The influence of electronegativity on triangular three-centre two-electron bonds: the relative stability of carbonium ions, π-complex chemistry and the −2hβ effect

Using the HMO approximation, bond energy equations for triangular three-centre, two-electron [3c-2e] bonded species AB2+ (π-complexes) and the isomeric systems (AB−B+, BB−A+, BA−B+ and A++BB) are described. The electronegativity difference (Δχ) between the atoms or groups A and B is assumed to be related to the difference (h) in their Coulomb integrals and the variation of relative energies with electronegativity difference is explored. The bond energy curve for π-complexes is displaced relative to those of the two-centre, two-electron [2c-2e] bonded species and this displacement accounts for the significant influence of electronegativity difference on reactions proceeding via [3c-2e] bonded intermediates or transition states. The origin of the displacement of the bond energy versus electronegativity difference curve for the π-complexes is identified as a −2hβBB term in the bond energy equation. In contrast to [2c-2e] bonds, this term makes the influence of electronegativity difference on triangular [3c-2e] bonds directional, that is, the bond energies of AB2+ and BA2+ are different in contrast to those of AB and BA. A more electronegative atom A destabilises the [3c-2e] bond by removing electron density from the bonding interaction BB (βBB) whereas a less electronegative atom A will strengthen the bond by increasing the electron density between the atoms B. Reactions involving [3c-2e] AB2+ bonds are classified as homo- or heteroprocesses and the influence of electronegativity difference on these discrete transformations is discussed in terms of the contribution of h, h2 and −2hβ functions to differences in bond energy. The analysis is extended to π-complexes with back-donation and the equivalence of the description of onium ions using either two [2c-2e] bonds or two [3c-2e] bonds is demonstrated. Extension of the analysis to 2-norbornyl cations suggests that, due to the shape of the bond energy versus electronegativity difference curve, this cation exists within a window of stability between the alternative isomers. 1,2-Disubstituted norbornyl cations are used as a model of π-complexes and the influence of substituent effects on relative stability is explored using the AM1 method. After allowance for resonance and hyperconjugation effects, the results are found to be consistent with the general conclusions of the simple HMO model.