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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. 

We introduce in this work a unique parameter for the quantitative assessment of the intrinsic strength of the π interaction between two monomers forming a complex. The new parameter is a local intermonomer stretching force constant, based on the local mode theory, originally developed by Konkoli and Cremer, and derived from the set of nine possible intermonomer normal vibrational modes. The new local force constant was applied to a diverse set of more than 70 molecular complexes, which was divided into four groups. Group 1 includes atoms, ions, and small molecules interacting with benzene and substituted benzenes. Group 2 includes transition metal hydrides and oxides interacting with benzene while Group 3 involves ferrocenes, chromocenes, and titanium sandwich compounds. Group 4 presents an extension to oxygen π–hole interactions in comparison with in-plane hydrogen bonding. We found that the strength of the π interactions in these diverse molecular complexes can vary from weak interactions with predominantly electrostatic character, found, e.g., for argon–benzene complexes, to strong interactions with a substantial covalent nature, found, e.g., for ferrocenes; all being seamlessly described and compared with the new intermonomer local mode force constant, which also outperforms other descriptors such as an averaged force constant or a force constant guided by the electron density bond paths. We hope that our findings will inspire the community to apply the new parameter also to other intermonomer π interactions, enriching in this way the broad field of organometallic chemistry with a new efficient assessment tool. 

We systematically investigated iodine–metal and iodine–iodine bonding in van Koten’s pincer complex and 19 modifications changing substituents and/or the transition metal with a PBE0–D3(BJ)/aug–cc–pVTZ/PP(M,I) model chemistry. As a novel tool for the quantitative assessment of the iodine–metal and iodine–iodine bond strength in these complexes we used the local mode analysis, originally introduced by Konkoli and Cremer, complemented with NBO and Bader’s QTAIM analyses. Our study reveals the major electronic effects in the catalytic activity of the M–I–I non-classical three-center bond of the pincer complex, which is involved in the oxidative addition of molecular iodine I2 to the metal center. According to our investigations the charge transfer from the metal to the σ* antibonding orbital of the I–I bond changes the 3c–4e character of the M–I–I three-center bond, which leads to weakening of the iodine I–I bond and strengthening of the metal–iodine M–I bond, facilitating in this way the oxidative addition of I2 to the metal. The charge transfer can be systematically modified by substitution at different places of the pincer complex and by different transition metals, changing the strength of both the M–I and the I2 bonds. We also modeled for the original pincer complex how solvents with different polarity influence the 3c–4e character of the M–I–I bond. Our results provide new guidelines for the design of pincer complexes with specific iodine–metal bond strengths and introduce the local vibrational mode analysis as an efficient tool to assess the bond strength in complexes. 

Abstract This work provides a detailed multi‐component analysis of aromaticity in monosubstituted (X = CH₃, C, C, NH₂, NH⁻, NH⁺, OH, O⁻, and O⁺) andpara‐homodisubstituted (X = CH₃, CH₂, NH₂, NH, OH, and O) benzene derivatives. We investigate the effects of substituents using single‐reference (B3LYP/DFT) and multireference (CASSCF/MRCI) methods, focusing on structural (HOMA), vibrational (AI(vib)), topological (ELF_π), electronic (MCI), magnetic (NICS), and stability (S₀–T₁splitting) properties. The findings reveal that appropriateπ‐electron‐donating andπ‐electron‐accepting substituents with suitable size and symmetry can interact with theπ‐system of the ring, significantly influencingπ‐electron delocalization. While the charge factor has a minimal impact onπ‐electron delocalization, the presence of ap_zorbital capable of interacting with theπ‐electron delocalization is the primary factor leading to a deviation from the typical aromaticity characteristics observed in benzene.