Using these equations, it is straightforward to obtain the S 2 matrix elements in the basis of the ESDs, as within SOA only ⟨Φ| Ŝ2 |Φ⟩ and ÊF + ÊG -Φ Ŝ2 Φ are non-zero. Next, we illustrate the flow of the spin adaptation procedure of the ECISD basis, for an exemplary two-chromophore system. Let us assume that a set of singlet and triplet site states has been given on each of the two fragments. This yields the initial (non-spin-adapted) ECISD basis containing the following ESDs: