  We present a study of fixed and partial-node approximations in Slater
determinant basis sets, using full configuration interaction quantum Monte
Carlo (FCIQMC) to perform sampling. Walker annihilation in the FCIQMC method
allows partial-node simulations to be performed, relaxing the nodal constraint
to converge to the FCI solution. This is applied to ab initio molecular
systems, using symmetry-projected Jastrow mean-field wave functions for
complete active space (CAS) problems. Convergence and the sign problem within
the partial-node approximation are studied, which is shown to eventually be
limited in its use due to the large walker populations required. However the
fixed-node approximation results in an accurate and practical method. We apply
these approaches to various molecular systems and active spaces, including
ferrocene and acenes. This also provides a test of symmetry-projected Jastrow
mean-field wave functions in variational Monte Carlo (VMC) for a new set of
problems. For trans-polyacetylene molecules and acenes we find that the time to
perform a constant number of fixed-node FCIQMC iterations scales as O(N^{1.44})
and O(N^{1.75}) respectively, resulting in an efficient method for CAS-based
problems that can be applied accurately to large active spaces.
