The lengths of covalent bonds

From the early days of structural chemistry there has been considerable interest in discussing bond lengths in terms of radii assigned to the elements, and it has become customary to do this in terms of three sets of radii, applicable to metallic, ionic, and covalent crystals. Distances between non-bonded atoms have been compared with sums of van der Waals radii , assumed to be close to ionic radii. The earliest covalent radii for non-metals were taken as one-half of the M—M distances in molecules or crystals in which M forms % — N bonds N being the number of the Periodic Group), that is, from molecules such as F2, HO-OH, H2N--NH2, P4, Sg, and the crystalline elements of Group IV with the diamond structure. This accounts 

The situation with regard to heteronuclear bonds (M-X) is different. Shortening due to TT-bonding is to be expected in many bonds involving 0, S, N, P, etc. and is presumably the major reason for variations in the length of a particular bond such as S—0. This is consistent with the values of the stretching frequencies of the bonds  

Moreover, the electronegativity correction is by no means sufficient for bonds such as those in the molecules Sip4 and PF3  

In this connection it is interesting to note that the difference between pairs of bond lengths M-F and M-Cl is approximately equal in many cases to the difference between the ionic radii (0-45 A) rather than to the difference between the covalent radii (0 27 A) of F and Cl. This is to be expected for ionic crystals and molecules (for example, gaseous alkali-halide molecules) but it is also true for the following molecules  

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A polymer coil does not only possess a structure on the atomistic scale of a few A, corresponding to the length of covalent bonds and interatomic distances characteristic of macromolecules are coils that more or less, obey Gaussian statistics and have a diameter of the order of hundreds of A (Fig. 1.2) [17]. Structures of intermediate length scales also occur e. g., characterized by the persistence length. For a simulation of a polymer melt, one should consider a box that contains many such chains that interpenetrate each other, i. e., a box with a linear dimension of several hundred A or more, in order to ensure that no artefacts occur attributable to the finite size of the simulation box or the periodic boundary conditions at the surfaces of the box. This ne-... 

However, this cannot be the whole story, because gradient corrections usually and correctly shrink the lengths of covalent bonds to hydrogen [14,15,17], counter to expectations based upon the statement at the end of the previous paragraph. 

How are the lengths of covalent bonds related to their strength (Chapter 8)... 

Since the length of covalent bond changes with its partial ionicity, it is necessary to use electronegativity difference as another atomic parameter, together with covalent radii for the data processing work if the ionic nature of the chemical bond is obvious. 

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. 

A number of empirical methods exist for the adjustment of covalent bond lengths for ionic effects.34,35 These are based primarily on formulas that involve the sum of the covalent radii corrected by a factor that is dependent on the electronegativity difference between the atoms. In many instances, quite good agreement is obtained between the predicted and experimental values, as shown by the listing in Table I. 

The concept of back-bonding is not necessary to account for the lengths of polar bonds that are shorter than the sum of the covalent radii. These bonds are short because of the attraction between the atoms due to their opposite charges. 

Atomic radii and distances are now usually expressed in picometers (pm 1 pm = 10 m). The old angstrom unit (A, A = 100 pm) is now obsolete. The length of single bonds approximately corresponds to the sum of what are known as the covalent radii of the atoms involved (see inside front cover). Double bonds are around 10-20% shorter than single bonds. In sp -hybridized atoms, the angle between the individual bonds is approx. 110° in sp -hybridized atoms it is approx. 120°. 

Each atom makes a characteristic contribution, called its covalent radius, to the length of a bond (Fig. 2.17). A bond length is approximately the sum of the covalent radii of the two atoms (44). The O—H... 

Covalent (electron pair) bond strengths vary between approximately 60 and 90 kcal/mol for most elements present in hard materials, but the cube of covalent bond length varies even more approximately 3.65 A3 for C-C, 6.1 A3 for Si-O, and 14.3 A3 for Ni-As. The heavier elements generally offer more bonds per atom, but this usually does not compensate for the larger molar volumes except in certain interstitial compounds such as WC and TiN. Thus, the hardest materials are generally made of... 

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