Homoaromaticity energy-based

The presence or absence of a homoaromatic interaction is often based solely on the distance between the non-bonded atoms. Distances greatly over 2.0 A are thought to lead to a p-p overlap that is too small to make any significant contribution. This simplistic approach is not necessarily reliable as shown by Cremer et al. (1991). Their calculations on the homotropylium cation [12] indicate a double-minimum potential energy surface with respect to variations of the C(l)-C(7) distance at the Hartree-Fock level of theory. At the MP4(SDQ) level of theory, only a single-minimum curve was found with the minimum at 2.03 A. The calculated potential energy curves are quite flat in this region. 

A semiempirical predictor of homoaromaticity has been developed based on the interactions between atoms obtained from an energy partitioning scheme (Williams et al., 1988). This technique correlates the energy lowering two-centre interactions of two non-bonded atoms with homoaromaticity. A second part of the predictor is the demonstration of the necessity of including at least a minimal 2x2 configuration interaction (Cl) treatment. This semiempirical predictor has been verified by correctly interpreting the interactions in cycloheptatriene [5], 1,6-... 

Early MO descriptions of homoaromatic compounds were based on Huckel MO (HMO) theory. Through-space interactions between interacting C centres were modelled by assuming a value for the resonance integral For example, in the case of the homotropenylium cation, Winstein took P (C1,C7) = 0.5 and obtained a resonance energy comparable to that of the tropenylium cation. He concluded that, despite the insertion of the CH2 group into the Ti-system of the tropenylium cation, delocalization of TT-electrons is largely retained. 

Cremer and co-workers extended and widely applied the Bader topological analysis of atoms in molecules to a range of (potential) homoaromatic molecules. The recommended bond or interaction indices of item 2 are derived from such an analysis and are based on the electron densities calculated at the bond critical point (for bond homoaromaticity) or at the midpoint of the homoconjugative internuclear gap (for no-bond homoaromaticity where no bond critical point exists). Williams, Kurtz, and Farley developed semiempirical discriminators for the confirmation of homoaromaticity based on two-center energy partitioning terms (a negative value indicates... 

---