Due to their relevance to this work, we want to highlight two additional perturbation theoretical approaches: Retaining the excitation degree (RE) perturbation theory defines the unperturbed Hamiltonian to possess exactly those terms of the exact electronic Hamiltonian which do not excite or deexcite electrons within the unperturbed system. In a CI expansion, this corresponds to the unperturbed Hamiltonian containing all diagonal blocks of Ĥ and the perturbation to contain all off-diagonal blocks. Two relevant consequences of this definition are that RE2 is always exact in energy through third order, but at the cost increasing the computational complexity of a simple implementation to O(M 6 ). The other approach we want to mention here is perturbation adapted perturbation theory (PAPT). This method optimises the unperturbed Hamiltonian such that it best recreates the physics of the perturbed system. A direct result of this is that the PAPT series converges much quicker than the corresponding MP series for increased perturbation order. However, its performance at low perturbative order is not drastically improved in comparison to MP, and creating the appropriate unperturbed Hamiltonian also scales as O(M 6 ).