Effective size of atoms

An approach based on orbital radii of atoms effectively rationalizes the structures of 565 AB solids (Zunger, 1981). The orbital radii derived from hard-core pseudopotentials provide a measure of the effective size of atomic cores as felt by the valence electrons. Linear combinations of orbital radii, which correspond to the Phillips structural indices and have been used as coordinates in constructing structure maps for AB solids. 

On compression of non-hydrogen atoms the energy levels, which in this case are occupied by electrons, respond in the same way. Apart from level crossings, interelectronic interactions now also lead to an internal transfer of energy and splitting of the magnetic sub-levels, such that a single electron eventually reaches the ionization limit on critical compression. The calculated ionization radii obey the same periodic law as the elements and determine the effective size of atoms in chemical interaction. 

When two or more atoms are forced together, they repel each other, and experience van der Waals repulsion as the electrons associated with each atom start to occupy a common space. The effective size of atoms is given by the van der Waals radii (Table 4.3), which are related to how close atoms or groups can come without severe repulsion. Van der Waals repulsion is also called steric hindrance, and the energy of that interaction is steric strain. In the eclipsed conformation of propane, the hydrogen atoms at C-1 and C-3 are not close enough to produce a large van der Waals repulsion. 

Other substituted cyclohexanes are similar- to methylcyclohexane. Two chair confonnations exist in rapid equilibrium, and the one in which the substituent is equatorial is more stable. The relative fflnounts of the two confor-rnations depend on the effective size of the substituent. The size of a substituent, in the context of cyclohexane confor-rnations, is related to the degree of branching at the atom connected to the ring. A single... 

Van der Waals radius (Section 2.17) A measure of the effective size of an atom or a group. The repulsive force between two atoms increases rapidly when they approach each other at distances less than the sum of their van der Waals radii. 

Figure 19-4 contrasts the effective sizes of the halide ions. Each of these dimensions is obtained from the examination of crystal structures of many salts involving the particular halide ion. The effective size found for a given halide ion is called its ionic radius. These radii are larger than the covalent radii but close to the van der Waals radii of neutral atoms. 

Steric isotope effects may be ascribed to differences in effective size of isotopic atoms. The early part of our discussion will be concerned with the problem of the meaning of this concept. The experimental results which are to be explained are differences in the positions of chemical equilibria and in reaction velocities arising from this difference in size . 

Here we see clearly the large concentration of density around the oxygen nucleus, and the very small concentration around each hydrogen nucleus. The outer contour is an arbitrary choice because the density of a hypothetical isolated molecule extends to infinity. However, it has been found that the O.OOlau contour corresponds rather well to the size of the molecule in the gas phase, as measured by its van der Waal s radius, and the corresponding isodensity surface in three dimensions usually encloses more than 98% of the total electron population of the molecule (Bader, 1990). Thus this outer contour shows the shape of the molecule in the chosen plane. In a condensed phase the effective size of a molecule is a little smaller. Contour maps of some period 2 and 3 chlorides are shown in Figure 8. We see that the electron densities of the atoms in the LiCl molecule are only very little distorted from the spherical shape of free ions consistent with the large ionic character of this molecule. In... 

The structurally related salts [M(Cp )2] [M (tds)2] (M = Fe, Mn, Cr M = Ni, Pt) and [Fe(Cp )2][Pt(tds)2] allowed a systematic study of the effect of a diversity of variables on the magnetic behavior of these compounds, such as the variation of the spin of the cation, the role of the single ion anisotropy, the effect of the variation of the size of atoms involved in the intermolecular contacts. Furthermore, the analysis of the intermolecular contacts in these compounds provided a reasonable interpretation of the intra and interchain magnetic coupling, and its relative strength within the series [44, 45]. 

The first problem was resolved when it was shown that the Es values for symmetric groups are a linear function of van der Waals radii42. The latter have long been held to be an effective measure of atomic size. The second and third problems were solved by... 

The first problem was resolved when it was shown that the Es values for symmetric groups are a linear function of van der Waals radii41. The latter have long been held to be an effective measure of atomic size. The second and third problems were solved by Charton, who proposed the use of the van der Waals radius as a steric parameter42 and developed a method for the calculation of group van der Waals radii for tetracoordinate symmetric top substituents MZ3 such as the methyl and trifluoromethyl groups43. In later work the hydrogen atom was chosen as the reference substituent and the steric parameter v was defined as ... 

The reason why the sizes of atoms do not simply increase with atomic number is because electrons often are added successively to the same subshell. These electrons do not fully screen each other from the nuclear charge (they do not effectively get between each other and the nucleus). Consequently, as each electron is added to a subshell and the nuclear charge increases by one unit, all of the electrons in this subshell are drawn more closely into the nucleus. 

Intexmolecular forces can be repulsive as well as attractive in nature. Tuo molecules ultimately reach a miniimm distance between them as they approach one another, and this distance is the sum of the van der Waals radii of the interacting groape. Hence, the van der Waals radius is considered a measure of the effective size of an atom in noncovalent interactions. Van der Waals radius is correlated with another measure of steric repulsion, Es.)... 

The effective size of an atom or group varies with the phenomenon studied. Atoms are better pictured as somewhat compressible than as hard balls. 

Interpretation of diffraction effects of non-crystalline substances. It has been pointed out in Chapter V that there is no sharp dividing line between crystalline and amorphous substances with decrease of crystal size, X-ray diffraction patterns become more and more diffuse until, finally, any attempt to calculate crystal size by the method given earlier in this chapter gives a figure of only a few Angstrom units— that is, about one unit cell in these circumstances the word crystal , with its implication of pattern repetition, is inappropriate. The alternative word amorphous is not entirely satisfactory either on account of the sizes of atoms and their preference for particular environments, the distribution of atomic centres.cannot be entirely random. The word non-crystalline is really preferable. 

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