Since the repartitioning operator ŵ is block-diagonal, the unitary orbital rotation operator Û, which maps the canonical orbital basis to the dressed orbital basis, as well as its anti-Hermitian generator are also block diagonal. This means that the recanonicalization equation is naturally decoupled between the occupied and virtual space. The aforementioned choice of ŵ furthermore implies that |Φ 0 ⟩ is still an eigenstate of Ĥ(0) , now with eigenvalue given by