The quantum mechanical resonance energy of transition states. An indicator of transition state geometry and electronic structure

This paper discusses the quantum mechanical resonance energy (B) of three-center transition states having three and four delocalized electrons, such as in atom transfer X-X-X and in polar group transfer reactions (X-A-X)^-. It is shown that B is proportional to the energy difference between the HOMO and LUMO of the transition state, and any geometric variation that lowers the energy gap between these two orbitals of the transition state will also decrease its B property. The main causes for possessing a small B are shown to be the geometric looseness of the three-center transition state and its bending away from linearity. The quantum mechanical resonance energy B depends also on the overlap S₁₂, between the resonating bonding schemes, and decreases as S₁₂ increases. For four-electron/three-center transition states, of polar group transfer reactions such as S_N2, the overlap S₁₂ increases in proportion to the ionicity of the resonating bonding schemes, and therefore B decreases with an increase of the triple ionic character (X^- A⁺ X^-) of the transition state. It is shown thereby that B can serve as a probe of transition-state geometry, charge character, and electronic structure. A simple estimation method is devised of quantum mechanical resonance energies of transition states and their ground-state analogues, and the results are compared with recent valence bond ab initio computations of B.