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

## TL;DR

This paper introduces a new method to analyze spin interactions in molecules, enabling better understanding of magnetic couplings and electron localization.

## Contribution

A novel spin-permutation diabatization framework that enables direct mapping to spin-effective Hamiltonians without orbital localization.

## Key findings

- The method provides real-space decomposition of electronic states into localized spins.
- Exchange couplings are evaluated straightforwardly for various molecular systems.
- Applications demonstrate clear physical interpretations of spin interactions in complex systems.

## Abstract

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.