Covalent, and Ionic Radii

There are similar challenges in determining the size of ions. Because the stable ions of the different elements have different charges and different numbers of electrons, as well as different crystal structures for their compounds, it is difficult to find a suitable set of numbers for comparison. Earlier data were based on Pauling s approach, in which the ratio of the radii of isoelectronic ions was assumed to be equal to the ratio of their effeetive 

Source Data from R. T. Sanderson, Inorganic Chemistry, Reinhold, New York, 1967, p. 74 and E. C. M. Chen, J. G. Dojahn, W. E. Wentworth, J. Phys. Chem. A, 1997, i0i,3088. 

Source DatafromR. D. Shannon,Acfa Crystallogr. 1976, A32,751 for six-coordinate ions. A longer list is given in Appendix B-1. 

Factors that influence ionic size include the coordination number of the ion, the covalent character of the bonding, distortions of regular crystal geometries, and delocalization of electrons (metallic or semiconducting character, described in Chapter 7). The radius of the anion is also influenced by the size and charge of the cation. Conversely, the anion exerts a smaller influence on the radius of the cation. The table in Appendix B-1 shows the effect of coordination number. 

TABLE 2.11 Crystal Radius and Total Number of Electrons 

Shannon, Acta Crystallogr., 1976, A32,751. Johnson, Inorg. Chem., 1973, 72, 780. 

The values in Table 2-10 show that anions are generally larger than cations with similar numbers of electrons (F and Na differ only in nuclear charge, but the radius of fluoride is 37% larger). The radius decreases as nuclear charge increases for ions with the same electronic structure, such as Na , and Mg, with a much larger 

Additional information on the history of atomic theory can be found in J. R. Partington, A Short History of Chemistry, 3rd ed., Macmillan, London, 1957, reprinted by Harper Row, New York, 1960, and in the Journal of Chemical Education. A more thorough treatment of the electronic structure of atoms is in M. Gerloch, Orbitals, Terms, and States, John Wiley Sons, New York, 1986. 

---

Tin-based Lewis acids can be divided into two groups, Sn11 and SnIv. Although Sn11 is more cationic than SnIV, the covalent and ionic radii of Sn11 (1.02 A) are larger than those of SnIV (0.71 A).333 Tin Lewis acids have been applied to many kinds of reactions, including several asymmetric versions. 

Table 5. Comparison of sums of covalent and ionic radii...

Keywords Covalent and ionic radii, Golden ratio, hydrogen bond length... 

The electrostatic potential y(r) is a physical observable, which can be determined experimentally by diffraction methods as well as computationally. It directly reflects the distribution in space of the positive (nuclear) and the negative (electronic) charge in a system. V (r) can also be related rigorously to its energy and its chemical potential, and further provides a means for defining covalent and ionic radii" ... 

Van der Waals, covalent, and ionic radii from Dean (1999). 

The covalent and ionic radii are listed in A units. In view of the marked effects of environment on interatomic and interionic distances (Chaps. 9 and 12), the values given are fairly rough approximations. Covalent radii for the metals generally refer to one half the smallest interatomic distance in the elemental metal itself. 

All atoms, covalent and ionic radii were taken basically according to Belov-Bokii. For atoms C, N and O also the possibility to change covalent radii depending upon the bond repetition factor was taken into consideration. For the same elements average statistical values of P-parameters are given as PE / k - where k - hybridization coefficient, that assumes the possibility to further calculate average value of bond energy. 

The second important difference from covalent bonds is that hydrogen bonds are not atom-pair but group-pair properties. Since covalent and ionic bonds are atom-pair properties as a first approximation, they can be decomposed into atomic properties such as covalent and ionic radii, which are additive. They are almost un-... 

The electronegativity of Sn(II) and Sn(IV) is shown in Table 1 [3,4]. Sn(II) is more electropositive and hence cationic than Sn(IV), and is expected to coordinate with nucleophilic ligands. The covalent and ionic radii of Sn(II) are, on the other hand, larger than those of Sn(IV) (Tables 1 and 2) [3-11]. This is because electronic repulsion of the unpaired electrons of Sn(II) weakens the <5-bond because Sn(II) uses the p-orbital for bonding. 

The first two elements of Gp.III, although they have the configuration ns npi, are effectively tervalent since promotion to ns np occurs very readily. They form cations with an inert-gas structure much less readily than the elements of Gp.II which precede them, and their bonding is predominantly covalent. The covalent and ionic radii are given in Table 49. 

Its 3d 4s2 structure gives element 21 properties similar to the lanthanides and to lanthanum (Sd s ) in particular. The covalent and ionic radii, 1.44 A and 0.68 A, respectively, are however much smaller than those of the lanthanides. In consequence the Sc ion has a greater polarising power and more readily forms complexes for instance crystalline KgScFg can be obtained. The ionisation potentials 1st, 6.56 eV 2nd, 12.9 cV 3rd, 21.8 cV are not much larger than those of the lanthanides so far as they are known, and the metal itself is almost as reactive. 

PhysProp Effective Nuclear Charge - Ionisation energy - Electron Affinity - Covalent and Ionic Radii - Electronegativity - Orbital Energies and Promotional energies. 

Applications of molecular electrostatic potentials to a variety of areas - chemical reactivity and biological interactions [97-105], solvation [98,106], covalent and ionic radii [107], prediction of condensed-phase physical properties [108-110], atomic and molecular energies [89,92,111] -have been reviewed elsewhere, as indicated. Our purpose here is to relate V(r) to sensitivity. 

Van der Waals, metallic, covalent and ionic radii for the s-, p- and first row cZ-block elements... 

The metallic, covalent and ionic radii of A1 are 143, 130 and 54 pm respectively the value of rjon is for a 6-coordinate ion. (a) How is each of these quantities defined (b) Suggest reasons for the trend in values. 

This is a straightforward LEGO principle of combining atomic/ionic radii to construct the dimensions of the bonds in a molecule. Tables 9.1 and 9.2 list covalent and ionic radii of main group elements, and they allow us to highlight the power of the idea in Figure 9.10 with two applications. 

The covalent and ionic radii of transition metals (TM) have also been determined, and we show some of them in Appendix 9.A.I. These data allow you to construct the complete 3D structure of TM complexes. It is important to remember that all the radii are averaged over many bonds, and therefore, we cannot expect that our predictions will be perfectly accurate for every molecule, ionic material, or TM complex we try to construct with Tables 9.1, 9.2 and 9.A.I. Such usage will provide, however, a very helpful way to imagine the structure of matter and acquire a more thorough... 

Radii. Note the covalent and ionic radii of the atoms from i,P to, iSc as given in Table 7.6 (page 112). (a) With what neutral atom are all these ions isoelectronic (b) Explain the variation in atomic size, and the relation between the size of each ion and of its parent atom. 

---