Spin-Permutation Diabatization: A General Framework for Spin Localization and Exchange Coupling

We present a spin-permutation diabatization strategy that transforms ab initio spin-pure eigenstates into spin-localized diabatic states, enabling direct mapping to spin-effective Hamiltonians without projection or orbital localization. The method provides both a real-space decomposition of electronic states in terms of localized spins and a straightforward evaluation of exchange couplings. Applications to several representative systems, including ethylene torsion, prototypical diradicals (benzynes, xylylenes, methylene), trimethylenebenzene triradical, singlet-triplet excited states of organic chromophores, and triplet-pair states in a tetracene dimer, demonstrate that the approach provides magnetic couplings and affords a clear physical interpretation of interacting spins. This general and conceptually transparent framework bridges ab initio electronic structure theory and spin models, and is expected to be especially valuable for systems with nontrivial distributions of unpaired electrons, such as delocalized or strongly correlated molecular magnets and spin-active chromophores.