Surfaces periodic slab

Kruger and Rosch implemented within DFT the Green s matrix approach of Pisani withm an approximate periodic slab enviromnent [180]. They were able to successfiilly extend Pisani s embeddmg approach to metal surfaces by smoothing out the step fiinction that detenuines the occupation numbers near the Fenui level. 

While quantum-chemical calculations related to gas-phase reactions or bulk properties have become now a matter of routine, calculations of local properties and, in particular, surface reactions are still a matter of art. There is no simple and consistent way of adequately constructing a model of a surface impurity or reaction site. We will briefly consider here three main approaches (1) molecular models, (2) cluster models, and (3) periodic slab models. 

As to periodic slab models, their application is rather straightforward, but poses many problems in the cases when the activation energy should be found for a surface reaction at a bulky surface group. On the other hand, this is probably the best approach to determine the structural properties of an active site and the interaction energies between an active site and the reacting species. 

Detailed models of the (0001) - O terminated polar surfaces were investigated using interatomic potentials within the two-dimensional periodic slab model realized within the MARVIN code. Two typical local environments were identified as terrace termination and interstitial vacancy sites the latter has been used as the active site for the majority of calculations, as illustrated in Figure 5. The atoms highlighted in the figure indicate the surface embedded quantum region. For... 

Atomic and molecular adsorption at vanadium oxide surfaces have been studied theoretically using both periodic slab and cluster models where so far studies are restricted to the pentoxide, V2O5, as a substrate due to its possible importance in catalytic applications as mentioned before. Further, adsorbate species include in all cases atoms (H [122-123, 126, 136-142], O (see below)) or rather small molecules (O2 (see below), H2O [143-144], NH3 [145-147], NO [146, 148], C2H4 [149], propene (CsHg) [140], toluene (CeHsCHj) [140]) that are of catalytic interest but also small enough to make meaningful calculations feasible. 

Up to now, theoretical work on molybdenum oxide surfaces has been restricted to only few periodic slab as well as local cluster studies on the single valence oxide surfaces Mo03(010), (100) and MoO2(011). As for vanadium oxide, there is very little experimental information on quantitative microscopic details of these complex surfaces despite their importance concerning catalytic applications. The following discussion of theoretical results will be based exclusively on cluster studies that have yielded rather detailed microscopic insight. 

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. 

In this chapter we review the field of electronic structure calculations on metal clusters and nano aggregates deposited on oxide surfaces. This topic can be addressed theoretically either with periodic calculations or with embedded cluster models. The two techniques are presented and discussed underlying the advantages and limitations of each approach. Once the model to represent the system is defined (periodic slab or finite cluster), possible ways of solving the Schrddinger equation are discussed. In particular, wave function based methods making use of explicit inclusion of correlation effects are compared to methods based on functionals of the... 

FIGURE 10.6 Computational models of Au surfaces. Models are shown with optimized O2 geometries. For Au(m) and Au(211), a single unit cell of the periodic slab is shown [34]. Reprinted with permission from [34]. Copyright (2005) American Chemical Society. 

Reliable and accurate potential energy surfaces on the basis of quantum chemistry for the interaction between molecules and ions with the metal surface are stiU very scarce. Especially, cluster calculations fail to reach the limit in which the cluster of metal atoms begins to exhibit metallic properties. Methods based on periodic slabs appear to be more promising for the future to... 

C-H bond cleavage as high as 79.4 kcal/mol. When the triplet PES was taken into account, the initial barrier was reduced to 55.0 kcal/mol, which is still too high to be compared with the experimental number (23.7 kcal/mol [61]). They did not study the H-abstraction mechanism. On the contrary, cluster model studies by Goddard [57] (c.f. Fig. 9) and by Sauer [66] clearly showed that H-abstraction mechanism was dominant for propane activation over V-based catalyst, consistent with our calculations. Fan et al. [67] have carried out a periodic slab calculation on mechanisms for ODHP over V2O5 (001) surface. Three possible mechanisms have been explored, namely, oxo-insertion mechanism, concerted mechanism, and radical mechanism, which resembles TS5, TS4, and TS6 in Fig. 5, respectively. Based on their slab model calculations, the authors claimed that for initial C-H... 

FIGURE 7.10 Side view models showing the system and protocol adopted for the reactive molecular dynamics simulation of the interaction of chloride ions with passivated copper surfaces. Left Cu(l 11) slab covered by CU2O thin films with O-deficient (top) and O-enriched (bottom) terminations after thermal relaxation at 300 K. Middle filling the gap with 20 M Cl" aqueous solution (pH 7). Right complete system after relaxation for 250 ps at 300 K showing preferential interaction of the chlorides ions with the O-deficient surface. Periodic boundary conditions apply along the x-, y-, and z-directions.Adapted from Jeon et al. [135], 1229, with permission from the Ameriean Chemical Society. 

Dissolution reactions, for example, need to take into account the surrounding water molecules. In conventional MO-TST, one may use larger clusters and any of the two hydration schemes. An alternative is a periodic slab to model a crystal surface, explicitly adorned with water molecules and optionally given an implicit hydration treatment. The significance of applying these continuum solvation methods on MO-TST studies has not been well established in geochemistry. 

Atomistic Simulation. The simplest models of surfaces are based on an ionic model in which the structure of the surface is largely controlled by electrostatic considerations. In these cases, the electrostatic interaction between ions can be modeled using periodic adaptations of the Coulombic sum, usually the Ewald sum for the 3D periodic slab calculations and its 2D adaptations for dedicated surface simulation codes such as METADISE (397) and MARVIN (398). The inclusion of anion polarizability via the shell model is easily incorporated into these calculations since the shell can be treated as an additional interaction center and its interaction with its own core subtracted after the periodic sum has been carried out. 

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