The distinction between using effective Hamiltonians for analysis of electronic structure and method development is not always binary. For example, introduction of Hubbard's repulsion term U into a density functional expression allowed Anisimov and co-workers to develop a widely used DFT+U method . Mayhall and Head-Gordon noticed that the effective exchange couplings J from single spin-flip (SF) calculations agree with the couplings extracted from more computationally expensive n-SF methods , which lead to the development of an effective computational scheme for strongly correlated systems exploiting a coarse-graining idea . In Mayhall's protocol, a single spin-flip calculation is performed first. Then, under the assumption of Heisenberg's physics, the exchange couplings are extracted, and an effective Hamiltonian is constructed to compute the spin states that are not reachable by a single spin-flip calculation.