Polyynes are linear chains of sp-hybridized carbon that can exhibit helical MOs visually similar to those seen in ↵,!-substituted even [n]cumulenes. Similarly, odd [n]cumulenes can also exhibit helical MOs when the end-groups are rotated away from a co-planar orientation as we show at the top of Figure . There is almost free rotation for the end-groups of polyynes with the ground-state orientation determined by the type of end-groups. The ground state of odd [n]cumulenes is the coplanar geometry and there are considerable barriers to torsion. Because the ground state for both molecules converges to coplanar end-groups, all MOs for structures with a dihedral angle > 0 are single-point calculations where the dihedral angle has been set manually with the remaining internal degrees of freedom frozen. Note that to avoid confusion, we systematically use degrees for the torsion angles of the end-groups, whereas radians are used to denote the helical twist of the MOs. Starting with the diphenyl-diyne, at the top-left of Figure , we show its HOMO at three different dihedral angles of the end-groups. For the molecule to retain C 2 -symmetry, the final step of twisting is at 89.5 instead of at 90 . If we were to rank the three HOMOs shown in terms of their helicality on the basis of visual inspection, it is clear that the 0 -case is the least helical. However, we can not easily distinguish whether the end-group at 45 or 89.5 leads to the most helical MOs, or if the helicality is perhaps equal. The analysis of the cumulated sum of angles provides a quantitative answer to this problem. When the dihedral angle of the end-group is 0 , the cumulated sum of angles increases with a series of steps as we expect from a rectilinear MO. By increasing the dihedral angle of the end-groups, the cumulated sum of twist through the HOMO gradually becomes less staircase-like. Instead, it approaches the constant increase we associate with a helix. We see that increasing the dihedral angle of the end-group correlates systematically with a decrease in the MAD. Therefore, we can quantitatively say that an increase in the torsion angle gives an increase in helicality. This analysis also reveals that the HOMO does not achieve perfect helicality, instead, the increase in helicality saturates with a MAD ⇠ 30 as we approach a dihedral angle of 90 .