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Free, publicly-accessible full text available June 19, 2026
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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 densitiesNU. 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 betweenNFODandNUvalues 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 temperatureTelfor 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.more » « less
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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 densities NU. 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) has 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 between NFOD and NU values 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 temperature Tel for the FT-DFT calculation. We also established an optimal temperature for the semi-empirical extended tight-binding GFN2-xTB method. These findings significantly broaden the applicability of FOD analysis across various DFT functionals and semi-empirical methods.more » « less
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Free, publicly-accessible full text available July 17, 2026
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Molecular π-magnets based on single organic molecules have attracted increasing attention for their potential applications in optoelectronics and spintronics. Global aromaticity in conjugated macrocyclic polyradicaloids is still an open question that has only been tackled in molecules with an even number of electrons. Here, we report the on-surface synthesis of a cyclopenta-ringfused oligo(m-phenylene) macrocycle, 9MC, with an odd number of electrons. The generated polyradicaloid undergoes a surface-induced distortion to a D3h symmetry with a fully delocalized doublet ground state. Interestingly, 9MC exhibits two aromatic annulene-within-an-annulene (AWA) ring currents in the inner and outer rings.more » « less
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The nonplanar character of graphene with a single carbon vacancy defect (SV) is investigated utilizing a pyrene-SV model system by way of complete active space self-consistent field theory (CASSCF) and multi-reference configuration interaction singles and doubles (MRCISD) calculations. Planar structures were optimized with both methods showing the 3B1 state as the ground state with three energetically close states within an energy range of 1 eV. These planar structures constitute saddle-points. However, upon following the out-of-plane imaginary frequency yields more stable (by 0.22 to 0.53 eV), but non-planar structures of CS symmetry. Of these, the 1A’ structure is the lowest in energy and is strongly deformed into an L-shape. Following a further out-of-plane imaginary frequency in the non-planar structures leads to the most stable, but most deformed singlet structure of C1 symmetry. In this structure a bond is formed between the carbon atom with the dangling bond and a carbon of the cyclopentadienyl ring. This bond stabilizes the structure by more than 3 eV compared to the planar 3B1 structure. Higher excited states were calculated at MR-CISD level showing a grouping of four states low in energy and higher states starting around 3 eV.more » « less
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The phenalene (triangulene) and olympicene molecules belong to the polycyclic aromatic hydrocarbons (PAHs) class, which attracted substantial technological interest due to their unique electronic properties. Electronic structure calculations serve as a valuable tool in investigating the stability and reactivity of these molecular systems. In the present work, the multireference calculations, namely the complete active space second-order perturbation theory (CASPT2) and multireference averaged quadratic coupled cluster (MR-AQCC), were employed to study the reactivity and stability of phenalene and olympicene isomers, as well as their modified structures where the sp3-carbon at the borders were removed. The harmonic oscillator model of aromaticity (HOMA) and the nucleus-independent chemical shift (NICS) as geometric and magnetic indexes calculated with density functional theory were utilized to assess the aromaticity of the studied molecules. These indexes were compared with properties such as the excitation energy and natural orbitals occupation. The reactivity analyzed using the HOMA index combined with MR-AQCC revealed the radical character of certain structures, as well as the weakening of their aromaticity. Moreover, the results suggest that the removal of sp3-carbon atoms and the addition of hydrogen atoms did not alter the π network and the excitation energies of the phenalene molecules.more » « less
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