Clusters of atoms

First-principles models of solid surfaces and adsorption and reaction of atoms and molecules on those surfaces range from ab initio quantum chemistry (HF configuration interaction (Cl), perturbation theory (PT), etc for details see chapter B3.1 ) on small, finite clusters of atoms to HF or DFT on two-dimensionally infinite slabs. In between these... 

Most elements thermally vaporize as atoms but some, such as Sb, C, and Se, have a portion of their vapor as clusters of atoms. For these materials, special vaporization sources, called baffle sources, can be used to ensure that the depositing vapor is in the form of atoms by causing the material to be vaporized from multiple hot surfaces before it leaves the source. 

In Secondary Ion Mass Spectrometry (SIMS), a solid specimen, placed in a vacuum, is bombarded with a narrow beam of ions, called primary ions, that are suffi-ciendy energedc to cause ejection (sputtering) of atoms and small clusters of atoms from the bombarded region. Some of the atoms and atomic clusters are ejected as ions, called secondary ions. The secondary ions are subsequently accelerated into a mass spectrometer, where they are separated according to their mass-to-charge ratio and counted. The relative quantities of the measured secondary ions are converted to concentrations, by comparison with standards, to reveal the composition and trace impurity content of the specimen as a function of sputtering dme (depth). 

Molecules are clusters of atoms. Two types of molecules are possible. Some molecules are clusters of atoms in which all the atoms in a cluster are identical some molecules contain two or more different kinds of atoms. These two kinds of molecules are given different names. 

A molecule is a cluster of atoms that persists long enough to have characteristic properties which identify it. The questions we would like to answer are Why does the cluster of atoms persist and Why does the clustering result in characteristic properties In this chapter we... 

Though OH is reactive, it is a cluster of atoms with sufficient stability to be identified as a molecule. It is present in a number of high temperature flames, for example. Its chemistry might be expected to be like that of fluorine atoms. Compare the electron dot formulas... 

For Au( 111) in nearly nonadsorbing solutions (0.1 MHC104)at E = -0.3 V (SCE), a reconstruction similar to that existing in UHV has been detected by STM, while at a > Othe (1 x 1) structure has been observed.188,467,538 At a > 0, strings and clusters of atoms disappearing with time have been found on the deconstructed surface. Therefore the more positive. 0 value is probably related to the reconstructed surface (Table 9). 

The absence or very low intensity of 111, 311, 331, 333 and 511 indicates that clusters of atoms, perhaps 13-20, occupy the centres of the hexakaidecahedra, around iij and so on. There are also smaller clusters, probably of four atoms, inside the pentagonal dodecahedra, increasing the number of atoms in the 25.73-A cube to between 1,120 and 1,176. The composition of the alloys may be changed from MA16 by these additional atoms. 

The first complex intermetallic compound found to have large clusters of atoms with local icosahedral symmetry was Mg32Al4, which has 162 atoms in a body-centred cubic unit17. The unit cube contains 98 icosahedra, 20 Friauf polyhedra and 44 others. 

The representation of an essentially infinite framework by a finite SCF treated cluster of atoms, (with or without point-ions), inevitably leads to the problem of how to truncate the model-molecule . Previous attempts at this have included using hydrogen atoms l and ghost atoms . Other possibilities include leaving the electron from the broken bond in an open shell, or closing this shell to form an ionic cluster. A series of calculations were performed to test which was the host physically realistic, and computationally viable, solution to this problem for this system. 

We now describe a relatively simple MD model of a low-index crystal surface, which was conceived for the purpose of studying the rate of mass transport (8). The effect of temperature on surface transport involves several competing processes. A rough surface structure complicates the trajectories somewhat, and the diffusion of clusters of atoms must be considered. In order to simplify the model as much as possible, but retain the essential dynamics of the mobile atoms, we will consider a model in which the atoms move on a "substrate" represented by an analytic potential energy function that is adjusted to match that of a surface of a (100) face-centered cubic crystal composed of atoms interacting with a Lennard-Jones... 

By single-site catalysts we mean catalysts where the breaking and formation of chemical bonds occurs at isolated active centers whose chemical activity is dominated by the electronic properties of a single atomic species or of a small cluster of atoms that can act in an independent way with respect to others. 

When a supported metal on an oxide is prepared from an adsorbed precursor incorporating a noble metal bonded to an oxophilic metal, the result may be small noble metal clusters, each more-or-less nested in a cluster of atoms of the oxophilic metal, which is cationic and anchored to the support through metal-oxygen bonds [44,45]. The simplest such structure is modeled on the basis of EXAFS data as Re4Pt2, made from Re2Pt(CO)i2 (Fig. 6) [45]. 

The bombarding of the specimen surface by the primary beam of high energy ions leads to the ejection (sputtering) of both neutral and charged (+/—) species from the surface. The ejected species may include atoms, clusters of atoms and molecular fragments. The ions enter an extraction lens and the polarity of the applied voltages determines the polarity of the secondary ions that enter the analyser. 

Figure 9. Energy levels of an ammonia molecule showing the states investigated in the pump-probe experiments. Also shown are the threshold energies where H atoms can be produced. The upper hatched region denotes the ionization limit. Taken with permission from, NATOASI Series on Large Clusters of Atoms and Molecules Kluwer Academic Dordrecht, 1996, pp 371-404.

Thus, there is a size threshold that must be reached before a cluster of atoms becomes big enough to be detected and turns into a "condensation nuclei". Recent work by Madelaine and coworkers (Perrin, et al, 1978 Madelaine, et al., 1980) have extended the size of measurable ultrafine particles to the order of 0.003 ym. They find rapid coagulation of this ultrafine aerosol to a larger average diameter one that is easily observable. 

There is great interest in the electrical and optical properties of materials confined within small particles known as nanoparticles. These are materials made up of clusters (of atoms or molecules) that are small enough to have material properties very different from the bulk. Most of the atoms or molecules are near the surface and have different environments from those in the interior—indeed, the properties vary with the nanoparticle s actual size. These are key players in what is hoped to be the nanoscience revolution. There is still very active work to learn how to make nanoscale particles of defined size and composition, to measure their properties, and to understand how their special properties depend on particle size. One vision of this revolution includes the possibility of making tiny machines that can imitate many of the processes we see in single-cell organisms, that possess much of the information content of biological systems, and that have the ability to form tiny computer components and enable the design of much faster computers. However, like truisms of the past, nanoparticles are such an unknown area of chemical materials that predictions of their possible uses will evolve and expand rapidly in the future. 

While in principle all of the methods discussed here are Hartree-Fock, that name is commonly reserved for specific techniques that are based on quantum-chemical approaches and involve a finite cluster of atoms. Typically one uses a standard technique such as GAUSSIAN-82 (Binkley et al., 1982). In its simplest form GAUSSIAN-82 utilizes single Slater determinants. A basis set of LCAO-MOs is used, which for computational purposes is expanded in Gaussian orbitals about each atom. Exchange and Coulomb integrals are treated exactly. In practice the quality of the atomic basis sets may be varied, in some cases even including d-type orbitals. Core states are included explicitly in these calculations. 

With such calculations one can approach Hartree-Fock accuracy for a particular cluster of atoms. These calculations yield total energies, and so atomic positions can be varied and equilibrium positions determined for both ground and excited states. There are, however, drawbacks. First, Hartree-Fock accuracy may be insufficient, as correlation effects beyond Hartree-Fock may be of physical importance. Second, the cluster of atoms used in the calculation may be too small to yield an accurate representation of the defect. And third, the exact evaluation of exchange integrals is so demanding on computer resources that it is not practical to carry out such calculations for very large clusters or to extensively vary the atomic positions from calculation to calculation. Typically the clusters are too small for a supercell approach to be used. 

The minimum size to which a sample can be reduced without qualitatively changing its properties corresponds to the correlation length. If the correlation length is small the properties of the system can be calculated by a variety of methods, for instance Hartree-Fock. The assumption is that the properties of matter in the bulk can be related to the properties of a small cluster of atoms, noting that even a cluster of three has too many degrees of freedom to be solved without considerable simplification. 

The most critical aspect of atomistic simulations is thus the representation of the interactions between atoms by an algebraic function. If covalency is important, a part of the expression should contain details of how the interaction changes with angle, to mimic directional covalent bonds. In cases where a simulation is used to predict the location of a cluster of atoms within or at the surface of a solid, interactions between the atoms in the cluster, interactions between the atoms in the solid, and interactions between the atoms in the cluster and those in the solid must all be included. 

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