Lewis-Based Valence Bond Scheme: Application to the Allyl Cation

A method for expressing the wave function in terms of Lewis structures is proposed and tested on the allyl cation. This computational scheme is called valence bond BOND (VBB). The compact VBB wave function gives consistent results with the breathing orbital valence bond method (BOVB) for the resonance energy of the allyl cation (54 and 55 kcal/mol for VBB and BOVB, respectively). The optimization of the sigma orbitals, in such a way they adapt to each resonance structure, makes use of the breathing orbital effect. It is shown that this "breathing" of the sigma frame is more efficient in the resonant hybrid than in the localized state, so that a resonance energy of 63 kcal/mol is obtained at this level of computation.