In this work, ab initio density functional theory (DFT) calculations have been performed on the 3,3-sigmatropic rearrangements of hexa-1,5-diene (Cope) and N-vinylprop-2-en-1-amine (3-aza-Cope) in the gas phase. The barrier heights and heats of reactions calculated at the B3LYP/6-311G** level of theory were in good agreement with experimental data. Transition states optimized with B3LYP/6-311G** theory were used for calculating the nucleus independent chemical shift (NICS) and, a natural bond orbital (NBO) analysis was also performed at the same level of theory. Our results indicate that the aromaticities of the transition states are controlled by the out-of-plane component and that the chair-like transition state of the Cope rearrangement exhibits the strongest aromatic character. Analysis of donor-acceptor (bonding and anti-bonding) interactions of σ3–4 → π*1–2 suggests that the TS structure in the hexa-1,5-diene reaction (the Cope rearrangement) has more aromatic character than the N-vinylprop-2-en-1-amine reaction (the 3-aza-Cope rearrangement). The NBO results show that in the hexa-1,5-diene and N-vinylprop-2-en-1-amine rearrangements, activation energies are controlled by σ3–4 → π*1–2 and σ3–4 → π*1–2 resonance energies. [...]
To investigate the influence of C-doping on the electrostatic structure properties in the frame work of density functional theory (DFT), we considered beryllium monoxide nanotubes (BeONTs), consisting of 60 Be and 60 O atoms. Full geometry optimizations are performed for all structures, i.e., all atoms are allowed to relax. Afterwards, the chemical shielding (CS) tensors are calculated for Be-9, O-17 and C-13 nuclei in the C-doped forms and also pristine models of the (10, 0) zigzag and (5, 5) armchair BeONTs. Formation energies indicate that C-doping of Be atom (CBe form) could be more favorable than C-doping of O atom (CO form) in both zigzag and armchair BeONTs. Gap energies and dipole moments detected the effects of dopant in the (5, 5) armchair models; however, those parameters did not indicate any significant changes in the C-doped (10, 0) zigzag BeONT models. The results show that the CS values for the Be and O atoms-contributed to the Be-C bonds or those atoms close to the C-doped region-in the CO form of BeONTs (zigzag and armchair) are changed. The same values only for the O atoms-contributed to the O-C bonds- in the CBe form of BeONTs (zigzag and armchair) are changed.
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