A method for describing resonance between generalized valence bond wavefunctions

In a valence bond (VB) description of wavefunctions there may be several distinct but energetically similar bonding structures. Examples include aromatic molecules (e.g. benzene) and excited states of molecules with equivalent chromophores (e.g. glyoxal). The variational generalization of VB theory, the generalized valence bond (GVB) method, has limitations for such systems since it can only describe one of the bonding structures, allowing no explicit mixing or "resonance" with the other structures. We present herein a method for evaluating the matrix elements necessary to optimize the mixing between the various distinct bonding structures. Evaluation of such matrix elements has heretofore been computationally difficult since the wavefunctions in general have nonzero overlap. Applications of the method are presented for the resonance in allyl radical and the splitting of the localized core hole states of N₂⁺.