Calculation of Surface Structure

LEED studies have revealed that the atoms in this platinum surface are in the positions expected from the projection of the X-ray unit cell to the surface (5). The diffraction pattern that is exhibited (Fig. 4) clearly indicates a sixfold rotational symmetry that is expected in such a surface. Calculations of surface structure from LEED beam intensities indicate that atoms are in those positions in the surface layer (with respect to the second layer) as indicated by the X-ray unit cell within 5% of the interlayer distance (6,7). 

We shall first review the basic principles of VASP and than describe exemplary applications to alloys and compounds (a) the calculation of the elastic and dynamic properties of a metallic compound (CoSi2), (b) the surface reconstruction of a semiconducting compound (SiC), and (c) the calculation of the structural and electronic properties of K Sbi-j, Zintl-phases in the licpiid state. 

Single slab. A number of recent calculations of surface electronic structures have shown that the essential electronic and structural features of the bulk material are recovered only a few atomic layers beneath a metal surface. Thus, it is possible to model a surface by a single slab consisting of 5-15 atomic layers with two-dimensional translational symmetry parallel to the surface and vacuum above and below the slab. Using the two-dimensional periodicity of the slab (or thin film), a band-structure approach with two-dimensional periodic boundary conditions can be applied to the surface electronic structure. 

Calculation of surface gravity as a marker for internal planetary structure... 

The structure and dynamics of clean metal surfaces are also of importance for understanding surface reactivity. For example, it is widely held that reactions at steps and defects play major roles in catalytic activity. Unfortunately a lack of periodicity in these configurations makes calculations of energetics and structure difficult. When there are many possible structures, or if one is interested in dynamics, first-principle electronic structure calculations are often too time consuming to be practical. The embedded-atom method (EAM) discussed above has made realistic empirical calculations possible, and so estimates of surface structures can now be routinely made. 

However, the advent of very fast spectroscopic techniques, such as nanosecond and picosecond LFP, now makes it possible to observe the hound itself, while the ever-increasing power of computational methods permits remarkably accurate calculations of the structures and energies associated with carbenes and other reactive intermediates, and often of the potential energy surfaces on which their reactions occur. 

DFT calculations of the structure of the molecularly adsorbed NO are in reasonable agreement with experiments, but overestimate the binding energy [197,198]. A barrier of 2.1 eV to dissociation is predicted by DFT, with the NO at the transition state nearly parallel to the surface and N and atoms in bridge sites [199]. This transition state geometry is similar to that of NO dissociation on other close-packed metal surfaces [200]. There is no global DFT PES so that all theoretical dynamics is based only on empirical model PES. 

In more detail, our approach can be briefly summarized as follows gas-phase reactions, surface structures, and gas-surface reactions are treated at an ab initio level, using either cluster or periodic (plane-wave) calculations for surface structures, when appropriate. The results of these calculations are used to calculate reaction rate constants within the transition state (TS) or Rice-Ramsperger-Kassel-Marcus (RRKM) theory for bimolecular gas-phase reactions or unimolecular and surface reactions, respectively. The structure and energy characteristics of various surface groups can also be extracted from the results of ab initio calculations. Based on these results, a chemical mechanism can be constructed for both gas-phase reactions and surface growth. The film growth process is modeled within the kinetic Monte Carlo (KMC) approach, which provides an effective separation of fast and slow processes on an atomistic scale. The results of Monte Carlo (MC) simulations can be used in kinetic modeling based on formal chemical kinetics. 

This approach was successfully used in modeling the CVD of silicon nitride (Si3N4) films [18, 19, 22, 23]. Alternatively, molecular dynamics (MD) simulations can be used instead of or in combination with the MC approach to simulate kinetic steps of film evolution during the growth process (see, for example, a study of Zr02 deposition on the Si(100) surface [24]). Finally, the results of these simulations (overall reaction constants and film characteristics) can be used in the subsequent reactor modeling and the detailed calculations of film structure and properties, including defects and impurities. 

One group of techniques is sensitive to electronic structure at the surface, and can probe the electronic band structure and density of states near the Fermi level. This electronic information is useful for understanding the bonding mechanisms responsible for chemical process operating at the surface. Structural information can also be obtained by comparing experimentally observed electronic structure with theoretical calculations of electronic structure for model systems (see part 4). 

As to the content of Volume 20, the Editors would like to thank the authors for their contributions, which give an interesting picture of part of the current state of art of the quantum theory of matter from computational methods of optimizing the electronic energy and molecular conformations, over coupled-cluster expansion methods for the study of the open-shell correlation problem and the calculation of lifetimes of metastable states by means of the method of complex scaling, to a survey of the current state of surface structural chemistry. 

More complex model reactions (selective butadiene hydrogenation) Apart from being accessible to surface spectroscopy, model catalysts also have the advantage that the nanoparticle morphology and surface structure can be accurately measured. This advantage allows the determination of the relative abundance of specific surface sites and calculation of surface site statistics, as shown, for example, in Table II. Knowledge of the exact number and type of available surface sites then allows calculation of more accurate (and perhaps more meaningful) turnover frequencies of catalytic reactions. 

The examples discussed in the previous material serve to illustrate the complexity of surface properties of minerals and related materials, the difficulties of adequate characterization, and the important role to be played by calculations of electronic structure. 

The modeling approaches used to describe the surface reactions of metal ions differ in their definition of surface structure and the charge/potential relationships within the compact layer of the EDL ( 2, 5,. In our previous calculations ( 2) we... 

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