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.