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Abstract This study explores open-shell biradical and polyradical molecular compounds based on extended multireference (MR) methods (MR-configuration interaction with singles and doubles (CISD) and MR-averaged quadratic coupled cluster (AQCC) approach) using the numbers of unpaired densitiesN_U. These results were used to guide the analysis of the fractional occupation number weighted density (FOD) calculated within the finite temperature (FT) density functional theory (DFT) approach. As critical test examples, the dissociation of carbon–carbon (CC) single, double and triple bonds and a benchmark set of polycyclic aromatic hydrocarbons (PAHs) have been chosen. By examining single, double, and triple bond dissociations, we demonstrate the utility and accuracy but also limitations of the FOD analysis for describing these dissociation processes. In significant extension of previous work (Phys Chem Chem Phys 25: 27380–27393), the assessment of FOD applications for different classes of DFT functionals was performed examining the range-separated functionals ωB97XD, ωB97M-V, CAM-B3LYP, LC-ωPBE, and MN12-SX, the hybrid (M06-2X) functional and the double hybrid (B2P-LYP) functional. In all cases, strong correlations betweenN_FODandN_Uvalues are found. The major task was to develop a new linear regression formula for range-separated functionals allowing a convenient determination of the optimal electronic temperatureT_elfor the FT-DFT calculation. We also established an optimal temperature for the semiempirical extended tight-binding GFN2-xTB method. These findings significantly broaden the applicability of FOD analysis across various DFT functionals and semiempirical methods. 

Abstract We report on the largest open‐shell graphenic bilayer and also the first example of triply negatively charged radical π‐dimer. Upon three‐electron reduction, bilayer nanographene fragment molecule (C₉₆H₂₄Ar₆)₂(Ar=2,6‐dimethylphenyl) (1₂) was transformed to a triply negatively charged species1₂^3.−, which has been characterized by single‐crystal X‐ray diffraction, electron paramagnetic resonance (EPR) spectroscopy and magnetic properties on a superconducting quantum interference device (SQUID).1₂^3.−features a 96‐center‐3‐electron (96c/3e) pancake bond with a doublet ground state, which can be thermally excited to a quartet state. It consists of 34 π‐fused rings with 96 conjugatedsp²carbon atoms. Spin frustration is observed with the frustration parameterf>31.8 at low temperatures in1₂^3.−, which indicates graphene upon reduction doping may behave as a quantum spin liquid. 

A unique trimeric radical cation with unequal charge distribution is obtained by chemical oxidation of triphenylene with GaCl₃. XRD determined structure is combined with computational modeling showing stabilizing pancake bonding in the π-stacks. 

The biradicaloid character of different types of polycyclic aromatic hydrocarbons (PAHs) based on small band gaps is an important descriptor to assess their opto-electronic properties.