  We present a perturbative correction within initiator full configuration
interaction quantum Monte Carlo (i-FCIQMC). In the existing i-FCIQMC algorithm,
a significant number of spawned walkers are discarded due to the initiator
criteria. Here we show that these discarded walkers have a form that allows
calculation of a second-order Epstein-Nesbet correction, that may be
accumulated in a trivial and inexpensive manner, yet substantially improves
i-FCIQMC results. The correction is applied to the Hubbard model, the uniform
electron gas and molecular systems.
