Resonance and Aromaticity:An Ab Initio Valence Bond Approach

Resonance energy is one of the criteria to measure aromaticity. The effect of the use of different orbital models is investigated in the calculated resonance energies of cyclic conjugated hydrocarbons within the framework of the ab initio Valence Bond Self-Consistent Field (VBSCF) method. The VB wave function for each system was constructed using a linear combination of the VB structures (spin functions), which closely resemble the Kekule valence structures, and two types of orbitals, that is, strictly atomic (local) and delocalized atomic (delocal) p-orbitals, were used to describe the pi-system. It is found that the Pauling-Wheland's resonance energy with nonorthogonal structures decreases, while the same with orthogonalized structures and the total mean resonance energy (the sum of the weighted off-diagonal contributions in the Hamiltonian matrix of orthogonalized structures) increase when delocal orbitals are used as compared to local p-orbitals. Analysis of the interactions between the different structures of a system shows that the resonance in the 6 pi electrons conjugated circuits have the largest contributions to the resonance energy. The VBSCF calculations also show that the extra stability of phenanthrene, a kinked benzenoid, as compared to its linear counterpart, anthracene, is a consequence of the resonance in the pi-system rather than the H-H interaction in the bay region as suggested previously. Finally, the empirical parameters for the resonance interactions between different 4n+2 or 4n pi electrons conjugated circuits, used in Randic's conjugated circuits theory or Herdon's semi-emprical VB approach, are quantified. These parameters have to be scaled by the structure coefficients (weights) of the contributing structures.