Relaxed atoms

Fig. 6.2. Top and side views (in top and bottom sketches of each panel) of adsorption geometries on various metal surfaces. Adsorbates are drawn shaded. Dotted lines represent clean-surface (relaxed) atomic positions arrows show atomic displacements due to adsorption...

Fig. 3 demonstrates partially relaxed atomic structure of the C33H3q[NV] clusters and distribution of isotropic Fermi contact coupling (IFCC) in it, calculated within DFT with 6-3IG basis set. In our previous calculations [8,9], it was shown that the spin density is located mainly at the three C atoms, which are the nearest neighbors to the vacancy of the NV -center. 

When bonds are switched, there is a strong torque on the central atoms, as illustrated by the resultant change in coordinates for atoms 2 and 5 of Fig. 1, and as embedded in the supercell shown in Fig. 2. To first order, only these two atoms move. This is the reason for relaxing atoms in spherical topological shells centered about the central bond. 

SIESTA code, the interactions of valence electrons with the atomic ionic cores are described by the norm-conserving pseudopotentials with the partial core correction of 0.6 au. on the oxygen atom. We used the optimized-zeta plus polarization (DZP) basis sets with medium localization in the SIESTA code. A mesh cutloff energy of 350 Ry, which defines the equivalent plane wave cut-off for the grid, was used. The forces on atomic ions are obtained by the Heilman IFeynman theorem and were used to relax atomic ionic positions to the minimum energy. The atomic forces within the supercell were minimized to within 0.035 eV/A and 0.05 eV/A in the SIESTA and CASTEP codes respectively. 

Fig. 1.79. Relaxed atomic configurations of H2O and O2 coadsorbed on free Ans and Au3o clusters (top) and on Aug/MgO(lOO) (bottom). For the free and snpported Ang cases, the difference-charge-density between the compiete adsorption system and the separated Au8/MgO(100) and O2-H2O complex are displayed, superimposed on the atomic configuration. Charge depletion is shown in dark grey and charge accumulation in gray-white. Light grey, dark, and white spheres correspond to An, O, and H atoms, respectively...

In purely geometric terms, a surface has no intrinsic thickness, but in practical terms a surface must comprise one or more layers of atoms or molecules. When dealing with the properties of solids and liquids, the surface and interior are usually considered separately. This is partly because, for any material of significant mass and volume, the number of atoms at the surface is negligible compared to the number of internal atoms. Mostly, however, it reflects the fact that the mathematical treatment of ordered substances is simplified if the structural periodicity is assumed to be infinite. The important point, and the reason that surface analysis is of interest at all, is that the surface differs in its properties from the bulk (internal) material even though it is made of exactly the same atoms. This is because atoms at the surface are relaxed, i.e., not all the bonds are constrained by interactions with neighboring atoms in the same material. Relaxed atoms have free bonds that are available to interact with atoms and molecules on the surface of the adjacent phase, such as the gas or liquid surrounding a crystalline solid. 

There is also another important problem concerning the nature of ki-netically nonequilibrium states of chemical systems. This problem can be formulated in the following way. What are we dealing with, a nonequilibrium mixture of equilibrium molecules or nonequilibrium molecules In any chemical process there appear molecules in nonequilibrium states. For low-molecular compounds, the electronic and vibrational relaxation after the elementary chemical act takes little time (as a rule, less than 10" -10" s). Therefore, there are relaxed atoms, ions, free radicals, and molecules, i.e., the particles in their equilibrium states, that take part in the subsequent chemical acts of chemical transformations. If a system consisting of low-molecular compounds is removed from the state of chemical equilibrium, then, as a rule, we can speak of a nonequilibrium ensemble of equilibrium molecules. 

In the PP method applied to transition metals one normally treats only the valence s, p, and d electrons, which total five per atom in V and Ta, and six per atom in Mo. Here special pseudopotentials in the Troulher-Martins form [48] have been constructed from scalar-relativistic atomic calculations to be accurate in the pressure range below 400 GPa. An important advantage of the PP method is that it provides accurate forces so that fuUy relaxed atomic configurations can be considered. We have used this capabihty here to obtain accurate relaxed 110 and 211 y surfaces for Ta, Mo, and V. It is also possible to use relaxed PP configurations to perform vahdating FP-LMTO calculations on relaxed defects and y surfaces, as was done previously at ambient pressure [13,45]. 

Judd-Ofelt tensor = rate of nonradiative relaxation = atomic number... 

Figure 6. Schematic for defects in the (B2) NiAl lattice showing the relaxed atomic positions attained when an A1 atom is added at site A A, A, A). The A1 atom at A moves into site B, which is a Ni sublattice site, generating an antisite defect. The Ni atom initially at B moves into position C, displacing the Ni atom at D, as indicated, and causing the A1 atoms at E and F to be displaced. A crowdion with an extra Ni atom along a <1 1 1> direction is produced. Open circles show initial positions, filled circles final ones (From Caro and Pedraza, 1991)...

Fig. 1. Generic labeling scheme for relaxations in a surface - top view. This Fig. shows only one shell (labeled s) of symmetrically equivalent atoms in one particular layer (labeled 1), surrounding the adsorbate site. The relaxed atomic positions are shown as black balls, displaced relative to the ideal bulk-like positions (gray balls). The relaxed radial position is labeled as r]s(l+Ari5), with an in-plane rotation angle of ttjj.

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