Bond radii

As in the case of ions we can assign values to covalent bond lengths and covalent bond radii. Interatomic distances can be measured by, for example. X-ray and electron diffraction methods. By halving the interatomic distances obtained for diatomic elements, covalent bond radii can be obtained. Other covalent bond radii can be determined by measurements of bond lengths in other covalently bonded compounds. By this method, tables of multiple as well as single covalent bond radii can be determined. A number of single covalent bond radii in nm are at the top of the next page. 

Deductions of bond lengths for any unknown can be made by adding bond radii, but these theoretical values often differ from the experimental values the greatest deviations occur when elements of widely different electronegativities are joined together. 

In Table VI3) and Fig. 3 there are given radii for use in compounds of this type. The sum of the singlebond radii for two atoms gives the expected distance between these two atoms in such a compound when they are connected by a covalent bond. The sum of their double-bond or triple-bond radii similarly gives the expected distance when they are connected by a double or a triple bond. 

It seems probable also that, to within one or two percent, doublebond and triple-bond radii for various atoms should bear constant ratios to single-bond radii. We have chosen 0.79 for the triple-bond factor, which gives agreement with the observed distance in the N2 molecule, and 0.90 for the double-bond factor. The radii given in Table VI are obtained with these factors. 

The discussion of interatomic distances in salts of oxygen acids of the second-row elements is presented in Table IV. In the first row of this table, below the names of the salts, there are given values of the electronegativity difference xa — xb, in the second row the sum of the single-bond radii, in the third row the Schomaker-Stevenson correction, and in the fourth row the single-bond interatomic distance. The next row contains the fractional amount of ionic character of the a bond, as given by the electronegativity difference with use of Table... 

Values of Single-bond Radii and Metallic Radii for Coordination Number 12... 

In applying the metallic radii in the discussion of the structure of a metal or intermetallic compound either the observed distances may be used with the single-bond radii to calculate the bond numbers, the sums of which may then be compared with the expected valences, or the distances may be compared with the sums of radii for suitable coordination numbers, such as CN12. The correction to be added to i (CN12) to give the radius for another coordination number, the va-... 

An equation has been formulated to express the change in covalent radius (metallic radius) of an atom with change in bond number (or in coordination number, if the valence remains constant), the stabilizing (bond-shortening) effect of the resonance of shared-electron-pair bonds among alternative positions being also taken into consideration. This equation has been applied to the empirical interatomic-distance data for the elementary metals to obtain a nearly complete set of single-bond radii. These radii have been compared with the normal covalent... 

Application of equation (10c) to the observed single-bond radii of scandium, titanium and vanadium (1-439,1-324,1-224 A) leads to 20, 27 and 35 % of d character, respectively (table 5). The gradual increase presumably results from the increasing stability of the 3d orbitals relative to 4s and 4p. 

Table 5. Single-bond radii and amount of d character...

Values of the single-bond radii for the metals of the series silver to tin and gold to lead are also given in table 6, as calculated by equations (10c) and (11c) for the pure valence states A, B, C and D and for certain intermediate valencies, corresponding to resonance among these states. 

It is possible that a small amount of oxygen is necessary to stabilize the -tungsten structure (see, e.g. Moss Woodward, 1959). A consideration of the effect of this oxygen might lead to a small revision in the values of the single-bond radii and amounts of d character. 

In the course of the work it was found that the value assumed five years ago for the carbon double-bond covalent radius (obtained by linear interpolation between the single-bond and the triple-bond radius) is 0.02 A. too large in consequence of this we have been led to revise the double-bond radii of other atoms also. 

Revised Values of Double-Bond Covalent Radii.—This investigation has led to the value 1.34 A. for the carbon-carbon double-bond distance, 0.04 A. less than the value provided by the table of covalent radii.111 4 Five years ago, when this table was extended to multiple bonds, there were few reliable experimental data on which the selected values for double-bond and triple-bond radii could be based. The single-bond radii were obtained -from the study of a large number of interatomic distances found experimentally by crystal-structure and spectroscopic methods. The spectroscopic value of the triple-bond radius of nitrogen (in N2) was found to bear the ratio 0.79 to the single-bond radius, and this ratio was as-... 

The new carbon-carbon double-bond distance corresponds to the value 0.87 for the double-bond factor. Moreover, there are now available three accurately known triple-bond distances 1.204 for C=C in acetylene, 1.154 A. for C=N in hydrogen cyanide, and 1.094 for N==N in the nitrogen molecule, whereas five years ago only the last was known. The ratios of these distances to the corresponding sums of single-bond radii are 0.782, 0.785, and 0.781, respectively. We accordingly now select 0.78 as the value of the triple-bond factor. Revised covalent radii26 for first-row atoms are given in Table XV. 

The revision leads to a difference of 0.06 A. between the interatomic distance in the normal oxygen molecule and the sum of the double-bond radii. This may be attributed to the presence of an unusual structure, consisting of a single bond plus two three-electron bonds. We assign this structure both to the normal 2 state, with ro = 1.204 A., and to the excited 2 state, with ro = 1.223 A., the two differing in the relative spin orientations of the odd electrons in the two three-electron bonds. We expect for the double-bonded state the separation n 1.14 A. 

Table 2.2 Single, Double, and Triple Bond Radii (pm)...

The length of a bond is equal to the sum of the bonding radii of the two bonded atoms. 

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