Bond Lengths and Covalent Radii

We discuss bond lengths in the next section, but we defer the discussion of bond angles to Chapters 4 and 5, where we discuss all aspects of molecular geometry. In later sections of this chapter we discuss bond strength in terms of bond enthalpies and force constants, the determination of approximate values for these properties in polyatomic molecules, and the determination and analysis of dipole moments. 

Bond lengths have usually been, and still often are, measured in angstroms (A) but, with the advent of SI units, the nanometer (10 9 m) and the picometer (10 12 m) are now being used more frequently. In this book we express bond lengths and other molecular dimensions in pi-cometers, which is for many purposes a more convenient unit than the angstrom (1 A = 100 pm). 

The covalent radii for most of the elements were obtained by taking one-half of the length of a single bond between two identical atoms. For example, the covalent radius of sulfur is obtained from the length of the S—S bond in the S8 molecule  

The values for the covalent radii of N and 0 given in the table dp not differ significantly from the Pauling values, but the value for fluorine is a little smaller. They were obtained by extrapolation of the values for the other period 2 elements (Robinson et al., 1997). In any case the covalent radii of oxygen and fluorine are of little use because, as we shall see later, essentially all bonds formed by these elements, except the O—O, O—F, and F—F bonds, which are abnormally weak and long, have too great an ionic character to justify the use of covalent radii to calculate bond lengths. 

The distance between the nuclei of two atoms forming a covalent bond is called the bond length. Interatomic distances and bond lengths 

The single bond covalent radius of carbon may be taken to be about 0.77 A, just half of the C—C bond length in diamond. Similarly, the covalent radii of chlorine and iodine may be set at 0.99 A and 1.33 A, respectively, one half of the interatomic distances in the Ch and I2 molecules. 

CONTRACTION IN BOND LEHGTHS WITH INCREASING POLARITY 

The Schomaker-Stevenson relationship proposes that such bond shrinkage is directly proportional to the electronegativity difference between the bound atoms and that the interatomic distance, rA B, is thus linearly related to the covalent radii, ta and r  

a is a constant. When E is in kcal a is happily close enough to the value 4.6 so that Huggins equation may be rewritten  

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L. Pauling, The Nature of the Chemical Bond. 3rd Ed. 1960 Cornell University Press. Chapter 7 discusses bond lengths and covalent radii. Chapter 9 discusses ionic radii. 

The ionic radii at, a were calculated from bond lengths and covalent radii [6, 7, 8], It should be noted that for a cation, such as CH3 - C = O, the C=0 and C-C bonds are shorter than those of the isoelectronic neutral species Observed solubilities are derived from as yet unpublished preparative experiments f Prom reference [9] ... 

The aromatic character of 1,3,4-thiadiazole can be demonstrated with the aid of micro-wave spectroscopy. Using the differences between the measured bond lengths and covalent radii, aromaticity, as shown by 7r-electron delocalization, diminishes in the order 1,2,5-thiadiazoles > thiophene > 1,3,4-thiadiazole > 1,2,5-oxadiazole (66JSP(19)283). The micro-wave spectrum was further refined by later workers (7lJST(9)l63). 

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. 

In Section 4 the data on bond lengths and strengths have been vastly increased so as to include not only the atomic and effective ionic radii of elements and the covalent radii for atoms, but also the bond lengths between carbon and other elements and between elements other than carbon. All... 

Bond type X Covalent radii"-4 (A) AEN Schomaker and Stevenson Blom and Haaland Observed bond lengths (A)... 

Table 2.6 Comparison of Observed Bond Lengths and Bond Lengths Calculated from the Sum of Covalent Radii...

Table 20 The Difference Between the Observed Rs Bond Lengths and the Pauling Covalent Radii49 (P.C.R.) giving the Apparent In-plane Radii of the Copper(II) Ion...

The atomic and covalent radii used to evaluate the bond lengths in Table 7. 

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