  We present an approach to combining selected configuration interaction (SCI)
and initiator full configuration interaction quantum Monte Carlo (i-FCIQMC). In
the current i-FCIQMC scheme, the space of initiators is chosen dynamically by a
population threshold. Here, we instead choose initiators as the selected space
(V) from a prior SCI calculation, allowing substantially larger initiator
spaces for a given walker population. While SCI+PT2 adds a perturbative
correction in the first-order interacting space (FOIS) beyond V, the approach
presented here allows a variational calculation in the same space, and a
perturbative correction in the second-order interacting space. The use of a
fixed initiator space reintroduces population plateaus into FCIQMC, but it is
shown that the plateau height is typically only a small multiple of the size of
V. Thus, for a comparable fundamental memory cost to SCI+PT2, a substantially
larger space can be sampled. The resulting method can be seen as a
complementary approach to SCI+PT2, which is more accurate but slower for a
common selected/initiator space. More generally, our results show that
approaches exist to significantly improve initiator energies in i-FCIQMC, while
still ameliorating the fermion sign problem relative to the original FCIQMC
method.
