Using the SIESTA code, a linear scalable implementation of first principles methods, we obtain the band structure, the density of states (DOS) and the energy gap for some graphene‐like lattices. We use the Generalized Gradient Approximation (GGA), a Perdew, Burke, and Ernzerhof (PBE) scheme and non‐local generation of the pseudopotentials. Si, Ge, GaN and GaAs hexagonal monolayer lattices are studied. The Si and Ge monolayers present a semi‐metal behavior while GaAs and GaN monolayers are semiconductors. The dispersion relations for the Si and Ge have a semi‐lineal behavior near to the fermi level.