outlying methylene bridge is comparable to that of the π-bond separating the corresponding carbon atoms in the tropylium cation. Although this experiment proved to be highly illuminating, UV spectra are generally considered to be poor indicators of aromaticity or homoaromaticity. More recent evidence for homoaromaticity More recently, work has been done to investigate the structure of the purportedly homoaromatic homotropylium ion by employing various other experimental techniques and theoretical calculations. One key experimental study involved analysis of a substituted homotropylium ion by X-ray crystallography. These crystallographic studies have been used to demonstrate that the internuclear distance between the atoms at the base of the cyclopropenyl structure is indeed longer than would be expected for a normal cyclopropane molecule, while the external bonds appear to be shorter, indicating involvement of the internal cyclopropane bond in charge delocalization. Molecular orbital description The molecular orbital explanation of the stability of homoaromaticity has been widely discussed with numerous diverse theories, mostly focused on the homotropenylium cation as a reference. R.C. Haddon initially proposed a Mobius model where the outer electrons of the sp3 hybridized methylene bridge carbon(2) back-donate to the adjacent carbons to stabilize the C1-C3 distance. Perturbation molecular orbital theory Homoaromaticity can better be explained using Perturbation Molecular Orbital Theory (PMO) as described in a 1975 study by Robert C. Haddon. The homotropenylium cation can be considered as a perturbed version of the tropenylium cation due to the addition of a homoconjugate linkage interfering with the resonance of the original cation. First-order effects The most important factor in influencing homoaromatic character is the addition of a single homoconjugate linkage into the parent aromatic compound. The location of the homoconjugate bond is not important as all homoaromatic species can be derived from aromatic compounds that possess symmetry and equal bond order between all carbons. The insertion of a homoconjugate linkage perturbs the π-electron density an amount δβ, which depending on the ring size, must be greater than 0 and less than 1, where 0 represents no perturbation and 1 represents total loss of aromaticity (destabilization equivalent to the open chain form). It is believed that with increasing ring size, the resonance stabilization of homoaromaticity is offset by the strain in forming the homoconjugate bridge. In fact, the maximum ring size for homoaromaticity is fairly low as a 16-membered annulene ring favours the formation of the aromatic dication over the strained bridged homocation. Second-order effects