Cation-anion, internuclear distance

We may attempt to make a rough quantitative statement about the bond type in these molecules by the use of the values of their electric dipole moments. For the hydrogen halogenides only very small electric dipole moments would be expected in case that the bonds were purely covalent. For the ionic structure H+X-, on the other hand, moments approximating the product of the electronic charge and the internuclear separations would be expected. (Some reduction would result from polarization of the anion by the cation this we neglect.) In Table 3-1 are given values of the equilibrium internuclear distances r0, the electric moments er0 calculated for the ionic structure H+X , the observed values of the electric moments /, and the ratios of these to the values of er0.ls These ratios may be interpreted in a simple... 

First tlie hydrogen bond is a bond by hydrogen between two atoms the coordination number of hydrogen does not exceed two.7 The positive hydrogcu ion is a bare proton, with no electron shell about it. This vanishingly small cation would attract one anion (which we idealize here as a rigid sphere of finite radius—see Chap. 13) to the equilibrium internuclear distance equal to the anion radius, and could then similarly attract a second anion, as shown in Figure 12-1, to form... 

Structural information on 133 was provided by Kohler and coworkers who, in 1986, reported the isolation of its lithium salt and the determination of its crystal structure280. This structure showed the lithium cation to be situated on the endo surface of the anion and coordinated with both the allyl portion and the C(6)—C(7) double bond. Key internuclear distances of the anionic portion of the salt are summarized in Scheme 42. 

Values of the ionic radii are derived from experimental data, which give the internuclear distances and electron densities, and generally take the distance of contacting neighbor ions to be the sum of the ionic radii of the cation and anion ... 

Similar substantially constant differences are obtained with other pairs of alkali halides of B 1 structure, having either a cation or an anion in common. As a result, the conclusion was reached that each ion makes a specific contribution toward an experimentally observed r0, well-nigh irrespective of the nature of the other ion with which it is associated in the lattice. In other words, characteristic radii should be attributable to the ions (1,2). However, a knowledge of the internuclear distances in the crystals is not sufficient by itself to determine absolute values for crystal radii of ions, and various criteria have been used to assign the size of a particular ion or the relative sizes of a pair of alkali and halide ions. 

Crudely we may illustrate what is happening in the following manner. Take a diatomic system and remove one electron from the cation M and from the anion X. Returning the electrons at the equilibrium internuclear distance of MX gives us, as a first approximation and assuming that (1 -j- x) of the electrons settle on the anion,... 

The determination of the sizes of ions has been a fundamental problem in inorganic chemistry for many years. Many indirect methods have been suggested for apportioning the internuclear distance between two ions, relatively easy to obtain, into cationic and anionic radii. Although these have been ingenious ai provide insight into atomic properties, they are no longer necessary. 

As the collection of X-ray diffraction data became more extensive, it was possible to describe the electron density distribution in ionic crystals in more detail. Using these data one can divide up the internuclear distance in the crystal on the basis of the minimum in the electron density between the two oppositely charged ions [3, 4]. For example, in the case of NaCl for which the internuclear distance is 281 pm, the minimum in the electron density leads to radii of 117 pm for Na" " and 164pm for CP. Radii derived on this basis are larger for cations and smaller for anions than those of Pauling. 

Although from a wave-mechanical viewpoint, the radius of an individual ion has no precise physical significance, for purposes of descriptive crystallography, it is convenient to have a compilation of values obtained by partitioning measured interatomic distances in ionic compounds. Values of the ionic radius (/-jon) may be derived from X-ray diffraction data. However, experimental data only give the internuclear distance and we generally take this to be the sum of the ionic radii of the cation and anion (equation 5.6). 

Internuclear distance between a cation and the closest anion... 

The internuclear distance cq = rcation + anion and, since the cation is constant, varies only as a function of ranjon-... 

Examination of electrostatic principles allows some conclusions to be drawn regarding the effect of ion pairing on the selectivity of salt partitioning or, equivalently, on the driving force for cation exchange. As outlined in a standard text [234], treatments of Fuoss [235] or of Bjerrum [236] may be applied to estimate the ion-pair association constant /Ca.,soc- The Fuoss treatment assumes contact ion pairs and is conceptually simpler to use and apply. As the simplification will not affect the conclusions to be drawn here, it will be employed with the additional proviso that the effect of water in the solvent will be neglected for the moment. According to Fuoss, the ion-pair association constant at 298 K may be expressed in terms of the solvent dielectric constant 6 and the internuclear distance i m-x (in nm) between the cation and anion ... 

The actual arrangement of ions in the solid state can frequently be predicted by a rather simple procedure. The larger ions (usually the X anion) are stacked in a three-dimensional, closest-packed array like billiard balls, and the smaller ions (usually the M"+ cation) are evenly distributed in the holes left in this structure. If the cations and anions are approximately the same size, the most efficient lattice for maximizing cation-anion interaction is one in which eight ions of one type surround one ion of the second type. If the halide has a fair amount of covalent character, a chain or layer, structure may result in which the internuclear distance between layers is greater than within a layer. 

We will emphasize an atomic radius based on the distance between the nuclei of two atoms joined by a chemical bond. The covalent radius is one-half the distance between the nuclei of two identical atoms joined by a single covalent bond. The ionic radius is based on the distance between the nuclei of ions joined by an ionic bond. Because the ions are not identical in size, this distance must be properly apportioned between the cation and anion. One way to apportion the electron density between the ions is to define the radius of one ion and then infer the radius of the other ion. The convention we have chosen to use is to assign 0 an ionic radius of 140 pm. An alternative apportioning scheme is to use F as the reference ionic radius. When using ionic radii data, carefully note which convention is used and do not mix radii from the different conventions. Starting with a radius of 140 pm for 0 , the radius of Mg can be obtained from the internuclear distance in MgO, the radius of CU from the internuclear distance in MgCl2, and the radius of Na" " from the internuclear... 

The concept of atomic or ionic size is one that has been debated for many years. The structure map of Figure 1 used the crystal radii of Shannon and Prewitt and these are generally used today in place of Pauling s radii. Shannon and Prewitt s values come from examination of a large database of interatomic distances, assuming that internuclear separations are given simply by the sum of anion and cation radii. Whereas this is reasonably true for oxides and fluorides, it is much more difficult to generate a self-consistent set of radii for sulfides, for example.A set of radii independent of experimental input would be better. The pseudopotential radius is one such estimate of atomic or orbital size. 

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