Atom identity

When atoms combine to form molecules, the atoms retain their atomic identities and characteristic molar masses. Thus, we can add elemental molar masses to obtain the molar mass of any compound. 

Fig. 19 The linkages between neighboring triacontahedral clusters in the Tsai-type 1/1 ACs along a the twofold axes, and b the threefold axes. The 2/1 ACs exhibit same linkages although they have different atom identities and symmetries. All decoration atoms of the triacontahedra are omitted for clarity. (Adapted with permission from [83], Copyright 2006 American Chemical Society)...

As a function of ligand atom identity and coordination number (CN). As a function of coordination number in minerals. ... 

There are two allotropic forms of polonium, both primitive, with one atom per unit cell. a-Po is simple cubic (3PO) and each Po atom has six nearest neighbors (3.366 A) at the vertices of a regular octahedron. The simple cubic structure is the same as that of NaCl (Figure 3.6) with all atoms identical. The structure of (3-Po is a primitive rhombohedral lattice. Each Po atom has six nearest neighbors forming a slightly flattened trigonal antiprism (or a flattened octahedron). 

As mentioned earlier, the information provided by EXAFS is limited to local effects and only the atomic identity of the immediate neighbours of the atom under investigation can be determined. Also, as can be seen from the examples quoted above, it cannot discriminate between oxygen and nitrogen atoms. This is understandable in view of their adjacent positions in the Periodic Table, but somewhat restrictive when they are both common ligating atoms of transition... 

In the realm of theory also, greater demands will be made. As such studies (37—39) as those of Cu—Ni (Fig. 13) and Ag—Pd (Fig. 14) have shown, the d levels of the two species in transition metal alloys tend to maintain their atomic identities, at least when the levels in the pure components are sufficiently well separated in energy. However, neither calculation nor experiment has been done with refinement sufficient for quantitative testing of a theory, such as the coherent potential approximation, designed to describe the d band behavior. In pure metals and intermetallic compounds, band calculations can be compared directly with experiment if transition probabilities and relaxation effects are understood. With care they can be used also in evaluation of the effective interelectronic terms which enter equations such as (18a). Unfortunately, one cannot, by definition, produce a set of selfconsistent band calculation results for a matrix of specific valence electron snpmdl.. . configurations thus, direct estimates for I of Eq. (18a) or F of Eq. (18b) cannot be made. However, band calculations for a set of systems can indicate whether or not it is reasonable to factor level shifts into volume and electron count terms, in the manner of Eqs. (18a) and (23). When this cannot be done, one must revert to a more general expression for a level shift, such as Eq. (1). 

A difficulty is that the phosphorus centers in DNA are not chiral, because two of the groups bound to the phosphorus atom are simple oxygen atoms, identical with each other. This difficulty can be circumvented by preparing DNA molecules that contain chiral phosphoryl groups, made by replacing one oxygen atom with sulfur (called a phosphorothioate). Let us consider EcoKV endonuclease. This enzyme cleaves the phosphodiester bond between the T... 

FIGURE 5.16. Structure of quartz, Si02, showing (a) a stereoview and (b) an indication of atomic identities in the helical packing in levorotatory quartz. 

Moreover, atom-type -state indices were proposed as molecular descriptors encoding topological and electronic information related to particular atom types in the molecule [Hall and Kier, 1995a Hall et al., 1995b]. They are calculated by summing the -state values of all atoms of the same atom type in the molecule. Each atom type is first defined by atom identity, based on the atomic number Z, and valence state, itself identified by the valence state indicator (VST) defined as ... 

I he previous chapters showed how the laws of conservation of mass and con--1- servation of atomic identity, together with the concept of the mole, determine quantitative mass relationships in chemical reactions. That discussion assumed prior knowledge of the chemical formulas of the reactants and products in each equation. The far more open-ended questions of which compounds are found in nature (or which can be made in the laboratory) and what types of reactions they undergo now arise. Why are some elements and compounds violently reactive and others inert Why are there compounds with chemical formulas H2O and NaCl, but never H3O or NaCli Why are helium and the other noble gases monatomic, but molecules of hydrogen and chlorine diatomic All of these questions can be answered by examining the formation of chemical bonds between atoms. 

Changing the number of atoms in a system is a special case of changing atomic identities. Atoms being deleted are perturbed into dummy particles for which all parameter values are zero. Typically, this technique would be combined with one or... 

Detailed vibrational (infrared and Raman) spectra of multiple salts of many of the anions listed in the Table have been reported and analyzed.1 7,108 As will be seen from Table 7, the tv-isomer is the most common and presumably the thermodynamically stable form, at least for oxidized anions with all addenda (M) atoms identical. In the molybdate system, reduction of the o-anions results in spontaneous isomerization to the /3-isomers, since the latter have more positive reduction potentials see Section 4.10.3.7. Rates of isomerization in the tungstate system are exceedingly slow, so that /3-isomers possess considerable kinetic stability. A recent density functional theory treatment109 of Keggin tungstates with central P, As, Si, Ge, Al, and Ga concludes that the /3-isomer becomes relatively more stable as the oxidation state of the central atom decreases see Table 8. 

This development is appropriate only for saturated alkanes - - because there is no provision for atom identity, bond types, or number of hydrogen atoms in each skeletal group (except for the case of saturated hydrocarbons.) This branching index is essentially a mathematical property of graphs it does not adequately represent molecular graphs. Further, a single index would appear to be insufficient to relate to the wide variety of molecular properties, especially when biological and environmental properties are of interest. 

Topological indexes should be based on the most significant features of molecular structure, including atom identity, bonding environment of each atom, and the existence of hydrogen atoms bonded to the skeletal atom. Each of these aspects is distinctly electronic in nature. 

With these considerations as a general background, let us summarize our approach. In the molecular connectivity approach, the molecule is represented by the hydrogen-suppressed graph. The key feature in the quantitation of the graph is the characterization of the atom in the molecular skeleton. The molecular connectivity method explicitly introduces the electronic character of atoms into the graphic representation of molecules. Atom identity is specified through the molecular connectivity delta values the simple delta, 6, and the valence delta,... 

The summation is over the A atoms of the skeleton. The zero order chi index carries a low level of structure information. Little of the connectedness of the skeletal network is encoded only the fact of the presence of the nearest neighbor to each atom is encoded. In the °X index, atom identities are quantitated. 

The first-order chi indexes contain more structure information than do the zero-order indexes. The immediate bonding environment of each atom is encoded by virtue of the edge weight. Further, the number of terms in the sum, P, is dependent on the graph type, especially on the number of cycles or rings. The x index encodes both the atom identities as well as the connectedness in the molecular skeleton. 

The variable A x in QSAR Eq. [33] provides discrimination only among the three molecular classes because the atom contribution to A x is zero for saturated carbon atoms. The A°x provides very little structure information with respect to skeletal variation, but it does encode the atom identities and some of the skeletal environment immediately surrounding the heteroatom. The addition of the A x variable greatly increases the discrimination among the three classes because it encodes skeletal information about the carbon atoms a to the heteroatom. The QSAR is improved considerably by the addition of A x. Finally, the addition of A x further improves the QSAR by adding information about the broader reaches of the skeletal environment of each heteroatom, namely, atoms p to the heteroatoms. It can also be seen that the effects of atoms P to the heteroatom are much less important than the heteroatom itself or the a carbon atoms. By the introduction of the delta-chi indexes, an atom level interpretation is made possible. 

Encoding atom identity can be accomplished in several ways. We have elected to modify the atom count. A, in Eqs. [50], [52], [54], and [55]. The modification is based on the awareness that a non-C(sp ) atom, counted in arriving at the value of A for the molecular graph, is contributing more or less than a C(sp ) contribution to the shape. Therefore, that particular atom should be counted more or less than 1, the increment or decrement called a, which is based on the size contribution of the atom in question relative to C(sp ). 

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