Ab initio modelling of a bilayer graphene

Using the electron density functional theory, numerical modelling of bilayer graphene has been performed. The structure and binding energy of the layers depending on the representation of the wave function of the system have been studied: plane waves (VASP package) and atomic-like orbitals (SIESTA package); and choice of approximation for the exchange-correlation (XC) functional. It has been shown that being in the free form the system creates a stable AB structure of bilayer graphene. The calculation of the layer binding energy has shown that the results of modelling performed with different basis for the wave function are consistent when using XC functionals corresponding to each other and considering the correction to the basis set superposition error in the tight binding method. As expected, the generalized gradient approximation (GGA) has shown underestimated values of the interaction energy of graphene layers. Comparison with experimental data has shown that the energy and geometric characteristics of bilayer graphene are best described by the local electron density approximation (LDA). The 2nd and 3rd generation semi-empirical Grimme corrections for GGA have given estimates of the binding energy higher than LDA, but also close to the experimental results.