A simple formulation of a generalized gradient approximation for the exchange and correlation energy of electrons has been proposed by Perdew, Burke, and Ernzerhof ͑PBE͒ ͓Phys. Rev. Lett. 77, 3865 ͑1996͔͒. Subsequently Zhang and Yang ͓Phys. Rev. Lett. 80, 890 ͑1998͔͒ have shown that a slight revision of the PBE functional systematically improves the atomization energies for a large database of small molecules. In the present work, we show that the Zhang and Yang functional ͑revPBE͒ also improves the chemisorption energetics of atoms and molecules on transition-metal surfaces. Our test systems comprise atomic and molecular adsorption of oxygen, CO, and NO on Ni͑100͒, Ni͑111͒, Rh͑100͒, Pd͑100͒, and Pd͑111͒ surfaces. As the revPBE functional may locally violate the Lieb-Oxford criterion, we further develop an alternative revision of the PBE functional, RPBE, which gives the same improvement of the chemisorption energies as the revPBE functional at the same time as it fulfills the Lieb-Oxford criterion locally. ͓S0163-1829͑99͒02711-3͔

A grid-based real-space implementation of the projector augmented wave ͑PAW͒ method of Blöchl ͓Phys. Rev. B 50, 17953 ͑1994͔͒ for density functional theory ͑DFT͒ calculations is presented. The use of uniform three-dimensional ͑3D͒ real-space grids for representing wave functions, densities, and potentials allows for flexible boundary conditions, efficient multigrid algorithms for solving Poisson and Kohn-Sham equations, and efficient parallelization using simple real-space domain-decomposition. We use the PAW method to perform all-electron calculations in the frozen core approximation, with smooth valence wave functions that can be represented on relatively coarse grids. We demonstrate the accuracy of the method by calculating the atomization energies of 20 small molecules, and the bulk modulus and lattice constants of bulk aluminum. We show that the approach in terms of computational efficiency is comparable to standard plane-wave methods, but the memory requirements are higher.

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Gradient-corrected density-functional theory ͑DFT-GGA͒ periodic slab calculations have been used to analyze the binding of atomic hydrogen on monometallic Pd͑111͒, Re͑0001͒, and bimetallic Pd ML /Re(0001) ͓pseudomorphic monolayer of Pd͑111͒ on Re͑0001͔͒ and Re ML /Pd(111) surfaces. The computed binding energies of atomic hydrogen adsorbed in the fcc hollow site, at 100% surface coverage, on the Pd͑111͒, Re͑0001͒, Pd ML /Re(0001), and Re ML /Pd(111) surfaces, are Ϫ2.66, Ϫ2.82, Ϫ2.25, and Ϫ2.78 eV, respectively. Formal chemisorption theory was used to correlate the predicted binding energy with the location of the d-band center of the bare metal surfaces, using a model developed by Hammer and Nørskov. The DFTcomputed adsorption energies were also analyzed on the basis of the density of states ͑DOS͒ at the Fermi level for the clean metal surfaces. The results indicate a clear correlation between the d-band center of the surface metal atoms and the hydrogen chemisorption energy. The further the d-band center is from the Fermi level, the weaker is the chemisorption bond of atomic hydrogen on the surface. Although the DOS at the Fermi level may be related to the location of the d-band, it does not appear to provide an independent parameter for assessing surface reactivity. The weak chemisorption of hydrogen on the Pd ML /Re(0001) surface relates to substantial lowering of the d-band center of Pd, when it is pseudomorphically deposited as a monolayer on a Re substrate.