Zero point motion effect on the electronic properties of diamond, trans-polyacetylene and polyethylene

It has been recently shown, using ab-initio methods, that bulk diamond is characterized by a large band-gap renormalization (similar to 0.6 eV) induced by the electron-phonon interaction. In this work we show that in polymers, compared to bulk materials, the larger amplitude of the atomic vibrations makes the real excitations of the system be composed by entangled electron-phonon states. We prove that these states carry only a fraction of the electronic charge, thus leading, inevitably, to the failure of the electronic picture. The present results cast doubts on the accuracy of purely electronic calculations. They also lead to a critical revision of the state-of-the-art description of carbon-based nanostructures, opening a wealth of potential implications.