Using the generalized valence bond (GVB) wave function, the pi electron systems of ethylene, allyl cation, allyl radical, s-trans-1,3- butadiene and benzene were examined. The results were in good agreement with full configuration interaction calculations demonstrating the quantitative accuracy of the GVB method. The GVB description of the valence states systems includes a description of resonance and provides a rigorous quantum mechanical description of resonance in terms of spin couplings. It was found that the resonance stabilization energy is due to two effects, delocalization of orbitals onto additional centers while still maintaining their basically localized nature, and spin coupling optimization in a manner identical to the valence bond description of resonance.
It was found that the GVB wave function imposed restrictions upon the orbitals of excited states. To remove these restrictions the GVB wave function was generalized by including a spatial projection operator. The GVB(SP) wave function imposes no restrictions upon individual orbitals and represents the most general independent particle wave function as yet presented. The GVB(SP) method was used to examine allyl radical and butadiene. All states were described by localized orbitals and energies were in excellent agreement with configuration interaction results. A molecules-in-molecules model using ethylene pi electron states was found to provide a qualitative description of all the states of allyl radical and butadiene examined.
