By K. Horn, M. Scheffler

This publication is the second one quantity within the instruction manual of floor technological know-how sequence and offers with facets of the digital constitution of surfaces as investigated by way of the experimental and theoretical equipment of physics. the significance of realizing floor phenomena stems from the truth that for lots of actual and chemical phenomena, the skin performs a key position: in digital, magnetic, and optical units, in heterogenous catalysis, in epitaxial development, and the applying of protecting coatings, for instance. as a result a greater figuring out and, finally, a predictive description of floor and interface homes is key for the development of recent expertise. An research of floor digital constitution is additionally valuable to our figuring out of all elements of surfaces from a primary standpoint. The chapters provided right here evaluate the ambitions completed within the box and map out the demanding situations forward, either in scan and thought.

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**Extra resources for Electronic Structure**

**Sample text**

The examples which will be discussed in later sections of this chapter as well as the other articles in this volume will give an overview of the structural, energetic, electronic, optical, and magnetic properties accessible through density functional calculations on surfaces. 5. Representation of wave functions for surfaces On surfaces, the three-dimensional periodicity of a crystal lattice is reduced to twodimensional translational symmetry. ~i (r, kll). 53) Here, T II denotes a two-dimensional translation by integer multiples of the lattice vectors al and a2 in real space (cf.

5. Start geometries for density functional calculations on surfaces are constructed either by using experimental data such as bulk lattice constants, from simpler computational approaches such as force field or semi-empirical methods, or from intuition. The start densities are then constructed from a superposition of atomic densities (calculated for individual free atoms or ions) or results from previous density functional computations are re-used. The fundamental quantities of density functional theory are the electron density and, in the case of spin-polarized systems, also the spin density.

49). 4. 12) depends on the charge density, which is constructed from the one-particle wave functions. These wave functions are solutions of the Kohn-Sham equations. In other words, in order to set up the Kohn-Sham equations one needs to know their solutions. This problem is solved by an iterative, selfconsistent procedure as shown in Fig. 5. Start geometries for density functional calculations on surfaces are constructed either by using experimental data such as bulk lattice constants, from simpler computational approaches such as force field or semi-empirical methods, or from intuition.