Analytic quadratic integration over the two-dimensional Brillouin zone

Wiesenekker, G.; Velde, G. te; Baerends, Evert Jan

doi:10.1088/0022-3719/21/23/012

Cited by 67 publications

(53 citation statements)

References 17 publications

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“…57 The k-space integration can be done accurately using the quadratic tetrahedron method. 58 No shape approximations are made to the potentials. The error in the binding energy as a result of the numerical methods used in BAND to solve the Kohn-Sham equations, such as the integrations in real space and in k space, are well below the errors in the binding energy due to intrinsic errors such as the choice of basis set, the size of the unit cell or coverage ͑to approximate single-molecule adsorption͒, and the number of layers in the slab, to be discussed below.…”

Section: A Density Functional Methodsmentioning

confidence: 99%

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Dissociation of H2 on Cu(100): Dynamics on a new two-dimensional potential energy surface

Wiesenekker

Kroes

Baerends

et al. 1995

The Journal of Chemical Physics

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A two-dimensional ͑2-D͒ potential energy surface ͑PES͒ has been calculated for H 2 interacting with the ͑100͒ face of copper. The PES is for H 2 approaching with its internuclear axis parallel to the surface and dissociating over a bridge site into neighboring hollow sites. The density functional calculations were performed both within the local density approximation ͑LDA͒ and within a generalized gradient approximation ͑GGA͒. The LDA surface shows no barrier to chemisorption, but the GGA surface has a barrier of height 0.4 eV. A fit of the GGA surface has been used to calculate reaction probabilities for H 2 in its vϭ0 and vϭ1 vibrational states, employing a wave packet method. The 2-D wave packet results for the vϭ0 and vϭ1 thresholds are consistent with experiment, indicating that the barrier height calculated within the GGA used is accurate. The GGA results for the value of the barrier height are also consistent with the GGA value ͑0.

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Section: A Density Functional Methodsmentioning

confidence: 99%

“…The irreducible wedge of the first Brillouin zone consists of two triangles. In each triangle six k points were chosen, allowing the use of the quadratic k-space integration method 58 in each triangle. The total number of k points is 9, of which 6 are symmetry unique.…”

Section: Figmentioning

confidence: 99%

Dissociation of H2 on Cu(100): Dynamics on a new two-dimensional potential energy surface

Wiesenekker

Kroes

Baerends

et al. 1995

The Journal of Chemical Physics

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“…The basis functions for Pd, Cd, Ag, Au, Cu, Ni, Pt, Pb, Sn, Fe, Rh and Ru were frozen up to the 3d, 3d, 3d, 4f, 2p, 2p, 4f, 4f, 4p, 2p, 3d and 3d shells, respectively. The accurate quadratic tetrahedron procedure [26] was used for Brillouinzone (BZ) integrations, and integration parameters were chosen to achieve convergence well within 50 meV.…”

Section: Model and Simulation Methodsmentioning

confidence: 99%

The influence of electronic structure on hydrogen absorption in palladium alloys

Kramer

Løvvik

2004

J. Phys.: Condens. Matter

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The influence of the electronic structure and the lattice constant on hydrogen absorption in bulk Pd 3 M 1 (M = Cd, Ag, Au, Pd, Cu, Ni, Pt, Pb, Sn, Fe, Rh, Ru) has been studied by density-functional calculations. We have assumed face-centred cubic structure for all the alloys, and hydrogen has been placed in the octahedral site surrounded by six Pd atoms. We have calculated the absorption energy of hydrogen in the alloys, and found that the influence of the electronic structure is much more important than that of the lattice constant. The results demonstrate that Miedema's empirical rule is also satisfied in this system, i.e., the higher the binding energy of the host alloy, the less stable the hydride. We have also calculated the detailed electronic structures of the alloys and their hydrides. We found that more stable hydrogen absorption is correlated with the hydrogen 1s electrons, palladium s electrons, palladium s-like electrons and the palladium d electrons moving higher in energy towards the Fermi level. The two latter relations have previously been described for bulk systems and surfaces respectively, while this study is apparently the first to point out the correlation between the position of the hydrogen band and the stability of the hydride, i.e., the deeper the hydrogen band, the less stable the hydride.

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“…The program uses accurate numerical integration methods for integrals in real space 67 and in k space. 68 There is considerable flexibility in the description of the one-electron states; the basis sets consist of numerical atomic orbitals ͑NAO's͒, Slater type orbitals ͑STO's͒ or a combination of both. The core-electrons can be modeled using the frozen core approximation, thus avoiding any arbitrariness that may be associated with the use of pseudopotentials.…”

Section: A Methodsmentioning

confidence: 99%

“…For both parallel and tilted ap-proaches the irreducible wedge of the first Brillouin zone consists of two triangles. In each triangle six k points were chosen so that the analytic quadratic method for numerical integration in k space could be used, 68 giving a total of nine symmetry unique k points.…”

Section: A Methodsmentioning

confidence: 99%

An analytical six-dimensional potential energy surface for dissociation of molecular hydrogen on Cu(100)

Wiesenekker

Kroes

Baerends

1996

The Journal of Chemical Physics

121

115

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A six-dimensional ͑6D͒ potential energy surface ͑PES͒ describing the molecule-surface interaction in the dissociative chemisorption system H 2 ϩCu͑100͒ is presented. The PES is based on slab calculations performed using the generalized gradient approximation ͑GGA͒ of density functional theory ͑DFT͒. To allow the use of the PES in dynamics calculations which can test the validity of the DFT/slab approach by comparing with available experiments on dissociative chemisorption, the PES was fit to an analytical form. The fit used describes the orientational dependence of the molecule-surface interaction above the high symmetry sites upto second order in spherical harmonics. The barriers to dissociation calculated for H 2 approaching with its molecular axis parallel to the surface are all located in the exit channel. Also, for different impact sites and orientations, the height and the distance to the surface associated with the barrier correlate well with the chemisorption energy of the H-atoms in the sites to which dissociation takes place; the lowest barrier ͑0.48 eV͒ is found for dissociation over the bridge site into the hollow sites, the atomic chemisorption energy being highest in the hollow sites.

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Analytic quadratic integration over the two-dimensional Brillouin zone

Cited by 67 publications

References 17 publications

Dissociation of H2 on Cu(100): Dynamics on a new two-dimensional potential energy surface

Dissociation of H2 on Cu(100): Dynamics on a new two-dimensional potential energy surface

The influence of electronic structure on hydrogen absorption in palladium alloys

An analytical six-dimensional potential energy surface for dissociation of molecular hydrogen on Cu(100)

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