Local-orbital occupancy formulation of density functional theory:: Application to Si, C, and graphene

A detailed discussion of the local linear combination of atomic orbitals (LCAO) orbital occupancy (OO) density functional approach, for calculating the total energy and electronic properties of solids, is presented. An approximation to the exchange-correlation energy within the OO approach is discussed to improve the computational efficiency. This exchange-correlation energy is incorporated into an efficient first-principles tight-binding code (FIREBALL) in which the Hartree contribution is also calculated as a function of the orbitals occupancies, combining the advantages of the FIREBALL and LCAO-OO approaches. The calculations performed for Si, diamond, and graphene (lattice parameter, cohesive energy, bulk modulus, and electronic band structure) show the good accuracy of the approximations discussed in the paper and indicate the suitability of the FIREBALL-OO approach for calculating the electronic properties of solids.