Metal coordination number cation size effects

The dominant features which control the stoichiometry of transition-metal complexes relate to the relative sizes of the metal ions and the ligands, rather than the niceties of electronic configuration. You will recall that the structures of simple ionic solids may be predicted with reasonable accuracy on the basis of radius-ratio rules in which the relative ionic sizes of the cations and anions in the lattice determine the structure adopted. Similar effects are important in determining coordination numbers in transition-metal compounds. In short, it is possible to pack more small ligands than large ligands about a metal ion of a given size. 

Why should the early transition metals form so many polyoxoanions The answer lies in the size of the M5/6+ cations and their -acceptor properties.1,5 The effective ionic radii of V5+ (0.68 A), Mo6+ (0.77 A) and W6+ (0.74 A) are consistent with the observation that these cations adopt four-, five- and six-fold coordination by oxide ion. With very few exceptions V, Mo and W atoms in heteropolyanions are six-coordinate. On the other hand Cr6+ (0.58 A) hap a maximum coordination number of four in oxides and oxoanions. Few isopoly- and heteropoly-chromates are known and they are all based on groups of corner-shared Cr04 tetrahedra [Cr207]2-, [Cr3O10]2-, [Cr4Oi3]2-, [03SOCrO3]2-, [02I0Cr03]-,... 

Scheme I and, in more detail, Table 4 represent the trend of ionic radii of these large cations which prefer formal coordination numbers in the range of 8-12 [77]. For example, considering the effective Ln(III) radii for 9-co-ordination, a discrepancy of 0.164 A allows the steric fine-tuning of the metal center [60]. The structural implications of the lanthanide contraction can be visually illustrated by the well-examined homoleptic cyclopentadienyl derivatives (Fig. 2) [78], Three structure types are observed, depending on the size of the central metal atom A, [( j5—Cp)2Ln(ji— 5 rf — Cp)] x, 1 < % < 2 B Ln(fj5 —Cp)3 C, [fo -CpJjLnCi- 1 ff1—Cp)], these exhibit coordination numbers of 11 (10), 9, and 8, respectively. Also a small change in ligand substitution leads to a change in coordination behavior and number (10), as...

All of the alkaline earth metals form saltlike MX2 dihahdes (see Alkaline Earth Metals Inorganic Chemistry). Within this group, we observe stmctural effects owing to both cation sizes and properties of the halide ions. From Be to Ba, coordination numbers monotonically increase from four (tetrahedral) in Be dihalides to eight (cubic) or nine (tricapped trigonal prismatic) in the Ba systems. 

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 (the anion exerts a smaller influence on the radius of the cation). The table in Appendix B-1 shows the effect of coordination number. 

One of the most widely known and used set of ionic radii are those estimated by Pauling [2] on the basis of interionic distances in ionic crystals. He noted that repulsive effects between ions of the same charge depend on the relative size of the cation and anion in the crystal, and also took into consideration the coordination number of the ion with oppositely charged neighbors in the crystal lattice. The results obtained for the alkali metal and halide ions for the case that the coordination number is six (rock salt structure) are summarized in table 3.1. 

Many X-ray diffraction studies of electrolyte solutions have been carried out in aqueous solutions [Gl, 4, 5]. Values of the most probable distance, between the oxygen atom in water and a number of monoatomic ions are summarized in table 5.1. In the case of the cations, this distance reflects the radius of the cation plus the effective radius of the water molecule measured in the direction of the lone pairs on oxygen. In the case of alkali metals, the effective radius of water increases from 122 pm for Li" " to 131 pm for Cs when the Shannon and Prewitt radii are assumed for the cations (see section 3.2), the average value being 127 pm. This result can be attributed to the observation that the coordination number for water molecules around an alkali metal or alkaline metal earth cation changes with cation size and electrolyte concentration. In the case of the Li" " ion, this number decreases from six in very dilute solutions to four in concentrated solutions [5]. Because of the electrostatic character of the interaction between the cation and water molecules, these molecules exchange rapidly with other water molecules in their vicinity. For this reason, the solvation coordination number should be considered as an average. 

Things are decidedly different for ionically bonded systems. Generally when an electron leaves a metallic atom to form a cation, the cation will be effectively smaller than the atom in a metallic bond even though the valence electron in the metal is delocalized. Similarly, the size of the anion that has gained the electron is generally larger than the neutral atom. A self-consistent set of ionic radii have been worked out for systems with a coordination number of 6 (rock salt structure). A correction of -1-0.008 nm must be added to the sum of the standard ionic radii for coordination number of 8 and a correction of —0.011 must be subtracted for tetrahedrally coordinated structures. 

For d-transition-metal ions, the number of water molecules in the primary coordination sphere (A-zone) is in most cases determined by the strength of orbital overlap between the metal ion and H2O molecules, crystal field stabilization effects, and cationic charge. Other species (e.g., alkaline earths, rare earths) interact with solvent molecules via ion-dipole forces with minimal orbital overlap conhibution to the bonding. Their solvation numbers are determined by a combination of coulombic attraction between cations and water molecules, steric fiictors, and van der Waals repulsion between the bound water molecules. The larger size and high charge of the lanthanides combine with the absence of directed valence effects to produce primary-sphere hydration numbers above eight for these metal ions. 

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