The parameters ΔEspin and J are important metrics for understanding the magnetic behavior of metal-free magnetism. ΔEspin gives the magnitude of the electron correlation. A large ΔEspin value signifies robust electron correlation and a stable spinpolarized state. In systems with partially-filled (quasi-)degenerate orbitals, the highspin configuration is more stable than the closed-shell one due to the Coulomb repulsion of unpaired electrons according to Hund's rule. ΔEspin is related to the on-site Coulomb repulsion, U, of the Hubbard model, which is critical in the physics of strongly correlated systems. It is also closely associated with Stoner magnetism, wherein the balance between electron correlation and electronic coupling underlies the origin of stable open-shell states and ferromagnetic interactions. We employ the domain-based local pair natural orbital coupled-cluster theory (DLPNO-CCSD(T)) method (see computational details section for more information) to calculate the energy difference between the closed-shell and high-spin states, i.e., triplet for the monomer and quintet for the dimer. In comparison to the conventional CCSD(T) method, the DLPNO-CCSD(T) approach offers higher computational efficiency, capable to achieve nearly linear scaling while maintaining comparable accuracy. As for J, it is of significance to evaluate the type and strength of magnetic interaction. If J > 0, the high-spin state is energetically favored, implying so-called ferromagnetic interaction (FM), whereas, if J < 0, the low-spin state is more stable for anti-ferromagnetic interaction (AFM). The ground state for the triangulene monomer is a triplet, and thus J > 0, while for the dimer, it is the OSS and J < 0. It is notable that the low-spin state, i.e. the OSS radical with an even number of unpaired spins, has at least two Slater determinants with large coefficients. This makes single-determinant approaches such as HF, CCSD(T), and also DFT unsuitable for the accurate description of these systems. CASSCF is a natural approach to treat the multi-configurational systems with strong static correlation, where a full-CI expansion of the active space is generated, and the multi-configurational character is correctly considered. In order to obtain the J value for the triangulene monomer and dimer, we performed the stateaveraged CASSCF (12, 12) calculations as implemented in the ORCA program (see computational details section for more information).