Multiple bond radii

The usefulness of the multiple-bond radii in the discussion of the electronic structure of molecules will be illustrated in later sections. 

For multiple bonds a different set of radii must be used because multiple bonds represent greater attractive forces between atoms than is true of single bonds. Consequently, atoms can approach each other more closely before repulsions cause an increase in energy. Multiple bond radii are therefore smaller than single bond radii. 

Multiple-bond radii can also be obtained. For example, the triple-bond radii of carbon and nitrogen can be calculated from the bond lengths in HC=CH and N=N as 0.60 and 0.55, giving 1.15 for C=Nas compared with experimental values of 1.16. It may be stated, as a general rule, that the higher the order of a bond between two atoms, the shorter it is. Thus, for carbon—carbon bonds the following are typical lengths C—C, 1.54 C=C, 1.33 C=C, 1.21. 

Each atom makes a characteristic contribution, called its covalent radius, to the length of a bond (Fig. 2.21). A bond length is approximately the sum of the covalent radii of the two atoms (36). The O—H bond length in ethanol, for example, is the sum of the covalent radii of H and O, 37 + 74 pm = 111 pm. We also see from Fig. 2.21 that the covalent radius of an atom taking part in a multiple bond is smaller than that for a single bond of the same atom. 

The radius of an atom helps to determine how many other atoms can bond to it. The small radii of Period 2 atoms, for instance, are largely responsible for the differences between their properties and those of their congeners. As described in Section 2.10, one reason that small atoms typically have low valences is that so few other atoms can pack around them. Nitrogen, for instance, never forms penta-halides, but phosphorus does. With few exceptions, only Period 2 elements form multiple bonds with themselves or other elements in the same period, because only they are small enough for their p-orbitals to have substantial tt overlap (Fig. 14.6). 

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-... 

Ideally one would wish to remove the need for statistics by directly and reproduce-ably measuring a single bond only. One problem with the measurement of specific individual bond energies is that it is extremely difficult, even with a tip of small radius, to isolate a single bond species between the tip and the sample. To form a single bond in a controlled way requires the cantilever to be stiffer than the maximum force gradient experienced during the approach, but stiffer levers exhibit less sensitivity. If multiple bonds are formed, then it can be difficult to make an independent calculation of the contact area and hence the number of bonds involved. 

The unique ligating behavior of the bridging 2,6-dimethoxyphcnyl ligand with respect to promoting a substantial decrease in the metal atom separation for molybdenum(II) dimers is even more prominent in the case of chromium. The chromium-chromium distance of 1.847(1) A in Cr2(DMP)4 (90) is more than 0.1 A less than the corresponding value in any other chromous dimer yet reported. To compare homonuclear multiple bonds among elements with inherently different atomic radii, Cotton, Koch, and Millar proposed a normalized value for intemuclear distances based on Pauling s atomic radius of the element in question (209). A simple definition of formal shortness as t/(M—M)/2r(M) then follows as a measure of the relative compactness of the attractive interaction (90). The formal shortness ratio of 0.778 for the quadruple bond in... 

The atomic radius of the atom X is defined as half the length of an X-X single bond. This can be obtained experimentally from the structures of elemental substances containing molecules X where the X-X bond order is believed to be unity, e.g. Cl2, P4, S8. It may also be obtained from the X-X distances found in molecules such as HO—OH, H2N—NH2 etc. for atoms which form multiple bonds in the elemental substance. Such atomic radii may be termed covalent radii. For atoms which form metallic elemental substances, metallic radii are obtained. These are usually standardised for 12-coordination of each atom, which is the most common situation in metals. Corrections can be made in the cases of metals which adopt other structures. 

Nitrogen differs greatly from other group members owing to its high electronegativity (X = 3.0), small size (radius of 74 pm), ability to form multiple bonds, and lack of available cf-orbitals. It is found with oxidation numbers from -3 to +5. 

The covalent radius of an element may be considered to be one half of the covalent bond distance of a molecule such as Cl, (equal to its atomic radius in this case), where the atoms concerned are participating in single bonding. Covalent radii for participation in multiple bonding are also quoted in data books. In the case of a single bond between two different atoms, the bond distance is divided up between the participants by subtracting from it the covalent radius of one of the atoms, whose radius is known. A set of mutually consistent values is now generally accepted and, since the vast majority of the elements take part in some... 

The calculation results of dissociation energy by the Eq. (4.7), given ion Table 4.2, demonstrated that Pc=flo- some molecules containing such elements as F, N and 0, the values of ion radius have been applied to register the bond ionic character for calculating Pg-parameter (in Table 4.2 marked with ). For such molecules as C, N, the calculations have been made by multiple bonds. In other cases the average values of bond energy have been applied. The calculated data do not contradict the experimental ones [2, 3]. 

On looking for a relationship between ionization radius and the chemistry of homonuclear covalent interaction, the classification into single and multiple bonds is followed as a first approximation. An immediate observation, valid for most single bonds, is a constant value of the dimensionless distance... 

Since both orbital and dipolar terms depend upon the inverse cube of the radius of the p orbitals on atoms A and B, it is expected that these terms will be of most importance when multiple bonding occurs. Their contributions may also be expected to vary periodically as implied by the data presented in Table 1. Thus heavy nuclei can be expected to have very large couplings with significant contributions from orbital, dipolar, and contact interactions. The latter interactions depend upon S (o), as shown by eq. 13, in which S (o) represents the s electron den-... 

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