Aromaticity of Bent Benzene Rings

For the description of the bent benzene, the flat benzene ring was the starting point. For this system, there is a clear a n separation. There is a clear distinction between the doubly occupied orbitals for the a-core and the 6 non-orthogonal p-orbitals for the 7i-system. 

The 7t-system is described by all five Rumer structures, which is the complete spin-space (i.e. Fig. 3 and Fig. 4). This allows a smooth transition from benzene, where the 2 Kekule structures are most important, to the highly bent Dewar benzene, where only one of the Dewar structures (Fig 4) is important. All the orbitals, doubly occupied and singly occupied are fully optimised. For each bent structure, the orbitals from the preceding less bent structure were used as initial guess. This and the choice of wavefunction ensure that an aromatic 7i-system can be identified, even when no symmetry separation exists. All orbitals were completely optimised so we have a wavefunction of the spin-coupled type. This is the type of wavefunction used by Cooper et al. [52] in their study of benzene. 

To obtain geometries, 10-orbital 10-electron complete active space self-consistent field (CASSCF) [82-84] calculations were performed with the GAMESS-UK program [6], The occupied orbital order in an SCF for flat benzene is n,2c,2n. In the bent molecule, there is no clear distinction between a- and tt-orbitals and we want to include all the tt-orbitals in the CAS-space. Thus, 10 orbitals in the active space are required. Obviously, the 5 structure VB wavefunction would have been a preferable choice to use in the geometry optimisation. However, at that time, the VB gradients were not yet available. The energies of the VBSCF at the CASSCF geometries followed the CASSCF curve closely. 

The geometry of the molecule at each point was optimised for a fixed bending angle J (Fig. 7), while all the other geometrical parameters were free. 

C2v symmetry has been used throughout. Calculations were performed for J from 0° to 90° with a step-size of 5°. All calculations were performed using the 6-31G basis set [72]. 

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