This inefficient sampling can be cured with GAS and weighted particle-selection. If we define the impurity orbital to be its own GAS space and the bath orbitals to be in a second GAS space, then there are three allowed supergroups [2, N e -2], [1, N e -1], [0, N e ], where we just listed the number of particles per GAS space. If we start now from the supergroup [2, N e -2] and assume that K is a spin-orbital index in the bath-orbitals, then we have SA K (i sg ) = 0 for all possible holes A. This implies that p PCHB 1 (K|i sg ) = 0 and only one of the two particles in the impurity is selected to be excited; each one with a probability of 1 2 .