Dewar and Zimmerman originated the idea that the favored transition states for pericyclic reactions are those containing an aromatic number of electrons. What constitutes an aromatic number of electrons depends upon the topology of the system of orbitals.

A Huckel aromatic system is the type with which we already are familiar: all of the interacting p-orbitals share a common nodal plane:

A Huckel system, of course, is aromatic (stabilized by cyclic delocalization) when 4n + 2 electrons are present, and antiaromatic (destabilized ....) when 4n electrons are present.

A Mobius aromatic system has an extra node, introduced by twisting the set of orbitals so that each one forms an angle, theta, with its neighbors.

A Mobius system is aromatic with 4n electrons, and antiaromatic with 4n + 2.

Using this topological dichotomy requires that we build a model of the pericyclic transition state that is as bonding as possible, except for any nodes that may be introduced by the connections formed in the reaction.