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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. 

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.