In the case of single excitations, the approximation of contracting over all orbitals when calculating the weights (equation ) is particularly poor for these Hartree-Fock orbitals, which means that PCHB weighting for single excitations does not have the same benefits as for the other systems. For this reason we see that purely uniform sampling (unif:unif) and uniform sampling of particles followed by fast-weighted selection of holes (unif:fast) are performing very similarly.