For each generator |I , before generating its set of |α 's, we pre-compute the diagonal of the Fock matrix associated with |I . is enables to compute the diagonal elements α| Ĥ|α involved in Eq. ( ) for a few ops. 154 e computation of Ψ (0) | Ĥ|α = ∑ J c J J| Ĥ|α is more challenging than the diagonal term since, at rst sight, it appears to involve the N det internal determinants. Fortunately, most of the terms amongst this sum vanish due to Slater-Condon's rules. Indeed, we know that the terms where |J is more than doubly excited with respect to |α vanish, and these correspond to the determinants |J which are more than quadruply excited with respect to |I . 154 To compute e ciently Ψ (0) | Ĥ|α , for each generator |I , we create a ltered wave function |Ψ (0) I by projecting |Ψ (0) on a subset J I of internal determinants {|J } where J| Ĥ|α is possibly non-zero. is yields Ψ (0) | Ĥ|α = Ψ (0) I | Ĥ|α , where Ψ (0) I is a much smaller determinant expansion than Ψ (0) . In addition, as we have de ned the |α 's in such a way that they do not interact with |J when J < I, all these |J 's can also be excluded from J I . is pruning process yielding to |Ψ (0) I will be referred to as the coarse-grained ltering. A ne-grained ltering of |Ψ (0) I is performed in a second stage to reduce even more the number of determinants, as we shall explain later.