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.

Czech Advanced Technology and Research Institute Palacký University Olomouc Olomouc 779 00 Czech Republic

Department of Condensed Matter Physics Faculty of Mathematics and Physics Charles University Prague 2 CZ12116 Czech Republic

Department of Theoretical Chemistry J Heyrovsky Institute of Physical Chemistry Czech Academy of Sciences Prague 18200 Czech Republic

Institute of Physics Czech Academy of Sciences Prague 16200 Czech Republic

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