Connection between slab and cluster models for crystalline surfaces

Abstract

Different models for the theoretical description of bare crystalline surfaces are compared and discussed in terms of stoichiometry and conservation of the point symmetry. While infinite models such as the semi-infinite model or the slab model in general preserve the symmetry of the perfect crystal surface, special care has to be taken when finite cluster models are considered. The connection between molecular cluster choice and surface unit cell of the slab model is demonstrated for metal oxides such as MgO, TiO 2 , V 2 O 5 , and Al 2 O 3 , analyzing how atoms of the primitive unit cell of the parent three-dimensional crystal are distributed in different planes of slab and cluster models. General rules for the construction of finite cluster models based on stoichiometry and symmetry considerations are given and illustrated with calculations on water adsorption at rutile (110).Crystalline surfaces are of high importance in many chemical and physical processes [1,2]. They are therefore subject of an increasing number of studies, both experimental and theoretical [3]. In the last decades, quantum-chemical calculations have become an important tool for investigations of structural, electronic and catalytic properties of surfaces. Methodological developments and the rapid improvement of computer hardware enabled theorists to treat systems of increasing complexity. Thereby it was possible not only to reproduce experimental findings with increasing accuracy, but also to aid in the interpretation of experimental results.For simulations of the electronic structure of surfaces of crystalline solids three basic approaches are used: cluster, slab, and semi-infinite crystal models [4]. The latter is the most appropriate, because it takes into account an infinite number of atoms of the crystal below the surface [5]. Slab and cluster models are nevertheless by far more popular, since they are more feasible from the computational point of view. The cyclic cluster model [4] is intermediate between slab and molecular cluster models. It takes into account the translational symmetry of the surface but considers only a finite number of interatomic interactions within a strictly defined region.The choice of the cluster model (both molecular and cyclic) for a surface allow to employ all those quantum chemical techniques that have been developed for molecular systems. It is also possible to study defects or adsorption reactions in the limit of low coverage. Care has to be taken in the selection of cluster size and shape due to the unavoidable presence of boundary effects. Different schemes have been developed to reduce boundary effects in the cluster model, either by embedding procedures or by the introduction of cyclic boundary conditions. Slab models eliminate twodimensional boundary effects and are widely used for the study of periodic surface structures.In the present work, the connection between slab and cluster models based on a symmetry analysis of the crystalline surface is considered. As far as we know, this connection has not...

Theoretical study of low-index surfaces of trigonal B2O3

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Hartree–Fock calculations of electronic structure of (110)‐surface of rutile TiO2: Comparison of single (2D) and periodic (3D) slab models

“…In the slab model, the surface plane is supposed to be fixed by its orientation relative to the bulk structure and its symmetry elements. All the atoms of the bulk primitive unit cell may be distributed within one or several atomic planes with the same 2D translation periodicity 13. These planes of atoms form a layer that is by definition stoichiometric.…”

“…1(b)]. In this case, the symmetry of the single slab model corresponds to a diperiodic space group DG 37 (one of 80 diperiodic or layer groups 13). This layer group is a subgroup of 3D space group G 47 (D), one of 30 space groups connected with the primitive orthorhombic lattice.…”

Computational study of titanium (IV) complexes with organic chromophores

“…While the determination of local properties such as the excitation of the chromophore or electronic‐vibrational couplings for chromophore modes can be obtained from models with rather small TiO 2 clusters, the study of properties that are related to surface and bulk properties of TiO 2 requires electronic structure methods capable of describing extended systems. Such properties of TiO 2 nanoparticles have been studied employing slab models 22, 24–26, 48, 49, embedded clusters 50, 51, or cyclic clusters 48, 52.…”