Triangulene monomer is a prototypical non-Kekulé diradical with a triplet ground state. Its dimer is also a free radical with four unpaired electrons (Figure ). In the dimer, triplet configuration of the monomers is maintained, and coupled in an anti-parallel alignment, resulting in an open-shell singlet (OSS) with S = 0. In these diradicaloid and other radicals with an even number of unpaired electrons, the closed-shell singlet (CSS), the OSS and the high-spin state (HS), such as triplet or quintet, are the three important states to be considered (Figure ). Among these states, the HS is wellrepresented by a single-determinant wavefunction, whereas the OSS is not, which poses a major challenge for computational chemistry. The relative energies of these three states are described by the spin-polarization energy ΔEspin and the magnetic coupling J (Figure ). The spin-polarization energy is defined as the energy difference between high-spin open-shell and closed-shell states, ΔEspin = EHS -ECSS. This value will directly indicate whether the open-shell state is more stable, in other words, if the molecule is a radical. The magnetic coupling J is derived from Heisenberg-Dirac-van Vleck (HDVV) Hamiltonian, 𝐻 ̂= -𝐽𝑆 1 ̂𝑆2 ̂ , where 𝑆 1 ̂ and 𝑆 2 ̂ are the spin angular momentum operators on sites 1 and 2, respectively. It is defined as the normalized energy difference between the low-spin OSS and high-spin states for triangulene monomer and dimer: nJ = EOSS -EHS, where n is 1 for the triplet (T) and 3 for the quintet (Q). For the triangulene monomer, the high-spin state is T and J = EOSS -ET, whereas it is Q for the dimer and J = (EOSS -EQ)/3.