Physics and Chemistry of Two-Dimensional Triangulene-Based Lattices.

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ConspectusTriangulene (TRI) and its heterotriangulene (HT) derivatives are planar, triangle-shaped molecules that, via suitable coupling reactions, can form extended organic two-dimensional (2D) crystal (O2DC) structures. While TRI is a diradical, HTs are either closed-shell molecules or monoradicals which can be stabilized in their cationic form.Triangulene-based O2DCs have a characteristic honeycomb-kagome lattice. This structure gives rise to four characteristic electronic bands: two of them form Dirac points, while the other two are flat and sandwich the Dirac bands. Functionalization and heteroatoms are suitable means to engineer this band structure. Heteroatoms like boron and nitrogen shift the Fermi level upward and downward, respectively, while bridging groups and functionalized triangulene edges can introduce a dispersion to the flat bands.The stable backbone architecture makes 2D HT-polymers ideal for photoelectrochemical applications: (i) bridge functionalization can tune the band gap and maximize absorption, (ii) the choice of the center atom (B or N) controls the band occupation and shifts the Fermi level with respect to vacuum, allowing in some cases for overpotential-free photon-driven surface reactions, and (iii) the large surface area allows for a high flux of educts and products.The spin polarization in TRI and in open-shell HTs is maintained when linking them to dimers or extended frameworks with direct coupling or more elaborate bridging groups (acetylene, diacetylene, and phenyl). The dimers have a high spin-polarization energy and some of them are strongly magnetically coupled, resulting in stable high-spin or broken-symmetry (BS) low-spin systems. As O2DCs, some systems become antiferromagnetic Mott insulators with large band gaps, while others show Stoner ferromagnetism, maintaining the characteristic honeycomb-kagome bands but shifting the opposite spin-polarized bands to different energies. For O2DCs based on aza- and boratriangulene (monoradicals as building blocks), the Fermi level is shifted to a spin-polarized Dirac point, and the systems have a Curie temperature of about 250 K. For half-filled (all-carbon) systems, the Ovchinnikov rule or, equivalently, Lieb's theorem, is sufficient to predict the magnetic ordering of the systems, while the non-half-filled systems (i.e., those with heteroatoms) obey the more involved Goodenough-Kanamori rule to interpret the magnetism on the grounds of fundamental electronic interactions.There remain challenges in experiment and in theory to advance the field of triangulene-based O2DCs: Coupling reactions beyond surface chemistry have to be developed to allow for highly ordered, extended crystals. Multilayer structures, which are unexplored to date, will be inevitable in alternative synthesis approaches. The predictive power of density-functional theory (DFT) within state-of-the-art functionals is limited for the description of magnetic couplings in these systems due to the apparent multireference character and the large spatial extension of the spin centers.