9bbeb5201e00da2140c96f58479 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/7b0d4680-9395-420b-a48a-8d0f211646c2/download 835269bda140c10400fe0606a14c3d21 https://www.rioxx.net/licenses/all-rights-reserved/ FCIQMC Full Configuration Interaction Quantum Monte Carlo Electronic structure Full configuration interaction