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 () 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 beyond , 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 . 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.
In the NECI FCIQMC code used in this work, a determinant with amplitude Ci will perform ⌊|Ci|⌋ spawning attempts with walker weight 1 and an extra attempt with probability |Ci| − ⌊|Ci|⌋. This approach is identical within statistical errors.