Recent progress in on-surface chemistry has enabled the synthesis of novel polyradical molecules with interesting electronic structure, which are hardly available in solution chemistry. Moreover, the possibility to characterize their electronic structure with scanning tunneling spectroscopy (STS) with the unprecedented spatial resolution opens new possibilities to understand their nontrivial electronic structure. However, experimental STS maps of molecules on surfaces are interpreted using one-electron STM theory within the framework of one-electron molecular orbitals nowadays. Although this standard practice often gives relatively good agreement with experimental data for closed-shell molecules, it fails to address multireference polyradical molecules. In this manuscript, we provide multireference STM theory including out-of-equilibrium processes of removing/adding an electron within the formalism of many-electron wave functions for the neutral and charged states. This can be accomplished by the concept of so-called Dyson orbitals. We will discuss the examples where the concept of Dyson orbitals is mandatory to reproduce experimental STS maps of polyradical molecules. Finally, we critically review the possibility of the experimental verification of the so-called SOMO/HOMO inversion effect using STS maps in polyradical molecules. Namely, we will demonstrate that experimental STS measurements cannot provide any information in case of strongly correlated molecules about the ordering of one-electron molecular orbitals and, therefore neither about the SOMO/HOMO inversion effect.

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Metal-organic frameworks (MOFs) represent an interesting class of versatile materials with important properties, including magnetism. However, the synthesis of atomically precise large-scale 2D MOFs with nontrivial strong magnetic coupling represents a current research challenge. In this regard, we report on the synthesis of a high-quality large-scale 2D MOF, with strong π-d magnetic exchange coupling. To this aim, we present a new two-step synthetic approach that consists of the initial formation of an extended supramolecular organic framework on a Au(111) surface, establishing the large-scale order of organic ligands and their subsequent metalation by single cobalt atoms assisted by annealing. Moreover, we show that the usage of radical asymmetric organic ligands enables us to form a magnetic 2D MOF with strong π-d electron interactions. According to the multireference calculations, the 2D MOF shows complex spin interactions beyond the traditional superexchange mechanism, with the interplay between antiferromagnetic and ferromagnetic couplings. We anticipate that this synthetic strategy can be adapted to different approaches, such as liquid interfaces or insulating substrates, to synthesize high-quality 2D MOFs. Accompanied by the high control with atomic precision over the magnetic properties of the ligands and metals, this approach enables the formation of large-scale 2D MOFs with complex spin interactions, which will open new avenues in the field of 2D magnetic materials.

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Triangulenes are prototypical examples of open-shell nanographenes. Their magnetic properties, arising from the presence of unpaired π electrons, can be extensively tuned by modifying their size and shape or by introducing heteroatoms. Different triangulene derivatives have been designed and synthesized in recent years thanks to the development of on-surface synthesis strategies. Triangulene-based nanostructures with polyradical character, hosting several interacting spin units, can be challenging to fabricate but are particularly interesting for potential applications in carbon-based spintronics. Here, we combine pristine and N-doped triangulenes into a more complex nanographene, TTAT, predicted to possess three unpaired π electrons delocalized along the zigzag periphery. We generate the molecule on a Au(111) surface and detect direct fingerprints of multiradical coupling and high-spin state using scanning tunneling microscopy and spectroscopy. With the support of theoretical calculations, we show that its three radical units are localized at distinct parts of the molecule and couple via symmetric ferromagnetic interactions, which result in a S = 3/2 ground state, thus demonstrating the realization of a molecular ferromagnetic Heisenberg spin trimer.

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Triangulene and its homologues are promising building blocks for high-spin low-dimensional networks with long-range magnetic order. Despite the recent progress in the synthesis and characterization of coupled triangulenes, key parameters such as the number of organic linking units or their dihedral angles remain scarce, making further studies crucial for an essential understanding of their implications. Here, we investigate the synthesis and reactivity of two triangulene dimers linked by two (Dimer 1) or one (Dimer 2) para-biphenyl units, respectively, on a metal surface in an ultra-high vacuum environment. First-principles calculations and model Hamiltonians reveal how spin excitation and radical character depend on the rotation of the para-biphenyl units. Comprehensive scanning tunneling microscopy (STM) in combination with density functional theory (DFT) calculations confirm the successful formation of Dimer 1 on Au(111). Non-contact atomic force microscopy (nc-AFM) measurements resolve the twisted conformation of the linking para-biphenyl units for Dimer 1. On the contrary, the inherent flexibility of Dimer 2 induces the planarization of the para-biphenyl, resulting in the spontaneous formation of two additional five-membered rings per dimer connected by a single C-C bond (Dimers 2'). Furthermore, scanning tunneling spectroscopy (STS) measurements confirm the antiferromagnetic (S=0) coupling of the observed dimers, underscoring the critical influence of dihedral angles and structural flexibility of the linking units in π-electron magnetic nanostructures.

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• open-shell character, scanning tunneling microscopy, surface chemistry, triangulenes, π-electron magnetism,
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On-surface synthesis is a promising strategy for the preparation of molecules that are not achievable otherwise. Understanding the mechanism of on-surface reactions requires knowledge of the molecular structure and possible organization of reactants into supramolecular assemblies during the reaction. Scanning probe techniques are essential for the unambiguous identification of the products and for determining their electronic and magnetic properties. However, these are generally not capable of imaging the surface at reaction conditions and, therefore, answering some of the key questions about the reaction mechanism. Here, we show that real-time low-energy electron microscopy (LEEM) can monitor the surface processes in real time and provide the necessary complementary mechanistic insights into on-surface reactions. We monitor the intramolecular ring-closure reaction of 1,3,5-tris(7-methyl-α-carbolin-6-yl)benzene on the Au(111) surface and show that it takes place in the 2D molecular gas phase at elevated temperatures. Products condense into separate islands upon cooling, enabling fast and efficient assessment of product yields. This makes LEEM an efficient tool for studying intramolecular chemical reactions.

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• Chirality, Low-Energy Electron Microscopy, On-Surface Synthesis, Scanning Probe Microscopy,
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The use of machine learning (ML) to refine low-level theoretical calculations to achieve higher accuracy is a promising and actively evolving approach known as Δ-ML. The density matrix renormalization group (DMRG) is a powerful variational approach widely used for studying strongly correlated quantum systems. High computational efficiency can be achieved without compromising accuracy. Here, we demonstrate the potential of a simple ML model to significantly enhance the performance of the quantum chemical DMRG method.

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