Atoms properties

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,... 

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). 

When additivity of atomic properties is valid then the skeleton S disappears and Eq. (1) can be rewritten as Eq. (2). 

For any molecule, additivity of atomic properties requires as many variables as there are different atom types contained in the molecule. For example, for acetic add, C2H+O2, three different atomic increments are needed, one each for a carbon, a hydrogen, and an oxygen atom. 

Clearly, simple additivity of atom properties will no longer suffice, as the contribution of an atom will diminish the hirther it is away from the atom whose property has to be estimated. In the following, we present two methods of accounting for the influence of one atom on another, attenuated over the distance between the two atoms. 

Figure 8-4. Comparison of 3D autocorrelation vectors of o-, m-, and j-xylene (without hydrogen atoms) Atomic property p = 1.

This theoretical foundation of electron diffraction as given by Wierl [26] and modification of this equation partly following suggestions made by Soltzberg and Wilkins [27] gives Eq. (24), with the atomic property p for the atoms i and j, a reciprocal distance s, and the distance tu between the atoms i and j. 

The chirality code of a molecule is based on atomic properties and on the 3D structure. Examples of atomic properties arc partial atomic charges and polarizabilities, which are easily accessible by fast empirical methods contained in the PETRA package. Other atomic properties, calculated by other methods, can in principle be used. It is convenient, however, if the chosen atomic property discriminates as much as possible between non-equivalent atoms. 3D molecular structures are easily generated by the GORINA software package (see Section 2.13), but other sources of 3D structures can be used as well. 

Each combination of four atoms (A, B. C. and D) is characterized by two parameters, e and e.. As for the CICC, is a parameter that depends on atomic properties and on distances, and is calculated by Eq. (27), with r, again being the sum of bond lengths between atoms on the path with the minimum number of bond counts. However c is now a geometric parameter (dependent on the conformation)... 

Figure 8-11. iD structure and representation offcoccia) versus u for (fi)-4 and [S)-4 at two different conformations (a and b) sampled at 50 evenly separated values between -0,100 e A and i-0.100 e A. Partial atomic charge was used as the atomic property. 

By including characteristic atomic properties, A. of atoms i andj, the RDF code can be used in different tasks to fit the requirements of the information to be represented. The exponential term contains the distance r j between the atoms i andj and the smoothing parameter fl, which defines the probability distribution of the individual distances. The function g(r) was calculated at a number of discrete points with defined intervals. 

Molecules are usually represented as 2D formulas or 3D molecular models. WhOe the 3D coordinates of atoms in a molecule are sufficient to describe the spatial arrangement of atoms, they exhibit two major disadvantages as molecular descriptors they depend on the size of a molecule and they do not describe additional properties (e.g., atomic properties). The first feature is most important for computational analysis of data. Even a simple statistical function, e.g., a correlation, requires the information to be represented in equally sized vectors of a fixed dimension. The solution to this problem is a mathematical transformation of the Cartesian coordinates of a molecule into a vector of fixed length. The second point can... 

This coding is performed in three steps (cf Chapter 8) First the 3D coordinates of the atoms arc calculated using the structure generator CORINA (COoRdlNAtes). Subsequently the program PETRA (Parameter Estimation for the Treatment of Reactivity Applications) is applied for calculating physicochemical properties such as charge distribution and polarizability. The 3D information and the physicochemical atomic properties are then used to code the molecule. 

If the secondary ion component is indeed negligible, the measured SNMS ion currents will depend only on the ionizing mode, on the atomic properties of the sputtered atoms, and on the composition of the sputtered sample. Matrix characteristics will have no effect on the relative ion currents. SNMS analysis also provides essentially complete coverage, with almost all elements measured with equal facility. All elements in a chemically complex sample or thin-film structure will be measured, with no incompleteness due to insensitivity to an important constituent element. Properly implemented SNMS promises to be a near-universal analytical method for solids analysis. 

The AIM facility in Gaussian can be used to predict a variety of atomic properties based on this theory. We will use it to compute atomic charges and bond order for the ally cation. 

Table 3.1 Atomic properties of hydrogen (protium), deuterium, and tritium...

The Group 1 elements are soft, low-melting metals which crystallize with bee lattices. All are silvery-white except caesium which is golden yellow "- in fact, caesium is one of only three metallic elements which are intensely coloured, the other two being copper and gold (see also pp. 112, 1177, 1232). Lithium is harder than sodium but softer than lead. Atomic properties are summarized in Table 4.1 and general physical properties are in Table 4.2. Further physical properties of the alkali metals, together with a review of the chemical properties and industrial applications of the metals in the molten state are in ref. 11. 

Table 5.1 lists some of the atomic properties of the Group 2 elements. Comparison with the data for Group 1 elements (p. 75) shows the substantial increase in the ionization energies this is related to their smaller size and higher nuclear charge, and is particularly notable for Be. Indeed, the ionic radius of Be is purely a notional figure since no compounds are known in which uncoordinated Be has a 2- - charge. In aqueous solutions the reduction potential of... 

Table 5.1 Atomic properties of the alkaline earth metals...

The atomic properties of the Group 13 elements (including boron) are compared in Table 7.4. All have odd atomic numbers and correspondingly few stable isotopes. The varying precision of... 

The atomic properties of Ge, Sn and Pb are compared with those of C and Si in Table 10,1, Trends noted in previous groups are again apparent. The pairwise similarity in the ionization energies of Si and Ge (which can be related to the filling of the Sd shell) and of Sn and Pb... 

Germanium, Tin and Lead Table 10.1 Atomic properties of Group 14 elements... 

Atomic properties are summarized in Table 17.3 and some physical properties are in Table 17.4. 

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