Simple LCAO basis sets for the first unoccupied bands in graphene

We present a simple way to describe the lowest unoccupied bands in graphene in density functional theory (DFT) calculations using a LCAO (linear combination of atomic orbitals) basis set. By comparison with calculations using a plane wave basis, we show how the symmetries giving rise to these states can be captured by adding long-range orbitals to the standard LCAO basis sets. In particular, using Bessel functions with a long range as additional basis functions retain a minimal basis size. This provides a smaller and simpler atom-centered basis set compared to the standard pseudo-atomic orbitals (PAOs) with multiple polarization orbitals or by adding non-atom-centered states to the basis.