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By K. Horn, M. Scheffler

This publication is the second one quantity within the guide of floor technology sequence and offers with elements of the digital constitution of surfaces as investigated through the experimental and theoretical equipment of physics. the significance of knowing floor phenomena stems from the truth that for plenty of actual and chemical phenomena, the outside performs a key position: in digital, magnetic, and optical units, in heterogenous catalysis, in epitaxial development, and the appliance of protecting coatings, for instance. consequently a greater realizing and, eventually, a predictive description of floor and interface houses is essential for the growth of contemporary know-how. An research of floor digital constitution can also be imperative to our figuring out of all features of surfaces from a primary perspective. The chapters offered the following evaluation the objectives accomplished within the box and map out the demanding situations forward, either in test and thought.

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L A . . ,L . ,h semi-infinite solid repeated slab single slab or thin film jellium layer KKR Green's functions PP-PW FLAPW LMTO FLMTO FLAPW localized orbital methods cluster localized orbital methods (numerical, STO's, Gaussians) Fig. 3. Geometric models for practical surface calculations. The geometry of a semi-infinite solid is mainly used in jellium calculations and methods employing Green's functions and matching techniques. Standard band structure methods using three-dimensional periodicity can be directly applied to a repeated slab geometry.

After a sweep over all bands the accuracy in the minimization procedure is tightened and each band is updated again. In pseudopotential plane wave calculations each basis function corresponds to a certain kinetic energy given by h2 TG=-~Ik+GI 2m 2. 71) 38 E. J. Freeman Each step in the conjugate gradient scheme tends to reduce errors in the trial wave function emphasizing a certain energy range. In order to ensure the proper weighting of the important low-energy (long wave length) components, convergence is improved by so-called preconditioning.

42) 18 E. J. Freeman If one takes the non-relativistic limit of Eq. 38) retaining the first relativistic correction, we obtain the familiar Pauli-type equation for a magnetic field coupling to the spins only (Baym, 1976) 2m 8m3c 2 ( -#B~" /~----(VV2mc h2e V 2 V ) ] ~ - - ( e - m c 2 ) ~ . 43) In this equation B and V are the effective magnetic fields and potentials which include the exchange-correlation effects. The set of self-consistent Eqs. 42), in principle, yields the correct charge and magnetization densities.

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