An efficient and accurate perturbative correction to initiator full configuration interaction quantum Monte Carlo

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.