Slab method, surface calculations

Using this model and calculational method, a calculation with just one water molecule in the space between the simulated copper slabs gave an on-top site (oxygen down) as the lowest energy water configuration on a 100 surface with a binding energy of about 0.4 eV. Then we did a calculation [35] with 245 molecules in the space between the planes and found the oxy-... 

The PES scans described in Sect. 3.1 involved moving slabs representing surfaces relative to one another to mimic shear and/or compression. Although that section focused on static calculations, this approach can also be used in conjunction with MD simulation methods. In this approach, one constructs a system composed of two slabs that are to be moved relative to one another, which are potentially separated by molecular species that are to be subjected to stresses. A typical example would place lubricant molecules between two surfaces to study lubrication, but this approach can be used in the context of studying other stress-induced processes as well. 

The electronic structures of high-symmetry TiC and WC surfaces have been investigated by Fujimori, Minomi and Tsuda (1982), Wimmer (1984), Wimmer, Neckel and Freeman (1985) and Mattheiss and Hamman (1984) using band methods. Fig. 8.12 shows the DOSs for nine- and five-layer slabs simulating (111) Ti carbide surfaces calculated by Fujimori et al (the calculations have been performed using the parametrised tight-binding method). The DOS near the Fermi level (mainly of the Tid-type) is essentially increased for the outer monolayer of polar surface. 

In the finite-difference appntach, the partial differential equation for the conduction of heat in solids is replaced by a set of algebraic equations of temperature differences between discrete points in the slab. Actually, the wall is divided into a number of individual layers, and for each, the energy conserva-tk>n equation is applied. This leads to a set of linear equations, which are explicitly or implicitly solved. This approach allows the calculation of the time evolution of temperatures in the wall, surface temperatures, and heat fluxes. The temporal and spatial resolution can be selected individually, although the computation time increa.ses linearly for high resolutions. The method easily can be expanded to the two- and three-dimensional cases by dividing the wall into individual elements rather than layers. 

The three-dimensional symmetry is broken at the surface, but if one describes the system by a slab of 3-5 layers of atoms separated by 3-5 layers of vacuum, the periodicity has been reestablished. Adsorbed species are placed in the unit cell, which can exist of 3x3 or 4x4 metal atoms. The entire construction is repeated in three dimensions. By this trick one can again use the computational methods of solid-state physics. The slab must be thick enough that the energies calculated converge and the vertical distance between the slabs must be large enough to prevent interaction. 

The Vacuum Reference The first reference in the double-reference method enables the surface potential of the metal slab to be related to the vacuum scale. This relationship is determined by calculating the workfunction of the model metal/water/adsorbate interface, including a few layers of water molecules. The workfunction, — < ermi. is then used to calibrate the system Fermi level to an electrochemical reference electrode. It is convenient to choose the normal hydrogen electrode (NHE), as it has been experimentally and theoretically determined that the NHE potential is —4.8 V with respect to the free electron in a vacuum [Wagner, 1993]. We therefore apply the relationship... 

These analyses require that the 10) values for normal incidence be modified for irradiation geometries where the field is incident other than perpendicular to the surface of the personal monitor. The methods used in developing these modifications to fl pdO) for nonnormal incidence included extensive Monte Carlo calculations of photon interactions in anthropomorphic phantoms (Xu, 1994) or in PMMA and tissue slabs and the ICRU sphere (Grosswendt, 1991 Grosswendt and Hohlfeld, 1982), and thermoluminescent dosimeter measurements in water cubes (Lakshmanan et al., 1991). Some of these modifications for /fp(lO) are presented in ICRU (1992). 

We evaluated adsorbed SO3 configuration on Pt (111) surface by using the first-principles calculations with a slab model in a periodic boundary condition. On the basis of the result of the calculations with a slab model, we evaluated the electronic states of SO3 in detail using the relativistic DV-Xa molecular orbital method. 

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