Predicting Magnetic Coupling and Spin-Polarization Energy in Triangulene Analogues

Triangulene and its analogue metal-free magnetic systems have garnered increasing attention since their discovery. Predicting the magnetic couplings and spin polarization energy is beyond the predictive power of todays density-functional theory (DFT) due to their intrinsic multi-reference character. Herein, we create a benchmark dataset of 25 magnetic systems with non-local spin densities, including the triangulene monomer, dimer, and their analogues. We calculate the magnetic coupling (J) and spin-polarization energy (Espin) of these systems using complete active space self-consistent field (CASSCF) and coupled cluster methods as high-quality reference values. This reference data is then used to benchmark 22 DFT functionals commonly used in material science. Our results show that, while some functionals consistently correctly predict the qualitative character of the ground state, achieving quantitative accuracy with small relative errors is currently not feasible. PBE0, M06-2X, and MN15 are predicting the correct electronic ground state for all systems investigated here, and also have the lowest mean absolute error for predicting both Espin (0.34 eV, 0.32 eV and 0.31 eV) and J (13.36 meV, 13.39 meV and 11.76 meV). They may therefore also serve as starting points for higher-level methods such as the GW or the random phase approximation. As other functionals fail for the prediction of the ground state, they cannot be recommended for metal-free magnetic systems.