Figure shows good agreement between the approximated and the exact single excitations. It also confirms the exponential decay of matrix elements with the distance and the importance of excluding spatially distant orbitals, which would be unnecessarily sampled in a uniform scheme. (a ↑ |1 ↑ ), on a stack of ten benzene molecules. The blue line shows the exact probability (Eq. 20) assuming that the starting determinant ||D i = |2, 2, 2, 0, 0, 0; 2, . . . is given by doubly occupying all π-orbitals and keeping all π *orbitals empty for each benzene molecule. The orange line shows the approximated PCHB probabilities for single excitations (Eq. 23). Only unoccupied α spin-orbitals, i.e. allowed holes, are considered. The orbital indices are sorted by decreasing exact probability (blue line). (b) Logarithmic scale of (a). The horizontal dashed line gives the probability of the corresponding unconstrained uniform distribution p uni 1 (a ↑ |1 ↑ )| a ↑ / ∈|D i as reference. The value is obtained from the inverse of the number of empty α-orbitals