Methods of Estimating Ionic Radii

The covalent radius can be simply calculated as half of the shortest homonuclear distance in the structure. Finding ionic radii is not so straightforward, because in ionic structures, ions of similar charge are never the nearest neighbours. Thus, at 

The first theoretical estimate of ionic radii has been made by Pauling [172] who partitioned interatomic distances in the crystals of alkali halides comprising iso-electronic ions (i.e. Na+ F , K+CP, Rb+Br and Cs+P) in an inverse relation to their effective nuclear charges, in accordance with Eq. 1.23, and obtained the following radii K+ 1.33, CP 1.81, Rb+ 1.48, Br 1.95, Cs+ 1.69 and P 2.13 A the radii of F (1.36 A) and 0 (1.40 A) were derived by additivity. These values agree with the empirical radii, especially the latest system of Brown [173]. Batsanov [174] applied Pauling s idea to molecular and crystalline halides MX (with iso-electronic M + and X ions) and calculated the halide radii for different Ac. This approach was applied also to the molecular and crystalline iso-electronic oxides and chalcogenides (Table 1.14). 

However, much more general is the dependence of the ionic radius on the bond energy (Fig. 1.7). For example, iVc(Cl) remains 1 in the molecules KCl, CaCl2, and ScCls, but the r(Cl) changes from 1.542 to 1.489 to 1.451 A, as the bond energy increases (433, 448, and 470 kJ/mol, respectively). Similarly, the ionic radii in the vdW complexes M+ Rg and X Rg are larger than in solids, even though increases from 1 in the complex to 6 or 8 in the solid [174]. 

The r(X ) = f(E) dependence being the same for molecular and crystalline halides, the radii of non-isoelectronic ions can be determined, provided the bond energies are known. The ionic radii for MX molecules and crystals are listed in Table 1.15, from which it follows that cationic and anionic radii change with to a similar degree. The radii of F (1.21 A), Cr (1.63 A), Br (1.71 A), and 1 (1.90 A) have been calculated from the Morse potential energy curves (calculated from the spectroscopic data) for the dissociation of molecular ions, X2 X +X, 

An independent method of calculating ionic radii [177] uses Sanderson s principle of equalization of atomic electronegativities (see Sect. 2.4.5), it shows the metal 

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