We have investigated whether equation 23 approximates well the exact probabilities, and which of the combinations from Table is the most efficient sampling scheme for single excitations. In Figure the p PCHB 1 (a ↑ |1 ↑ )| a ↑ / ∈|D i values are shown for the stack of ten benzene molecules with fragment localized MOs, (the probability of drawing the hole a ↑ after having drawn a ↑-particle from the first spatial orbital). For the exact probability (eq. 20) we assume that we start from the Hartree-Fock reference determinant, which is given by doubly occupying all π-orbitals and keeping all π * -orbitals empty (blue line in Figure ) The orange line shows the corresponding approximated probability p PCHB