Radius and coordination number

The physical properties of metal alkoxides depend primarily on the characteistics of the metal (e.g., the electronegativity, valence, atomic radius, and coordination number) and secondarily on the characteristics of the alkyl group (e.g., the size and shape). There is a change from the solid, nonvolatile ionic alkoxides of some of the alkali metals to the volatile covalent liquids of elements of valence 3, 4, 5, or 6 (e.g., Al, Si, Ti, Zr, Sb, and Te), whereas alkoxides of metals with intermediate electronegativities, such as La and Y, are mainly solids (Table 5.1). 

The radii av a2 and coordination numbers zv z2 follow from x-ray analysis (cf. Section I.B), and aQ/2 — 1.25 A corresponds to Pauling s van der Waals radius of 1.40 A for a covalently bound oxygen atom.25 The value of eQlk — 166.9°K was chosen to obtain agreement between calculated and experimental values of the equilibrium vapor pressure of argon hydrate at 0°C. 

The uncertainty of the proper coordination number of any particular plutonium species in solution leads to a corresponding uncertainty in the correct cationic radius. Shannon has evaluated much of the available data and obtained sets of "effective ionic radii" for metal ions in different oxidation states and coordination numbers (6). Unfortunately, the data for plutonium is quite sparse. By using Shannon s radii for other actinides (e.g., Th(iv), U(Vl)) and for Ln(III) ions, the values listed in Table I have been obtained for plutonium. These radii are estimated to have an uncertainty of 0.02 X ... 

On the contrary, a quite systematic behavior with the lanthanoid ion contraction is observed. A plot of the energy of CTI band versus the ionic radius at coordination number 8 of the Ln ions (16) indicates a linear decrease of this energy as the ionic radius increases. This is seen in Figure 3, and illustrates a bare size effect of the energy variation. The phenomenon is called "optical detection of the lanthanoid ion contraction by internal charge transfer absorption". 

A comparison of the metal-carbon bond lengths, ionic radii and formal coordination numbers of these compounds is summarized in Table 2. The formalism used in estabhshing coordination number assumes that a -cyclooctatetraene ligand is a 5 electron-pair donor. The ionic radii have been adjusted for both the charge of the central metal and coordination number (50). When the ionic radius for a given coordination number is not available, it has been estimated by interpolation from radii of other coordination numbers. It will be seen that the differ-... 

Rg. 4.18 Actual crystal structures of the alkali halides (as shown by the symbols) contrasted with the predictions cl the radius ratio rule. Tie figure is divided into three regions by the lines rjr. 0.414 and r+/h- a 0.732, predicting coordination number 4 (wurizite or zinc blende, upper left), coordination number 6 (rock salt, NaCl, middle), and coordination number 8 (CsCI, lower right). The crystal radius of lithium, and to a lesser extent that of sodium, changes with coordination number, so both ihe radii with C.N. 4 (left) and C.N = 6 Iright) have been plotted. 

The approach presented here allows us to calculate such a physically important observable quantity as the gyration radius of a closed chain unentangled with obstacles. Omitting the nonuniversal numerical coefficients depending on the space dimensionality and coordinational number of the lattice of obstacles, the following scaling relation obtained in Refs. [18,22] is fulfilled ... 

TfR-mediated endocytosis is a well-known uptake system Tf binds one or two Fe atoms, but only diferric Tf (Fe2Tf) has a high affinity for TfR to be taken up by the receptor-mediated endocytosis. This system uses a mobilization pathway that involves endosomal acidification, reduction of ferric Fe, and ferrous Fe transport [8]. Recently, it was clarified that divalent cation/ metal ion transporter (DCT1) or Nramp2 involves iron transport from the endosome to the cytosol [9, 10]. Al resembles Fe in chemical characteristics ionic radius, charge density, and coordination number [11]. Therefore, Al binds with Tf to form di—Al—Tf. Al bound to Tf even passes through the blood-brain barrier to enter the neuronal cells via Tf receptor-mediated endocytosis [12]. 

It is obvious from the table that the ionic radii of lanthanides are very similar to the ionic radius of the Ca2+ ion. Further, the ionic radii of lanthanides differ by about 0.3 A in changing the coordination environment from 6 to 12. The differences of 0.3 A in ionic radius between coordination number 6 and 12 makes the lanthanides(III) ions highly adaptable to many coordination environments. This has led to the development of a wide array of macrocyclic molecular complexes with exciting properties. From this point of view, lanthanides have been known as the chameleons of coordination chemistry [5]. 

The similarities cited permit Ln3+ ions to take the place of Ca2+ ions in biological reactions. Many Ca2+ binding sites exclude competing Mg2+ although the former might be present at lower concentrations. This selectivity is due to the small ionic radius (0.72 A) and coordination number of 6 (inflexible coordination geometry) and affinity for N atoms of Mg2+. It has also been observed that Ln3+ ions can occupy Mg2+ sites in t-RNA and some Mg2+ requiring enzymes. Ln3+ ions can also substitute for Fe3+, Fe2+ and Mn2+ in some cases. 

Table 5.2. Spatial arrangement of rigid spheres in relation to radius ratio and coordination number...

The ionic radius varies with the charge and coordination number of the ion a coordination number of 6 refers to octahedral coordination, and of 4 refers to tetrahedral unless otherwise specified. Data for the heavier d-block metals and the lanthanoids and actinoids are listed in Tables 22.1 and 24.1. 

Compiled from Hammond (1986). Ionic radius (A) for the -I- 3 oxidation state and coordination number = 6. 

---