The second particle has the highest probability to be selected on the same fragment, while quickly decaying for neighboring fragments. Any choice for the second particle further away than 6 Å (second-nearest fragment) is nearly negligible. The logarithmic plot (Figure ) reveals the exponential decay with increasing distance. This observation shows that the distribution is highly non-uniform and weighted sampling is preferred. Moreover, as the orbital space considered, CAS(60,60) is far from a case with an excess of occupied orbitals, it is advantageous to guarantee that the second picked orbital index is indeed occupied. By this argument fully-weighted sampling with p PCHB 2 (J|I)| J∈|D i is recommended. In addition, the weighted sampling automatically prefers geminal, i.e. opposite spin pair, excitations as can be seen from comparing the blue and orange line in Figure . The subsequent hole-selections are also highly non-uniform with no excess of empty orbitals which suggests