Fuzzy atoms

Fig. 6. Gaussian curves as a function of increasing width. As the degree of softness increases, the curves represent fuzzy atoms, and as the degree of softness deceases, the Gaussian converges to a point atom model.

Although the representation of these queries is very similar to a combinatorial library, there are some significant differences in both design and use. Since the exact compositions of the database structures are not determined until after the query has been posed, the query typically contains query features, such as fuzzy atoms and bonds and ambiguous connectivity. There is no need for these features to represent a combinatorial library, since all the structures are known. The syntax for representing R-groups in a query can also include features such as zero occurrences to reduce the retrieval of undesired records. Such a feature is unnecessary for a combinatorial library representation, since it is a complete set of specific structures and not an open-ended query. 

Clark AE, Sonnenberg JL, Hay PJ, Martin RL. Density and wave function analysis of actinide complexes what can fuzzy atom, atoms-in-molecules, Mulliken, Lowdin, and natural population analysis tell us J Chem Phys. 2004 121 2563-70. 

Torre A, Alcoba DR, Lain L, Bochicchio RC (2005) Determination of three-center bond indices from population analysis a fuzzy atom treatment. J Phys Chem A 109(29) 6587-6591... 

Matito, E., Salvador, P, Duran, M., Sola, M. (2006). Aromaticity measures from fuzzy-atom bond orders (FBO). The aromatic fluctuation (FLU) and the para-delocahzation (PDI) indexes. J. Phys. Chem. A 110,5108-5113. 

The space partitioning into nonoverlapping regions makes the evaluation of the properties of these regions much more straightforward than in interpenetrating (fuzzy atoms) schemes. If the density of property is well defined, the basin property is just the integral of the density of property over the basin volume. The case of the... 

Two other atomic properties have been used in the definition of atom type, thereby increasing its fuzziness relative to that in the ap and tt descriptors - atomic log P contribution (yielding hydrophobic pairs, hps, and torsions, hts) and partial atomic charges (charge pairs, cps, and charge torsions, cts). 

The atom pair (ap) and topological torsion (U) descriptors and their fuzzy binding property analogs bp and bt are again selected for illustrative purposes [24, 25]. 

Figure 3.11 Series of successive STM images, recorded during dosing of the O-covered Pt(l 1 1) surface with H2. (a-c) Frames (17 nm x 17 nm) from an experiment at 131 K [P(H2) = 8 x 1CT9 mbarJ.The hexagonal pattern in (a) is the (2 X 2)-0 structure O atoms appear as dark dots and bright features are the initial OH islands. In (c), the area is mostly covered by OH, which forms ordered structures. The white, fuzzy features are H20-covered areas.

The model of the atom in 1927. The fuzzy, spherical region that surrounds the nucleus represents the volume in which electrons are most likely to be found. 

Figure 2.2 Artist s depiction of the "fuzzy ball" atom whose electrons had no sharp boundaries but exhibited limits to the number of energy levels.

Figure 6.1 shows the stockholder decomposition of the theoretical deformation density of the cyanoacetylene molecule, H—Cs=C—C=N (Hirshfeld 1977b). The overlap density in the bonds is distributed between the bonded atoms. The assignment of part of the density near the hydrogen nucleus to the adjacent carbon atom manifests the difference between fuzzy and discrete boundary partitioning methods. 

The little man, or homunculus, as it was sometimes called, was imaginative, of course—the mind sometimes creates such illusions when examining an object too small or fuzzy to be clearly seen. The notion that the microscopic world consisted of familiar objects reduced to a small scale was also incorrect. As scientists probed the nature of particles, they realized that the behavior of small objects does not necessarily mimic larger ones. This discovery opened up new vistas in science as well as technology, including the subject of this chapter—technology on the scale of atoms and molecules. 

Further, ions are not hard, billiard ball like spheres. Since the wave functions that describe the electronic distribution in an atom or ion do not suddenly drop to zero amplitude at some particular radius, we must consider the surfaces of our supposedly spherical ions to be somewhat fuzzy. A more subtle complication is that the apparent radius of an ion increases (typically by some 6 pm for each increment) whenever the coordination number increases. Shannon10 has compiled a comprehensive set of ionic radii that take this into account. Selected Shannon-type ionic radii are given in Appendix F these are based on a radius for O2- of 140 pm for six coordination, which is close to the traditionally accepted value, whereas Shannon takes the reference value as 126 pm on the grounds that it gives more realistic ionic sizes. For most purposes, this distinction does not mat-... 

The fuzzy frontier between the molecular and the nanometric level can be elucidated from an electronic point of view. Molecules and small clusters can be described as systems in which the metal atoms form well-defined bonding and antibonding orbitals. Large clusters or small nanoparticles (quantum dots) with dimensions of a few nanometers are intermediate between the size of molecules and bulk material, presenting discrete energy levels with a small band gap owing to quantum-mechanical rules. Finally, larger particles tend to lose this trend and display a typical band structure similar to that of the bulk material. 

From a structural point of view, mechanism in a single crystal can be much closer to a set of identical atomic trajectories than to the kind of fuzzy statistical average with which one must be content in solution. It is not surprising that with this kind of structural uniformity the site problems that plague kinetic studies in rigid glasses disappear. Adherence to first-order rate laws can be as close in single crystals as it is in fluids, and equally valid activation parameters can be obtained for thermal unimolecular reactions of reaction intermediates [12]. 

So, a new model was proposed and accepted. The modern description of how electrons move around the nucleus in an atom is called the quantum mechanical model. In this model, the electrons do not follow an exact path, or orbit, around the nucleus the way they do in Bohr s model. Instead, for the new model, physicists calculated the chance of finding an electron in a certain position at any given time. The quantum mechanical model looks like a fuzzy... 

Quantum mechanical model The modern, more accurate model of the atom in which the chance of finding an electron in a certain position at any given time are calculated and plotted. The model resembles a fuzzy cloud. 

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