Predicting Magnetic Coupling and Spin-Polarization Energy in Triangulene Analogues

Triangulene and its analogue metal-free magnetic systemshave garneredincreasing attention since their discovery. Predicting the magneticcoupling and spin-polarization energy with quantitative accuracy isbeyond the predictive power of today's density functional theory(DFT) due to their intrinsic multireference character. Herein, wecreate a benchmark dataset of 25 magnetic systems with nonlocal spindensities, including the triangulene monomer, dimer, and their analogues.We calculate the magnetic coupling (J) and spin-polarizationenergy (Delta E (spin)) of these systemsusing complete active space self-consistent field (CASSCF) and coupled-clustermethods as high-quality reference values. This reference data is thenused to benchmark 22 DFT functionals commonly used in material science.Our results show that, while some functionals consistently correctlypredict the qualitative character of the ground state, achieving quantitativeaccuracy with small relative errors is currently not feasible. PBE0,M06-2X, and MN15 are predicting the correct electronic ground statefor all systems investigated here and also have the lowest mean absoluteerror for predicting both Delta E (spin) (0.34, 0.32, and 0.31 eV) and J (11.74, 12.66,and 10.64 meV). They may therefore also serve as starting points forhigher-level methods such as the GW or the randomphase approximation. As other functionals fail for the predictionof the ground state, they cannot be recommended for metal-free magneticsystems.

Automated summary

This study establishes a benchmark dataset of 25 magnetic systems, including triangulene monomer, dimer, and their analogues, to evaluate the performance of 22 commonly used density functional theory (DFT) methods in material science. The results show that achieving quantitative accuracy with small relative errors is currently not feasible. PBE0, M06-2X, and MN15 functionals are able to predict the correct electronic ground state for all systems and have the lowest mean absolute error for predicting Delta E (spin) and J. Therefore, they can serve as starting points for higher-level methods such as GW or the random phase approximation. Other functionals that fail to predict the ground state are not recommended for metal-free magnetic systems.