Signi cant improvements were also realized in the computation of the second-order perturbative correction, E . A natural idea was to take into account the tremendous number of tiny contributions via a stochastic Monte Carlo approach. E being itself an approximate quantity used for estimating the FCI energy, its exact value is indeed not required, as long as the value is unbiased and the statistical error is kept under control. Our scheme allows to compute E with a small error bar for a few percent of the cost of the fully deterministic computation.