Radii, covalent

Covalent radii are mostly used in organic chemistry. The simplest way to obtain a set of covalent radii is to half the distance between atoms linked by a covalent bond in a homonuclear molecule, such as H2. Covalent radii defined in this way frequently do not reproduce the interatomic distances in organic molecules very well, because these are influenced by double bonding and electronegativity differences between neighbouring atoms. In large molecules such as proteins, this has important structural consequences. 

The three widely used types of covalent radii are the normal (rnor), the tetrahedral (rte), and the octahedral (roc) ones rnor is defined as half the single-bond distance in a homo-atomic molecule with = v, and rte as half the bond distance in a diamondlike structure, hence r or = rte for tetravalent elements. The systems of tetrahedral and octahedral radii have been first introduced by Huggins and Pauling [128-131, 139-142], who observed that rte r nor for nonmetals while rte rnor for metals. The difference can be qualitatively explained by the fact that metals have fewer than 4 outer electrons, hence an increase of from 1 to 4 is bound to reduce the number of electrons per bond, while nonmetals have enough outer electrons to provide for all these bonds. 

At first, rte and roc have been calculated only for the elements, for which the corresponding coordination is more typical, i.e. ne for the Group 11-17 elements and Be, roc for the rest. Later, Van Vechten and Phillips [132] have determined ne and roc for the same elements and observed that always ne roc, and that either radius remains practically constant within the following series of elements, (i) Si, P, S, Cl (ii) Cu, Zn, Ga, Ge, As, Se, Br (iii) Ag, Cd, In, Sn, Te, I, probably because an increase of Z along a period is compensated by an increase of inter-electron repulsion. Note that the systems of ne derived by Pauling and Phillips, differ substantially, as do the r or published by different authors [133-139]. This is so because that additivity of the radii is perfect only for purely covalent (non-polar) bond, while polar bonds are shorter. This tendency, first rationalized by Schomaker and Stevenson [140], can be described by equations 

Now it is clear why sums of covalent radii cannot represent adequately the variety of polar bonds. Optimizing the radii can only tune the system to a certain range of polarities. The r values will vary depending on the choice of the reference structures and the optimization procedure, especially when metal atoms (with low ENs) are involved. Thus, Slater s atomic radii of the most electronegative elements (F, O, N) are underestimated. However, a simple additive model can work where all atoms happen to be of similar EN, as in many organic molecules. 

Batsanov [143-145] comprehensively revised the system of covalent radii was using the extensive structural data now available. As far as possible, the normal radii were derived directly from interatomic distances in homo-atomic molecules, elemental solids or compounds containing homo-atomic moieties. The only hetero-atomic bond distances used were the M-CH3 and M-H in metal alkyls and hydrides. 

State of an atom has been determined [148] taking into account the hybridization of orbitals and the influence of unpaired electrons (Table S1.7) in good agreement with the experiment. 

Different authors sometimes give slightly different covalent radii for the same element this is particularly true for alkali metals and alkali earth metals. Such a variation arises from the following factors  

As pointed out in Sections 14.3.3 and 14.3.4, the length of a C-C single bond ranges from 136 to 164 pm. Hence the data given in Table 3.4.3 are for reference 

The standard tetrahedral radii obtained by Pauling and Huggins have sometimes been referred to as tetrahedral covalent radii, but we prefer the original notation since we wish to reserve the term covalent for bonds to which each atom provides one electron. We shall return to this point in Sect. 9. Since these radii can only be used to predict bond distances between atoms that are both tetrahedrally coordinated, they are of limited utility. They were nevertheless of great interest at the time since they were the first radii that provided a quantitative illustration of the decrease of atomic bonding radii across the short periods of the periodic table and their increase as a group is descended. 

The bond distances in crystals with rock salt, fluorite, diamond, sphalerite, or wurtzite stmctures could be determined with great accuracy because they could be calculated directly from the unit cell dimensions. The determination of bond distances in molecular compounds in general requires the determination of the coordinates of the individual atoms within the unit cell. In the early 1930s, such studies were time consuming and difficult, and the resulting bond distances were 

Gas-phase electrrai diffraction as a technique for the determination of molecular structures was first developed by H. Mark and R. Wierl in 1930, but the usefulness of the method was demonstrated by studies of only a handful of molecules before the project was abandoned 3 years later [57]. After a visit to Mark s laboratory, L. Pauling and his graduate student L. Brockway built up an extremely productive electron diffraction group at California Institute of Technology, fri 1936 they were able to publish a review article with structural information on nearly 150 different molecules determined with error limits ranging from 1 to 3 pm. 

By 1939 Pauling was able to present a table of covalent radii for the hydrogen atom and the sixteen elements in the square defined by the positions of C, Sn, F, and I in the periodic table [37]. These radii were based on the bond distances in the crystalline elements of the Group 14 metals the Group 15 elements P, As, and Sb and the Group 16 elements S, Se, and Te, all determined by X-ray diffraction the bond distances in H2 and the dihalogen molecules determined by spectroscopic methods and finally by the bond distances in the gaseous methyl derivatives of all the seventeen elements except Sb, Se, and Te determined by gas electron diffraction. 

As an increasing number of molecules with bonds between F, O, or N atoms and very electropositive elements like Si were studied in the following years, it became clear that the correction for electronegativity differences suggested by Schomaker and Stevenson was too small. Thus the experimentally determined Si-F bond distance in FSiHs was 13 pm shorter than estimated, the Si-O bond distance in O (SiH3)2 was 16 pm shorter, and the Si-N distance in N(SiH3)3 was 9 pm shorter than estimated. 

The correction parameter c depends on the atoms concerned and has values between 2 and 9 pm. For C-X bonds no correction is necessary when X is an element of the 5th, 

6th or 7th main groups, except for N, O and F. The influence of bond polarity also shows up in the fact that the bond lengths depend on the oxidation states for instance, the P-O bonds in P406 (164 pm) are longer than in P4O10 (160 pm sum of the covalent radii 183 pm). Deviations of this kind are larger for soft atoms, i.e. for atoms that can be polarized easily. 

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The wave function T i oo ( = 11 / = 0, w = 0) corresponds to a spherical electronic distribution around the nucleus and is an example of an s orbital. Solutions of other wave functions may be described in terms of p and d orbitals, atomic radii Half the closest distance of approach of atoms in the structure of the elements. This is easily defined for regular structures, e.g. close-packed metals, but is less easy to define in elements with irregular structures, e.g. As. The values may differ between allo-tropes (e.g. C-C 1 -54 A in diamond and 1 -42 A in planes of graphite). Atomic radii are very different from ionic and covalent radii. 

Covalent radii for all the elements are readily available and the bond orders of all bonds are available from the molecular graph. Prior to describing the explicit default parameter scheme, it is nec-... 

Covalent radii (Table 4.7) are the distance between two kinds of atoms connected by a covalent bond of a given type (single, double, etc.). 

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... 

The strain energies of these five-membered heterocycles are relatively small with values of 23.5, 24.8 and S.SkJmoF estimated for tetrahydrofuran, pyrrolidine and tetrahy-drothiophene respectively (74PMH(6)199). The closeness of the values for the two former compounds reflects the almost identical covalent radii of oxygen (0.66 A) and nitrogen (0.70 A) atoms. The sulfur atom with a much larger covalent radius of 1.04 A causes a... 

Fig. 19-3. Covalent radii and van der Waals radii (in parentheses) of the halogens (in Angstroms).

Using the carbon atom covalent radius 0.77 A and the covalent radii given in Figure 19-3, predict the C—X bond length in each of the following molecules CF<, CBr4, CI4. Compare your calculated bond lengths with the experimental values C—F in CF4 = 1.32 A, C—Br in CBr = 1.94 A, C—I in CI4 = 2.15 A. 

Figure 19-4 contrasts the effective sizes of the halide ions. Each of these dimensions is obtained from the examination of crystal structures of many salts involving the particular halide ion. The effective size found for a given halide ion is called its ionic radius. These radii are larger than the covalent radii but close to the van der Waals radii of neutral atoms. 

Table 19-11 contains values for the covalent radii and the ionic radii of the halogens. Plot both radii versus row number. What systematic changes are evident in the two curves ... 

Compared to the sum of covalent radii, metal-silicon single bonds are significantly shortened. This phenomenon is explained by a partial multiple bonding between the metal and silicon [62]. A comparison of several metal complexes throughout the periodic table shows that the largest effects occur with the heaviest metals. However, conclusions drawn concerning the thermodynamic stability of the respective M —Si bonds should be considered with some reservation [146], since in most cases the compared metals show neither the same coordination geometries nor the same oxidation states. 

Very recently, synthesis and structure of molybdenum and tungsten complexes of the relatively unhindered disilene Si2Me4 were reported. The x-ray structure of 84 shows a metallacyclosilane structure with W — Si = 2.606(2) A and Si —Si = 2.260(3) A. The W — Si bond length is within the range of various estimates of the Si and W covalent radii and the Si —Si distance falls midway between the expected values for a single (2.35 A) and a double bond (2.14 A) (Fig. 13). 

The introduction of heteroatoms into cyclic systems produces significant variations in the molecular geometry that reflect the changes in covalent radii, relative electronegativity and effective hybridization. Consequently, there are changes in the bonding and the physico-chemical characteristics of these heterocyclic systems—particularly in small ring systems. 

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. 

Covalent radii typically decrease from left to right across a period. The reason is the same as for atomic radii (Section 1.15) the increasing effective nuclear... 

FIGURE 2.21 Cov.ilent radii ot hydrogen and the p-block elements (in picometers). Where more than one value is given, the values refer to single, double, and triple bonds. Covalent radii tend to become smaller toward fluorine. A bond length is approximately the sum of the covalent radii of the two participating atoms. 

The covalent radius of an atom is the contribution it makes to the length of a covalent bond covalent radii are added together to estimate the lengths of bonds in molecules. 

Use the covalent radii in Fig. 2.21 to calculate the bond lengths in the following molecules. Account for the trends in your calculated values, (a) CF4 (b) SiF4 (c) SnF4. 

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