Charge Density Analysis of Triplet and Broken Symmetry States Relevant to Magnetic Coupling in Systems with Localized Spin Moments

Comparison of electron charge density for triplet and broken symmetry solutions obtained from different computational methods together with the atoms-in-molecules (AIM) and electron localization function (ELF) topological analyses support the description of these systems through the Heisenberg Hamiltonian. The reduction of the low-energy spectrum to a purely spin Hamiltonian holds for all studied methods, although local density approximation (LDA) exhibits some noticeable deviation. The analysis of charge difference density plots clearly shows that the failure of LDA to describe magnetic coupling is due to the too-strong delocalization that leads to a qualitatively incorrect electron density in the region near the nuclei. Gradient-corrected and hybrid functionals correct this defect but in an exaggerated way. The role of mixing Fock exchange is also discussed.