Structure-resonance energy relationships

Quantitative structure-physical property relationships (QSPR). There are two types of physical properties we must consider ground state properties and properties which depend on the difference in energy between the ground state and an excited state. Examples of the former are bond lengths, bond angles and dipole moments. The latter include infrared, ultraviolet, nuclear magnetic resonance and other types of spectra, ionization potentials and electron affinities. 

A linear relationship has been shown to exist between structural aromaticity indices and resonance energies (92T335). From this so-called unified aromaticity index, IA, has been proposed. It makes for a more appropriate comparison the aromaticity of heterocycles of different size. 

An alternative, and widely used method of calculating resonance energies is from bond energies. By taking a standard set of bond energies the heat of formation of the non-resonating reference structure (i.e. one of the resonance structures) can be calculated, and compared with that of the actual molecule. The resonance energy of benzene, En would be calculated from the relationship... 

After the advent of Dewar and Hess—Schaad resonance energies on the basis of the MO theory, a new VB approach to the resonance energy was advanced. The method is rather formalistic in using VB structures in a way similar to how the old Hiickel method used connectivity. For benzenoid hydrocarbons, a linear relationship between these VB resonance energies and the DRE values could be established. 

KSC = Kekule structure count QSAR = quantitative structure-activity relationships QSPR = quantitative structure-property relationships SRWAC = self-returning walk atomic code TEMO = topological effect on molecular orbitals TRE = topological resonance energy TREPE = TRE per r-electron. 

Some fundamental structure-stability relationships can be employed to illustrate the use of resonance concepts. The allyl cation is known to be a particularly stable carbocation. This stability can be understood by recognizing that the positive charge is delocalized between two carbon atoms, as represented by the two equivalent resonance structures. The delocalization imposes a structural requirement. The p orbitals on the three contiguous carbon atoms must all be aligned in the same direction to permit electron delocalization. As a result, there is an energy barrier to rotation about the carbon-carbon... 

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