While performing production runs, we have noticed that the computation of E was faster than the CIPSI selection. Hence, we have slightly modi ed the routines computing E such that the selection of determinants is performed alongside the computation of E . is new on-the-y CIPSI selection performed during the stochastic PT2 calculation completely removes the conventional (deterministic) selection step, and the determinants are selected with no additional cost. We have observed that, numerically, the curves of the variational energy as a function of N det obtained with either the deterministic or the stochastic selections are indistinguishable, so that the stochastic algorithm does not harm the selection's quality.