Fully conjugated molecules are defined by extended p-systems; the product of p-orbital overlap resulting in delocalized electronic orbitals. One synthetically important class is the family of linear fully-conjugated molecules: the oligoynes (occasionally found in metal-organic frameworks)[1] and even-numbered-carbon cumulated alkenes such as cumulene, shown in Figure 1a and b, respectively. From the textbook molecular orbital description, odd-numbered-carbon cumulated alkenes like allene (shown in the Figure 1c) are not fully-conjugated due to the odd numbers of sp-hybridized carbons. Allene is also geometrically different from cumulene: the terminal groups are orthogonal. Whilst the textbook description predicts this, the definition is both incomplete and does not explain unprecedented organic reactivity observed in the allene family.Through the application of computational chemistry we have discovered that odd-numbered-carbon cumulated alkenes (the allene family) and extended conjugated oligoynes (ECOs) arefully conjugated with an unusual orbital topology: helical molecular orbitals. Here the HOMO is composed of degenerate right and left-handed helices, Figure 1d, which are separable by molecular substitutions allowing for selective orbital orientations. Our work provides a predictive tool for enantioselective [3+2] cycloadditions involving chiral allenes, predictions of novel materials involving the ECO family, and refined description of the molecular orbital structure of the allenes.[2][1] 'Conductive metal-organic frameworks and networks: fact of fantasy?'C. H. Hendon, D. Tiana, A. Walsh, Phys. Chem. Chem. Phys., 2013, 14 , 13120.[2] 'Helical frontier orbitals of conjugated linear molecules'C. H. Hendon, D. Tiana, A. T. Murray, D. R. Carbery, A. Walsh, Chem. Sci., 2013, 4  , 4278.

21<sup>st </sup>century misconceptions in fundamental organic chemistry: Cumulenes, oligoynes and 3-electron 2-centred bonds

247th National Meeting (2014)

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21st century misconceptions in fundamental organic chemistry: Cumulenes, oligoynes and 3-electron 2-centred bonds

21^stcentury misconceptions in fundamental organic chemistry: Cumulenes, oligoynes and 3-electron 2-centred bonds