Within the framework of methods of the electron density functional and the ab initio pseudopotential, we have obtained the spatial distributions of the valence electrons density, the electron energy spectra and the Coulomb potential for model composite structures consisting of graphene or graphene oxide and ZnO. They were computed using the above methods with the author's program complex. It has been determined that composite structures made of graphene and ZnO are more energy efficient to be formed with oxygen atomic plane of ZnO to graphene. Composite structures of graphene oxide and ZnO are more energy efficient as compared to composites on graphene.

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