3. Computational Details
The original molecular structures of the [4]cumulene, S-1,5-dimethyl-[4]cumulene and the were geometry-optimized at the PBE1PBE/aug-cc-pVTZ level of theory with empirical GD3-BJ52,53 dispersion correction using Gaussian09 rev E.0154 with default (tight) geometrical convergence criteria, an ’ultrafine’ DFT integration grid and an SCF convergence criterion of 10-10. All subsequent single-point calculations were also performed using these DFT parameters, basis set and convergence parameters. For the amine-substituted cumulene we start out from three of the six conformations55. At approximately –90° (-)S(-) is rotated into (-)R(-) conformation. Likewise, at approximately –90° (+)S(+) is rotated into (+)R(+) conformation; at approximately –90° (+)S(-) is rotated into (+)R(-) conformation. Variants of the geometry-optimized [4]cumulenes were then generated by ’freezing’ all bond lengths and angles, except for the H-C1-C2-C3-C4 -C5-H geometrical dihedral angle, where C1 and C5 are the carbon atoms at each end of the five-carbon atom chain which were constrained to take specific values. Geometrical dihedral angle = 0.0° was chosen as the angle reference. Hence, only the end groups attached to the C5 carbon atom were allowed to ’rigidly’ rotate about the dihedral axis - all other molecular geometrical degrees of freedom except the chosen dihedral angle were fixed. Positive and negative values of the dihedral angle were chosen in the range -180.0° ≤ 0.0° ≤ +180.0. For each dihedral angle, single-point calculations were performed and the resulting wavefunction analyzed using AIMAll45. The {q ,q ’} path-packets and eigenvector precession profiles were generated from the eigenvectors of the Hessian of the total charge density using the ’framepath’ and ’pathtool’ codes from our in-house code suite QuantVec-Tools56. In all cases, the precession profile reference direction was chosen to be thee1 eigenvector of the Hessian of the charge density at the C1-C2 BCP . The {q ,q ’} path-packets were visualized using the ’topviz’ interactive GUI, also part of QuantVec-Tools, based on the Python 3 ’mayavi2’ visualization library57.