Properties of a T=1 Möbius band with a 2p-AO
basis
- Model A: A 2p AO basis distributed
evenly along a band of finite width (and arbitrary height)
and twist T=1, lying in this plane (e.g. xy), can start at
any arbitrary point.
- Model B: An alternative distribution of the 2p AO
basis at 90° to the plane of the band (e.g. yz) is also
valid.
- After a journey of only one cycle, a node (phase
shift) in the AO basis must occur, due to the nature of the
2p AO.
- The variational (HMO) solution for an even basis is
degenerate for its lowest energy and will place the
node (phase shift) in the AO basis at precisely one or other
of the two intersections of the C2 axis with the
cycle.
- The variational solution for an odd basis is still
degenerate for its lowest energy (the highest level is
non-degenerate; a pattern inverted for an AO basis with
NO phase shift)
- The degeneracies are only true for a cycle of zero
width/height. For a cycle of finite
width/height and hence finite radius, one node
would lie along the axis, the other would be
perpendicular to the axis, the compression and
hence energy of each being clearly different.
© H. S. Rzepa 2006.