Nearest neighbor atoms

Utilize periodic boundary conditions, which permit reduction of the number of nonbonded interactions at greater distances by involving only the "nearest neighbor" atoms from copies of the system which are in different but adjacent cells. 

The remaining AOs are the four H 1, two C 1, and four C 2p orbitals. All lie in the molecular plane. Only two combinations of the C 2s and H U orbitals meet the molecular symmetry requirements. One of these, other combination corresponds to the symmetry of the ethylene molecule. 

The Fe(l1l) surface is composed of four-fold coordinated atoms and exposed second layer atoms that are seven-fold coordinated while the Fe(l10) and Fe(lOO) planes have only six-fold and four-fold coordinated atoms respectively. Here we have defined the coordination number as the number of nearest neighbor atoms. Dumesic s proposal that the seven-fold coordinated atom is an important component of the catalytically active site is not contradicted by our results ( ). It is also worth noting that the relative roughness or openess of the each plane follows the same progression as their catalytic activities. Table II also shows that the activity of each of the two less active surfaces was markedly enhanced by sputtering with Ar. It is possible that sputtering has exposed seven-fold coordinate atoms at the surface or that it is the roughness of the surface that is responsible for the structure senstivity of the reaction rate. 

There appears to be concentration of rhodium in the surface of the iridium-rhodium clusters, on the basis that the total number of nearest neighbor atoms about rhodium atoms was found to be smaller than the nunber about iridium atoms in both catalysts investigated. This conclusion agrees with that of other workers (35) based on different types of measurements. The results on the average compositions of the first coordination shells of atoms about iridium and rhodium atoms in either catalyst Indicate that rhodium atoms are also incorporated extensively in the interiors of the clusters. In this respect the iridium-rhodium system differs markedly from a system such as ruthenium-copper (8), in which the copper appears to be present exclusively at the surface. 

The effect can be applied, for example, to estimate a bond length or atomic spacing, to observe valence electron spin distribution around a specific atom and to derive information of the nearest neighbor atom distribution in a disordered system such as amorphous, under an expansion of the theory. 

Angular information is notably absent from the list of structural parameters normally obtained from XAS. One approach to obtaining angular detail is to make use of multiple scattering effects (17). Unfortunately, this technique is only useful for outer shells (non-nearest neighbor atoms) where there are atoms intervening between the absorber and the scatterer. This technique suffers from complications if the shells of interest overlap in distance with other shells of atoms. 

Figure 7.21 STM image ot a nickel(ll I) surface containing a few gold atoms. The nickel nearest-neighbor atoms of gold are seen to have different electronic properties from those of the other nickel atoms (from Besenbacher et at. [63]).

A detailed inspection of a metallic surface using an optical microscope, for instance, reveals the existence of irregularities. These irregularities exist in a variety of shapes and scales. Specifically, even in an area of no more than a square micrometer (1 /un is 10 " cm), one could expect to encounter several types of surface sites. Such sites are distinguishable by their number of nearest-neighbor atoms. Figure 13.1 depicts some of the possible surface atomic sites. This depiction is somewhat idealized. It creates the impression of a perfectly rigid bulk lattice immediately under the surface so that... 

The absorption spectrum in the form of Equation (9) is expected to have maxima for values of 1/X which correspond to reciprocal distances from the center of the atom under study to nearest neighbor atoms. As... 

Figure 5.2 Schematic views of the octahedral left) and tetrahedral right) interstitial sites that exist inside an fee metal. The octahedral site is formed by connecting six face center atoms, while the tetrahedral site is formed by connecting four adjacent nearest neighbor atoms.

Note that atoms on a given simple cubic lattice are not nearest, neighbor atoms of the fee lattice, hence their updating can be done simultaneously for the energy function chosen. 

Fig. 1.11. The nascent Si(lll) surface and its reconstruction, (a) The nascent Si(lll) surface has a threefold symmetry, with nearest-neighbor atomic di.stance 3.84 A. (b) The Si( 111) surface reconstructs immediately at room temperature to a metastable Si(lll)-2XI surface, which has a lower symmetry. Two rows of dangling bond states are formed One is filled, another is empty.

The corrugation inversion due to tip states is a universal phenomenon in the STM imaging of low-Miller-index metal surfaces. For most metals (except several alkali and alkaline earth metals, which have rarely been imaged by STM), the nearest-neighbor atomic distance a 3 A. Consequently, the numerical coefficients on Eq. (5.61) are very close to those for Au(lll). 

Since the electrons in a metallic lattice are in a gas, we must use the core electrons and nuclei to determine the structure in metals. This will be true of most solids we will describe, regardless of the type of bonding, since the electrons occupy such a small volume compared to the nucleus. For ease of visualization, we consider the atomic cores to be hard spheres. Because the electrons are delocalized, there is little in the way of electronic hindrance to restrict the number of neighbors a metallic atom may have. As a result, the atoms tend to pack in a close-packed arrangement, or one in which the maximum number of nearest neighbors (atoms directly in contact) is satisfied. 

By the use of mainly LEED and lately ion scattering techniques the location of many atomic adsorbates, their bond distances and bond angles from their nearest neighbor atoms have been determined. The substrates utilized in these investigations were low Miller Index surfaces of fee, hep and bcc metals in most cases, and low Miller Index surfaces of semiconductors that crystallize in the diamond, zincblende and wurtzite structures in some cases that could be cleaned and ordered with good reproducibility. 

In two-dimensional random walks with nearest neighbor atomic jumps, the displacement distribution is given by... 

Study by X-ray absorption spectroscopy of the extended X-ray absorption fine structure (EXAFS) has provided estimates of both the nature and the number of the nearest neighboring atoms around the Mo. The EXAFS spectra of xanthine dehydrogenase and of nitrate reductase from Chlorella confirmed the... 

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