What is it about?

The existence of equal energy states in long organic molecules has an important influence on electronic mobility and conductivity. This work explains the emergence of such degenerate electronic states in cyclic complex molecules made of benzene rings. Degeneracy tables for orientable and non-orientable (Moebius band) cases are obtained. Electronic waves propagating on the molecule produce effective segmentation, which simplifies the problem.

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Why is it important?

This work helps to understand conductivity in polymers at a molecular level. The so-called 'accidental' degeneracy is finally explained in terms of molecular geometry and symmetry.


In physics, there are very few examples of systems where extended symmetry groups can be used to explain equal energy states (beyond the obvious configurational regularity of the system). Other cases are dubbed 'accidental', and such was the case for degenerate states in long molecules. With the method of segmentation, we have found that certain wave patterns appear to disconnect the molecule effectively, producing independent wave functions that are equivalent from an energetic point of view. Now we expect this concept to be helpful in the description of more complex compounds.

Emerson Sadurni
Instituto de Física LRT, BUAP

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This page is a summary of: Hidden duality and accidental degeneracy in cycloacene and Möbius cycloacene, Journal of Mathematical Physics, May 2021, American Institute of Physics, DOI: 10.1063/5.0031586.
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