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
