Tetrahedral covalent radii

After rising at copper and zinc, the curve of metallic radii approaches those of the normal covalent radii and tetrahedral covalent radii (which themselves differ for arsenic, selenium, and bromine because of the difference in character of the bond orbitals, which approximate p orbitals for normal covalent bonds and sp3 orbitals for tetrahedral bonds). The bond orbitals for gallium are expected to be composed of 0.22 d orbital, one s orbital, and 2.22 p orbitals, and hence to be only slightly stronger than tetrahedral bonds, as is indicated by the fact that R(l) is smaller than the tetrahedral radius. 

A set of values of tetrahedral covalent radii 7 for use in crystals of these types is given in Table 7-13 and represented graphically in Figure 7-7. These values were obtained from the observed interatomic distances in crystals of these tetrahedral types and of other types in which the atom of interest forms four covalent bonds with neighboring atoms which surround it tetrahedraliy. For example, in pyrite, FeS. each sulfur atom is surrounded tetrahedraliy by three iron atoms and one sulfur atom, with all of which it forms essentially covalent bonds (Fig. 7-8) the substance is a derivative of hydrogen disulfide, H2S2. That the Fe—S bonds are essentially covalent is shown by the magnetic eri-... 

Pauling commented many years ago on the abnormally long M-X bonds in and Te X ions, comparing them with the sums of the tetrahedral covalent radii, which for Se and Te correspond to M(ii). A more direct comparison could be made of the M—X bond lengths in the following pairs ... 

The Be—C bridge bonds are considerably longer than the single Be—C bonds in monomeric dimethylberyllium or di-fert-butylberyllium = 1.70 A (see below), and 0.10 A longer than the sum of the tetrahedral covalent radii of Be and C = 1.83 A. The Be—Be distance on the other hand is slightly shorter than twice the tetrahedral covalent radius of Be =... 

In this compound, too, the intemuclear distances indicate that bonding between the metal atoms is important The Al-Al distance is only 0.10 A more than the value calculated for a single bond by doubling the tetrahedral covalent radius, and 0.24 A less than the Al—Al distance in the metal The Al—Cb bonds on the other hand are 0.18 A longer than the Al—Cj bonds. The latter are equal to the Al—C single-bond value 1.96 A, calculated from the tetrahedral covalent radii of carbon and aluminum and the revised Schomaker-Stevenson mle. 

Since the classical paper of Paulii and Huggins [4], it has become usual to calculate the distances between the atoms in crystals of covalent compounds and elements by the addition of certain constants known as the / atomic radii. At present, this term is understood to mean the extent of an atom along the direction of a bond [5]. Bearing this point in mind, we can use tables Of tetrahedral covalent radii [5,6] to calculate bond lengths in sp hybrid compounds with tetrahedral coordinations, employing the well-known formula of Schomaker and Stevenson [7]... 

Octahedral and tetrahedral covalent radii can be either calculated by additivity from the structures with corresponding Nc, or derived from r or using Pauling s equation [119] converted from bond distances to radii,... 

Van Vechten J, Philhps JC (1970) New set of tetrahedral covalent radii. Phys Rev B2 2160-2167... 

Pyykki) P (2012) Refitted tetrahedral covalent radii for solids. Phys Rev 885 024115... 

Phillips 1C (1967) A posteriori theory of covalent bonding. Phys Rev Lett 19 415-417 Phillips 1C (1968) Dielectric definition of electronegativity. Phys Rev Lett 20 550-553 Phillips 1C, Van Vechten JA (1970) New set of tetrahedral covalent radii. Phys Rev B 2 2147—... 

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 proper treatment of elements of the short periods is uncertain. The equality of the tetrahedral radius and normal covalent radius for the... 

The formation of dimeric products is unique for the case of boron, because analogous complexes with other elements are all monomeric [95]. This can be attributed to the small covalent radius of the boron atom and its tetrahedral geometry in four-coordinate boron complexes. Molecular modeling shows that bipyramidal-trigonal and octahedral coordination geometries are more favorable for the formation of monomeric complexes with these ligands. 

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 predominant effect on A in tetrahedral groups of a given period is a steric effect due to Zs. The steric effect due to M is much smaller. The magnitude of the Zs steric effect decreases as the covalent radius of M, ycm, decreases. Thus we obtain equation 46 ... 

Table 3. Atomic radii (in A) of the atoms which form B32 type compounds. rB32 is the half nearest neighbour distance in Zintl phases AB, r o , is the atomic radius according to Goldschmidt (C.N. 8), rjo is the ionic and r ov the covalent radius for tetrahedral coordination (C.N. 4) according to Pauling ...

Many tricobalt carbonyl clusters [Co3(CO)9ELn] are known, and a very useful survey of these compounds has appeared. The size of E has a limiting effect on the existence or non-existence of the c/ofo-core C03E structure. If the covalent radius of E exceeds 1.3 A such species are incapable of existence (e.g. with In, Sn, Pb, or W). However, these pfwerfo-tetrahedral structures are now known with E=B, Al, C, Si, Ge, P, As, or S, and Fe, Co, Ni, Mo, Ru, Rh, W, or Os. 

Covalent radius (tetrahedral) Ionic radii Resistivity Electronegativity Ionization potentials First Second Third Fourth... 

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. 

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