Slab calculations

Pisani [169] has used the density of states from periodic FIP (see B3.2.2.4) slab calculations to describe the host in which the cluster is embedded, where the applications have been primarily to ionic crystals such as LiE. The original calculation to derive the external Coulomb and exchange fields is usually done on a finite cluster and at a low level of ab initio theory (typically minimum basis set FIP, one electron only per atom treated explicitly). 

Philipsen P H T, te Velde G and Baerends E J 1994 The effect of density-gradient corrections for a molecule-surface potential energy surface. Slab calculations on Cu(100)c(2x2)-C0 Chem. Phys. Lett. 226 583... 

SLAB calculates chemical concentrations at positions downwind and heights above the ground. Tlic plume may be denser-than-air, neutrally-buoyant, or less dense than air. Thermodynamics effeci.s are accounted for, including latent heat exchanges due to the condensation or evaporation ot liquids, Time averaged results may be calculated. SLAB is the easiest of the publicly-available dense gas models to set up and mn. It has been extensively validated against large-scale field data. 

Recently, we hav measured the surface phonon dispersion of Cu(l 10) along the rx, rF, and F5 azimuth of the surface Brillouin zone (Fig. 13) and analyzed the data with a lattice dynamical slab calculation. As an example we will discuss here the results along the TX-direction, i.e. the direction along the close-packed Cu atom rows. 

As an example, the DFT-calculated surface energies of copper surfaces are shown in Table 4.2 for the same set of slab calculations that was described in Table 4.1. The surface energy of Cu(l 11) is lower than for Cu(100), meaning that Cu(l 11) is more stable (or more bulklike ) than Cu(100). This is consistent with the comment we made in Section 4.4 that the most stable surfaces of simple materials are typically those with the highest density of surface atoms. We can compare our calculated surface energy with an experimental... 

Keywords Atomic scale characterization surface structure epoxidation reaction 111 cleaved silver surface oxide STM simulations DFT slab calculations ab initio phase diagram free energy non-stoichiometry oxygen adatoms site specificity epoxidation mechanism catalytic reactivity oxametallacycle intermediate transition state catalytic cycle. 

Fig. 7. Models of platinum slabs (a) Pt(lll) slab, (b) Pt(211) slab. Shaded atoms illustrate the supercell used for slab calculations. Adapted from (53).

The main advantage of periodic boundary conditions is the elimination of edge effects or terminal atom problems that occur in the finite cluster approach. The Hamiltonian in slab calculations is generally limited to density functional theory11, an approach that is not always an appropriate choice. 

Comparison of surface densities of V, C and M0S2 slabs calculated according to an hexagonal geometrical model (31). 

It is normal to set the cell vector lengths based on the bulk optimized structure at the level of theory to be used in the slab calculations. This choice gives lattice parameters with zero strain in the bulk which is a likely constraint on the surface repeat unit. 

The electronic structure of the a-Al203(0001) surface also shows features that differ from the bulk material [30]. Figure 8.16 compares the calculated DOS for the dense phase with that of a slab calculation. In the DOS for the slab (Figure 8.16b) a state just below the bottom of the conduction band can be seen which... 

In our lit, the subsurface (n = 1) peak of the clean sample falls approximately halfway between the surface and bulk resonances. This is in very good agreement with a five-layer slab calculation (70) and shows that more than half of the spectrum contains information from the surface region. It should be noted that NMR layer model considers directly the layer-to-layer variation of the NMR shift, whereas it would perhaps be more reasonable physically to start from a hypothesis concerning the variation of the density of states (Section VI.C). 

A simple test of this suggestion is the comparison of a five-layer slab calculation for the Knight shift in platinum (70) with the spectral fits of the layer model (Fig. 48). In both cases the surface resonance is shifted about 4% to low field wuth respect to the bulk signal, and the subsurface signal is found at approximately the halfway point. Another test is qualitatively to compare experimental results for hydrogen chemisorption on platinum (Fig. 55) with a calculation for hydrogen on palladium (175) in both cases an important diminution of the surface LDOS on the metal is found. 

Polar M/C interfaces have only been studied sparsely. The polar (111) and nonpolar (100) Cu/MgO interfaces were compared in a slab calculation within the LDA. ° As expected from the image model theory, the polar interface displayed a considerably higher work of separation. In addition, these authors found a larger charge transfer and Cu-MgO orbital mixing for the polar interface. 

Hjj extended Hiickel slab calculations for Pt on a-Al203(0001). Both authors agree that Pt binds to the -terminated surface by 0.1 eV/Pt, but for the Al -terminated surface Ward et find 3.7 eV/Pt whereas Anderson et obtain 2.5 eV/Pt. Interestingly, in the same study. Ward et al. find that Rh does not bind at all whereas Pd does, opposite to the nobleness trend found for the termination. 

In slab calculations, a finite number of layers mimicks the semi-infinite system, with a two-dimensional (2D) translational periodicity. A minimal thickness dmin is required, so that the layers in the slab centre display bulk characteristics. Practically speaking, dm-,n should be at least equal to twice the damping length of surface relaxation effects, which depend upon the surface orientation. In plane wave codes, the slab is periodically repeated... 

Calvo and Balbuena examined the structure and reactivity of Pd-Pt nanoclusters with 10 atoms in the oxygen reduction reaction. In contrast with what is expected in a periodic slab calculation, they found that mixed states with randomly distributed Pd atoms in a Pt7Pd3 cluster was more stable than an ordered cluster structure due to more eflective charge transfer in the mixed state. They found that increasing the concentration of Pd in the surface favors formation of the OOH species in the first step of the reaction, but Pt atoms were needed to promote the second stage of the oxygen reduction reaction. They report that due to charge transfer eflhcts the Pd atoms have an intermediate reactivity between pure Pd and Pt, and in the mixed cluster the Pd atoms the Pd atoms act more similarly to Pt than in the ordered cluster. 

DF slab calculations have been used to study in a systematic way the effects of bimetallic bonding on the valence band of Pd and many other metals [14,36,101,102]. For metal overlayers, the strain induce by the metal substrate on... 

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