From the figure above, it can also be seen that the interaction between two consecutive  AOs is attenuated by the incremental twisting between orbitals by , where  is the angle of twisting between consecutive orbitals, compared to the usual Hückel system.  For this reason resonance integral  is given by
where  is the standard Hückel resonance integral value (with completely parallel orbitals).
Nevertheless, after going all the way around, the Nth and 1st orbitals are almost completely out of phase. (If the twisting were to continue after the th orbital, the st orbital would be exactly phase-inverted compared to the 1st orbital).  For this reason, in the Hückel matrix the resonance integral between carbon  and  is .<br />
For the generic  carbon Möbius system, the Hamiltonian matrix  is:
Eigenvalues for this matrix can now be found, which correspond to the energy levels of the Möbius system. Since  is a  matrix, we will have  eigenvalues  and  MOs. Defining the variable
we have:
To find nontrivial solutions to this equation, we set the determinant of this matrix to zero to obtain
Hence, we find the energy levels for a cyclic system with Möbius topology,
In contrast, recall the energy levels for a cyclic system with Hückel topology,