Applications of the generalized-gradient approximation to atoms, clusters, and solids

Calculations have been performed using the generalized-gradient approximation (GGA) for the exchange-correlation functional of Perdew, Burke, and Ernzerhof (PBE) within density-functional theory for atoms, clusters, and crystals, including crystalline C, Al, Si, and GaAs. The calculations of the atomic total energy and the first ionization energy with the PBE functional are more accurate than with the local density approximation. An efficient vector form of exchange-correlation potentials by Hamann was used for the GGA exchange-correlation potential calculations. Structural properties of the small Si clusters and solids, such as cohesive energy, lattice constant, bulk modulus, and phonon energy, are investigated and compared with other calculations and experiments.