Nature of interlayer carbon–carbon covalent bonding in graphene-based materials

This study provides a fundamental understanding of the nature of C–C interlayer covalent bonding in graphene-based materials by using the dispersion-corrected density functional theory B3LYP-D3/6-31+G(2df,p)//B3LYP-D3/6-31G(d,p) (single-point energies at the larger 6-31+G(2df,p) basis set using fully optimized geometries at the B3LYP-D3/6-31G(d,p) level). With a bilayer hydrogenated graphene model, a partial covalent bonding was found upon dehydrogenation from opposite layers between interior carbon atoms even at the distance of greater than 4.00 A. To facilitate such bonding carbon atoms must transform from its sp3 to sp2 hybridization upon dehydrogenation so that pz orbitals can extend farther for better overlap at a large distance. The structure containing a single partial covalent bond was found to be less stable compared to its nonbonding triplet state. However, adding normal interlayer covalent bonds at the edge helps to stabilize such partial bond. In addition, forming a partial interlayer covalent bond greatly reduces band gap to 1 eV, whereas the formation of a normal covalent bond causes only a slight change in the band gap. Thus, controlling the population of the two types of interlayer bonds can, therefore, open up a promising way to control the band gap for organic semiconductor materials.