Single atom properties

Sets of atom properties, such as point charges, atomic lipophilicity parameters or any other atom properties, can be used to describe properties of molecules. However, the use of such single atom properties as descriptors requires an atom-to-atom mapping of all atoms considered of all compounds of the dataset. This is not possible in most cases and, therefore, it is necessary to compute more general descriptors from these parameters  

Reduce the number of parameters to some typical atoms that are common to all structures considered. 

Summarize the parameters for common groups which are present in all structures considered. 

Summarize the parameters for the compounds (e.g., calculate logP values or dipole moments). 

Calculate autocorrelation or cross-correlation coefficients to work out typical patterns of parameter arrangement in the compounds. 

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Clusters of Ag atoms have metal-like properties at 55 atoms, but they are not metals. The gap between HOMO and LUMO being 0.2 eV is still 10 times larger than kT expected for a bulk metal. The work function is calculated to be 1 eV larger than that of the bulk, and the cohesive energy is only about one-third that expected for bulk. The electrons behave like free electrons. The trend in each of these quantities with size is in the direction from single atom properties toward bulk metal properties. Ousters of Pd have characteristics that differ from bulk metal properties in much the same way as do Ag clusters. One exception is the calculated number of unoccupied d states per atom of small clusters, which is very close to bulk values of 0.6. 

The atom indices are typical single atom properties and are thus not suitable for a direct comparison of molecules in general (see Section 9.3.6). Normally they have to be transformed into more general representations (e. g., by calculating autocorrelation or cross-correlation coefficients), or the molecule topological indices -which, however, include less information - have to be used. 

The most simple way is using the same single atom properties as for the topological autocorrelation descriptors. The distance now is not measured as the number of bonds between the two atoms in consideration, but as the real distance between the atoms. The distances are assigned to classes (e.g., distance between 0.1 nm and 0.2 nm) in order to get a limited number of descriptors (e.g., 20), and the coefficient is calculated for each class [87]. 

It is, of course, true that most properties of the elements are determined by the outer-electron configurations of their atoms. These configurations are, of course, the basis for the arrangement of elements in the periodic table. However, this effect of the valence electrons is often quite indirect. Along with properties of single atoms, properties exist that are collectively determined, for example, by the lattice structure. 

Metallic and semiconductor nanoparticles or nanocrystals —chunks of matter intennediate in size and physical properties between single atoms and tire macroscopic bulk materials—are of great interest botli for tlieir... 

Bonds Single bonds are omitted double, triple, and aromatic bonds are indicated by the symbols " = " and " ", respectively. In contrast to SMILES, aromaticity is not an atomic property,... 

If S is a single atom or a group of atoms with the bonds attached to the same atom (such as a CHi group), then we have the additivity of bond properties, liie first-order approximation, as given by Eq. (3). 

A convenient orbital method for describing eleetron motion in moleeules is the method of molecular orbitals. Molecular orbitals are defined and calculated in the same way as atomic orbitals and they display similar wave-like properties. The main difference between molecular and atomic orbitals is that molecular orbitals are not confined to a single atom. The crests and troughs in an atomic orbital are confined to a region close to the atomic nucleus (typieally within 1-2 A). The electrons in a molecule, on the other hand, do not stick to a single atom, and are free to move all around the molecule. Consequendy, the crests and troughs in a molecular orbital are usually spread over several atoms. 

Equation 1-5 was written for a sample containing a single element upon which monochromatic x-rays are incident. In so far as x-ray absorption is an atomic property, the mass absorption coefficients for other samples are additive functions of the weight-fractions of the elements, free or combined, that are present that is,... 

The Characterization and Properties of Small Metal Particles. Y. Takasu and A. M. Bradshaw, Surf. Defect. Prop. Solids p. 401 1978). 2. Cluster Model Theory. R. P. Messmer, in "The Nature of the Chemisorption Bond G. Ertl and T. Rhodin, eds. North-Holland Publ., Amsterdam, 1978. 3. Clusters and Surfaces. E. L. Muetterties, T. N. Rhodin, E. Band, C. F. Brucker, and W. R. Pretzer, Cornell National Science Center, Ithaca, New York, 1978. 4. Determination of the Properties of Single Atom and Multiple Atom Clusters. J. F. Hamilton, in "Chemical Experimentation Under Extreme Conditions (B. W. Rossiter, ed.) (Series, "Physical Methods of Organic Chemistry ), Wiley (Interscience), New York (1978). 

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. 

Thermodynamic processes play an important, or even dominant, role in all branches of science, from cosmology to biology and from the vastness of space to the microcosmos of living cells. Energy and entropy determine and direct all the processes which occur in the observable world. Thermodynamics only describes the properties of large populations of particles it cannot make any statements about the behaviour of single atoms or molecules. The most important properties of a system are determined by ... 

While oxygen is present in the air, it is even more abundant in water. It is also found in chemically combined form in rocks, sand, and in all plants and animals. In the air it occurs as the free uncombined element but, like hydrogen, the form of oxygen in this state is not a single atom, O, but is a molecule containing two atoms, formula 02. Like H2, it is a colorless, odorless gas, but some of its other properties are quite different. 

Single atomic ions confined in radio frequency traps and cooled by laser beams (Figure 7.4a) formed the basis for the first proposal of a CNOT quantum gate with an explicit physical system [14]. The first experimental realization of a CNOT quantum gate was in fact demonstrated on a system inspired by this scheme [37]. In this proposal, two internal electronic states of alkaline-earth or transition metal ions (e.g. Ba2+ or Yb3+) define the qubit basis. These states have excellent coherence properties, with T2 and T2 in the range of seconds [15]. Each qubit can be... 

Some properties of these ions make them particularly appealing as solid state spin qubits. The fact that they can be diluted into diamagnetic crystals offers a simple method to optimize their quantum coherence. Similarly to trapped ions, they are simple each qubit is embodied by a single atom. Yet, their immediate... 

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