Covalent radii table

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.). 

Calculated from the Schomaker-Sievenson equation. bSum of the covalent radii (Table 2.1). 

The SiF bond in SiF4 has a length of 155.5 pm compared to the value of 169 pm calculated using the Schomaker-Stevenson equation and the value of 177 pm calculated from the sum of the covalent radii (Table 2.6). So Pauling wrote resonance structures such as the following ... 

Of the linear clusters, the organogermanium-substituted transition metal carbonyl compounds are the simplest. In every case, the coordination at germanium is tetrahedral, while the transition element retains the geometry of the parent carbonyl compound (50,108,119,155, 157, 181). The Ge—M bond is almost without exception shorter than the sum of the Ge—M covalent radii (Table VI), which is cited as evidence for (d — d)-n multiple bonding. 

As reference data, the normal values M-M single-bond lengths are calculated from the covalent radii (Table 3.4.3) and the normal bond lengths of M=M double bonds are estimated as 0.9 x (single-bond lengths). Thus the... 

Coordination numbers (CN) of zirconium and hafnium range from 4 to 12, but because of the large values of their ionic and covalent radii (see Covalent Radii) (Table 1), their complexes typically have CNs of 6-8 (see Coordination Numbers Geometries). They have a varied stereochemistry... 

Use covalent radii (Table 9.4) to estimate the length of the P—F bond in phosphorus trifluoride, PF3. 

Some physical constants for selenium are given in Table 1. More extensive data and many sources are available (1 5). For a selenium atom, the covalent radius is ca 0.115 nm, the electron affinity for two electrons is ca —2.33 eV, ie, energy absorbed, and the first ionization potential is 9.75 eV. 

In other crystals an octahedral metal atom is attached to six non-metal atoms, each of which forms one, two, or three, rather than four, bonds with other atoms. The interatomic distance in such a crystal should be equal to the sum of the octahedral radius of the metal atom and the normal-valence radius (Table VI) of the non-metal atom. This is found to be true for many crystals with the potassium chlorostannate (H 61) and cadmium iodide (C 6) structures (Table XIB). Data are included in Table XIC for crystals in which a tetrahedral atom is bonded to a non-metal atom with two or three covalent bonds. The values of dcalc are obtained by adding the tetrahedral radius for the former to the normal-valence radius for the latter atom. 

The covalent radius between identical atoms also decreases within a period when the group number is increased, due to the larger nuclear charges exerting more attraction on the electrons (table 4.10). 

Table 4.10 Covalent radius change within a period ...

Octahedral Radii.—In pyrite (Fig. 7-8) each iron atom is surrounded by six sulfur atoms, which are at the corners of a nearly regular octahedron, corresponding to the formation by iron of 3d 24 4p bonds. The iron-sulfur distance is 2.27 A. from which, by subtraction of the tetrahedral radius of sulfur, 1.04 A, the value 1.23 A for the cPsp9 octahedral covalent radius of bivalent iron is obtained (Table 7-15). 

The value of the effective van der Waals radius of an atom in a crystal depends on the strength of the attractive forces holding the molecules together, and also on the orientation of the contact relative to the covalent bond or bonds formed by the atom (as discussed below) it is accordingly much more variable than the corresponding covalent radius. In Table 7-20 there are given the ionic radii of nonmet llic elements for use as van der Waals radii. They have been rounded off... 

It is interesting to note that the van der Waals radii given in Table 7-20 are 0.75 to 0.83 A greater than the corresponding single-bond covalent radii to within their limit of reliability they could be taken as equal to the covalent radius plus 0.80 A. 

Table 8.1 lists covalent radii obtained by dividing homonuclear bond distances by two. In many cases the appropriate homonuclear single bond has not been measured and the assigned covalent radius is obtained indirectly by subtracting the covalenl radius of element B in a heteronuclear bond AB to obtain the radius of atom A. 

Afl distances are in piconuXcts. The radns of the metal was obtained by subtracting the covalent radius of Ihe ligating atom (Table 8.1) from the M—X didance. 

Covalent bond distances and angles tell us how the atomic nuclei are arranged in space but they do not tell us anything about the outside surfaces of molecules. The distance from the center of an atom to the point at which it contacts an adjacent atom in a packed structure such as a crystal (Fig. 2-1) is known as the van der Waals radius. The ways in which biological molecules fit together are determined largely by the van der Waals contact radii. These, too, are listed in Table 2-1. In every case they are approximately equal to the covalent radius plus 0.08 nm. Van der Waals radii... 

The interatomic distance at the bottom of the potential well, the most favorable distance of separation, is known as the van der Waals contact distance. A particular atom has a characteristic van der Waals radius (Table 11.3). These radii are additive, so that the optimal distance of contact between two atoms may be found by the addition of their two van der Waals radii. The van der Waals radii are not as sharply defined as covalent bond radii. This is because the potential energy wells are so shallow that contact distances may vary by 0.1 A (0.01 nm) or so... 

The effectiveness of overlap of bonding orbitals of ihe same symmetry appears to decrease as the principal quantum number increases and as the difference between the principal quantum numbers increases. This is reflected in the bond strengths shown in Table 10, The covalent radius of hydrogen is especially subject to effects of this kind, and has the values 0.3707, 0.362, 0.306. 0.284 and 0.293 A respectively in H2. HF. HCI. HBr and HI. The apparent anomaly of the P-P, S-S. and Cl-Cl bonds being stronger than the N—N. O-O. and F—F bonds has been considered in paragraph (I). 

Going to the right in the periodic table, we find a decrease in covalent radius. This decrease can be attributed, as before, to the effect of increasing nuclear charge, which tends to pull together the outer electrons which are all in the same principal quantum number level. In a family the radii increase from... 

The electron cloud around an atomic nucleus makes the concept of atomic size somewhat imprecise, but it is useful to refer to an atomic radius. One can arbitrarily divide the distance between centers of two bonded atoms to arrive at two radii, based on the crude picture that two bonded atoms are spheres in contact. If the bonding is covalent, the radius is called a covalent radius (see Table 8-2) if it is ionic, the radius is an ionic radius (see Table 9-2). The radius for non-bonded atoms may be defined in terms of the distance of closest non-bonding approach such a measure is called the van der Waals radius. These three concepts of size are illustrated in Figure 7-2. 

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