Pauling radii

It is possible to discuss the interatomic distances in relation to the valences of lead and thallium. From the system of metallic radii (Pauling, 1949) and the relation =DX-0-600 log n... 

Sources For van der Waals radii, Chauvin, R, (1992) Explicit periodic trend of van der Waals radii, J. Phys. Chem. 96, 9194-9197, For covalent radii, Pauling, L, (1960) Nature of the Chemical Bond, 3rd edn, Cornell University Press, Ithaca, NY... 

In many cases the M—S bond has been found to be normal in length, i.e. the bond distances agree fairly well with the sum of the covalent radii (Pauling s scale, data appropriate to coordination number and oxidation state). However, in some complexes the M—S distances are significantly shorter than the calculated ones, for example in thioether compounds with Cr°, Pd11, Pt, Cu1 and Au1. This observation has often led to the suggestion that the shortening is due to some Jt-back-donation from the metal to the sulfur. 

This is certainly much more probable than the assumption of a partial double bond character in order to explain the observed shortening of the Si—F distance (sum of atomic radii Pauling 1.81 A Stevenson and Schomaker 1.69 A obs. 1.54 A). 

There are several definitions and values assigned to covalent radii. Pauling created an early scale using bond lengths in simple homonuclear compounds as the starting point. An extended version of this scale is listed as covalent in Table 1.5. A related, but more comprehensive, approach is to examine structural data to determine covalent radii that best correlate with observed bond distances. This approach was developed by Slater. An extensive tabulation of bond lengths derived from structural data was published in 1987. These values are labeled stmctural in Table 1.5. A set of... 

Figure 5. These are four Sr(2) (at 3.898 A), four Sb (at 3.451 A), and four Sr(l) atoms at the very short distance of 3.537 A. The atomic distribution around the Sr(2) atoms in the B layers consists of thirteen atoms, four Sb (at 3.589 A) in its own B layer, one Sb (at 3.335 A) and four Sr(2) (at 4.464 A) in the adjacent B layer, and four Sr(l) (at 3.898 A) in the adjacent A layer. The average Sr—Sb distance of 3.499 A is appreciably smaller than the value of 3.70 A obtained from the sum of the metallic radii (Pauling) and assuming co-ordination numbers of 9, 12, and 13 for Sb, Sr(l), and Sr(2) respectively. This, together with the small Sr(l)—Sr(l) distance, indicates a pronounced deviation from metallic behaviour towards a partial ionic character for these atoms. ...

Value obtained in this work using the SCFVAC and radii=Pauling parameters in the PCM model Values obtained in this work using free-eneigy curves from ab initio potentials and MD simulations Experimental value obtained by Guthrie, Ref. [16]... 

Arguments involving exact details of what should be a metallic atom s size appear to be unimportant in questions of structural stability. Any reasonable self-consistent set of radii is sufficient for discussion, and Pauling s R(i) — R( ) = 0.3 log n rule can be used to convert radii appropriate for one coordination number to another. Regardless of the failings of any particular set of metallic radii, Pauling s rule appears to be very reliable. 

For the relation between the bond order n and the interatomic distance or more specifically the atomic radius Pauling uses the formula rx — rn = 0.300 log n (rx bond radius for a pure single bond). Such an expression is found to be valid for the C—C bond with a coefficient of 0.353. 

Mass magnetic susceptibility (as a solid) Ionic radius (Pauling)... 

Since the atomic sizes are different in the substances with different kinds of chemical bond. It is necessary to assign the atoms of elements three kinds of system of atomic radius. In ionic systems, we call the size of ions as ionic radius. In covalent compounds, system of covalent radius is used. And the atomic radius in metallic systems is called metallic radius of elements. In his classical work, Pauling has assigned the values of these three kinds of radius. Pauling s values of atomic or ionic radii have been widely used till now. But there are still other systems proposed by other authors in later years. 

Element Atomic number Outer electrons Atomic radius (nm) m.p. (K) h.p. (K) 1st ionisation energy (kj Electro- negativity (Pauling)... 

When a specific value above is n ot hn own, the rule of Pauling (the van der Waals radius is approximately 0.76 A larger than the cova-len t radiiis) is u sed. 

IP, ionization potential [/], EA, electron affinity [7], av atom polanzabihty [2], r, van der Waals radius [3], Xp- Pauling electronegativity... 

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. 

It is furthermore to be anticipated that the cation-cation repulsion will operate in some cases to displace the cations from the centers of their coordinated polyhedra. This action will be large only in case the radius ratio approaches the lower limit for stability, so that the size of the polyhedron is partially determined by the characteristic anion-anion repulsive 21 Linus Pauling, Z. Krist., 67, 377 (1928). 

This system is based on the observations (Pauling 1947) that a linear relation between single-bond radius and atomic number holds for bonds of constant hybrid character, and that for an element the single-bond radius is (at least approximately) linearly dependent on the d character of the dsp hybrid bond orbitals. 

It has been found that a carbon-oxygen double bond decreases the single-bond radius of the carbon atom involved Pauling and Brockway, paper to be submitted to This Journal. 

According to the first Pauling rule the cation/anion radii ratio, allowed for octahedral coordination (C ,) has to be in the range of 0.41 - 0.73. For tetrahedral co-ordination this ratio (f,a) has to be within the range of 0.22-0.41. To estimate the above ratios for the cations used a value of 1.4 A is taken for the O anion radius value [14]. Results are presented in the Tab 3... 

The critical sizes of the reactant molecules were estimated and are shown in Figure 5, where the figures for 2-hexanol, isopropylacetate, sec-butylacetate and cyclohexylacetate are estimated by MM2 from Pauling s atomic radius and molecular model [18]. Therefore, the unique catalysis of Cs2.2 is understood if one assumes that it is active only for small molecules. In other words, this catalyst exhibits "reactant shape selectivity", where the catalyst differentiates the reactants according to their size. 

Figure 2.2 A contour plot of the electron density in a plane through the sodium chloride crystal. The contours are in units of 10 6 e pm-3. Pauling shows the radius of the Na+ ion from Table 2.3. Shannon shows the radius of the Na+ ion from Table 2.5. The radius of the Na+ ion given by the position of minimum density is 117 pm. The internuclear distance is 281 pm. (Modified with permission from G. Schoknecht, Z Naiurforsch 12A, 983, 1957 and J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed., 1993, HarperCollins, New York.)...

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