Both Kahn and Briat's localized orbital approach and Hay, Thibeault, and Hoffmann's symmetry-adapted orbital method emphasize that ferromagnetic coupling depends on two-electron exchange integrals, while antiferromagnetic coupling involves both one-and twoelectron integrals. R. Hoffmann et al. noted in 1975 that for small structural changes or variations in the substituents, changes in the two-electron parts are negligible compared to changes in the orbital energies. This implies that small geometric adjustments can significantly alter the overlap of the magnetic orbital pairs and the squared orbital energy differences while leaving the exchange and Coulomb interactions relatively unaffected. Thus, the total magnetic coupling can be decomposed into ferromagnetic and antiferromagnetic components through a multicomponent fitting using equation 2. This decomposition procedure was first demonstrated by Ruiz and coworkers, who illustrate a linear dependence of the overall J coupling on the squared orbital energy differences of the σ orbitals in hydroxoand alkoxo-bridged copper dinuclear complexes using canonical orbitals from DFT. The overlap of magnetic orbitals S ab can be obtained via orbital transformations from broken-symmetry DFT (BS-DFT). However, since broken-symmetry solutions are not spin eigenstates, the resulting energy differences between high-spin and broken-symmetry determinants cannot be directly compared with experimental data. Instead, projection schemes, such as those proposed by Noodleman, Ruiz et al., and Yamaguchi, must be applied to extract meaningful J coupling constants. Among these, the Yamaguchi scheme is widely used due to its robustness in predicting magnetic coupling constants across a broad range of coupling strengths. While BS-DFT is useful for predicting the sign and magnitude of the magnetic coupling, it has major limitations in decomposing the individual ferromagnetic and antiferromagnetic contributions. First, magnetic orbitals, though derived from canonical orbitals, do not contain energy information since they are not optimized in a self-consistent field. Second, the total interaction is simplified to the sum of pairwise orbital interactions, (e.g., a pair of σ g,u -orbitals), neglecting dynamic charge polarization or spin polarization effects, which can significantly contribute to the overall coupling in systems with non-negligible hole-particle excitations.