Other Covalent Radii

Other Covalent Radii.—Bipositive nickel, palladium, and platinum and tripositive gold form four coplanar dsp bonds, directed to the comers of a square, with attached atoms. Examination of the observed values of interatomic distances reveals that square dsp radii of atoms have the same values as the corresponding octahedral d sp radii, as given in Table 7-15. This is shown by the comparisons on the following page. 

Bipositive copper often forms four strong bonds directed toward the comers of a square. The observed interatomic distances correspond to the radius 1.28 A, about 0.08 A larger than for square-ligated nickel (II) the increase is to be attributed to the presence of the extra elec- 

In molybdenite and tungstenite the metal atom is surrounded by six sulfur atoms at the corners of a right trigonal prism with axial ratio unity (Fig. 5-14).48 From the observed interatomic distances the trigonal-prism radius values of 1.37 A for Mo(IV) and 1.44 A for W(IV) are obtained. 

The average Mo—C bond distance in K4Mo(CN)s 2HiO is 2.15 A,49 which corresponds to the value 1.38 A for the octacovalent radius of Mo(IV). The close approximation of this value to the trigonal-prism radius indicates that the bond orbitals are nearly the same for the two types of coordination. 

In Cu 0 and Ag 0 crystals (Fig. 7-9) each oxygen atom is surrounded tetrahedrally by four metal atoms, each of which is midway between two oxygen atoms and with which it probably forms two covalent bonds of the sp type.80 The interatomic distances in these crystals bad to the radius values 1.18 A for Cu(I) and 1.39 A for Ag(I), which are 0.17 A and 0.13 A less than the corresponding tetrahedral radii. By microwave spectroscopy61 of the linear molecules H CHgCl and HjCHgBr the bond lengths C—Hg = 2.061 A, Hg—Cl - 2.282 A, C—Hg = 2.074 A, and Hg—Br = 2.406 A. These correspond to the values 1.29, 1.29, 1.30, and 1.27 A for the radius of bicovalent Hg(II), 

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Other Covalent Radii. In Cu20 and Ag20 each metal atom is equidistant from two nearest oxygen atoms, the interatomic distances corresponding to the radius values 1.18 and 1.39 A for Cu1 and Agl with coordination number two. In KAg(GN)2, in which each silver atom is similarly attached to two cyanide groups1), the effective radius of Agl is 1.36 A. It has been pointed out to us by Dr. Hoard that the work of Braekken2) indicates the presence of strings —Ag—G=N—Ag—G... 

The amount of resonance energy for a metal or intermetal-lic compound is determined by" the number of resonance structures. The resonance energy affects the covalent radius, the stability (as evidenced by the resistance of the noble metals to chemical attack), and other properties, in ways that we hope to discuss later. 

In the course of the work it was found that the value assumed five years ago for the carbon double-bond covalent radius (obtained by linear interpolation between the single-bond and the triple-bond radius) is 0.02 A. too large in consequence of this we have been led to revise the double-bond radii of other atoms also. 

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. 

The only structurally characterized In—Sb adduct is (Me3SiCH2)3 In—Sb(Tms)3 19 [38], featuring an In—Sb bond distance of 300.8(1) pm. Due to the lack of other structurally characterized In—Sb adducts, no structural comparisons can be made. The In—Sb bond length found in 19 is supposed to be at the lower end of the In—Sb dative bond range since the covalent radius of In (r ov 143 pm) is about 17 pm larger than those of the lighter elements Al and Ga. Therefore, In—Sb dative bonds are expected to... 

Mean cobalt-cobalt and nickel-nickel distances observed in these complexes are very close to interatomic distances determined at ambient temperatures in cobalt and nickel metals (Co-Co 2.489(7) A vs. 2.507 A in a-cobalt (33) Ni-Ni 2.469(6) A vs. 2.492 A in the metal (39)). The mean M-H bond lengths, as well as hydride displacements from M3 faces, are less for nickel in H3Ni4(Cp)4 than for cobalt in HFeCo3(CO)9(P(OMe)3)3. Although the differences are marginally significant within error limits (Ni-H 1.691(8) A vs. Co-H 1.734(4) A displacements from plane Ni3 0.90(3) A vs. Co3 0.978(3) A), they are in the expected direction since the covalent radius should vary inversely with atomic number within a transition series. However, other effects such as the number of electrons in the cluster also can influence these dimensions. 

It is noteworthy that the Be—O distance (1.60 A) is of the same order as that found for other coordination compounds of beryllium and leads to the value of 1.0—1.1 A for the covalent radius of beryllium in this type of coordination.26 Clearly arguments based on relative ionic radii are invalid. Thus the dihydrate of zinc oxinate has been shown to form a distorted tetrahedron with two long Zn—H20 bonds while the lengths Zn—O and Zn—N to the ligand are 2.05 and 2.06 A respectively, whence the zinc radius is 1.38 A. Clearly the use of an ionic radius (Zn2+ = 0.74 A) would be misleading. Similarly the Cu—N bond in compounds of Cu11 with ammonia and ethylenediamine (1.99,2.05,2.01 A) implies a radius of 1.3-1.4 A in these coordination compounds, a value considerably larger than the ionic radius of 0.7 A.23... 

Covalent Radius. This is the radius of closest approach for atoms bonded together by electrons that are localized in the region between the atoms. It represents the distance at which the attraction of each nucleus for the bonding electrons is in equilibrium with the mutual repulsion of the two nuclei and the repulsion of the inner elecirons of each atom for the inner electrons of the other. 

BBr3 is a symmetrical planar molecule with all B—Br bonds lying at 120° to each other. The distance between Br atoms is found to be 324 pm. From this fact and given that the covalent radius of Br is 114 pm, estimate the covalent radius of boron. Assume all bonds are single bonds. 

Hightened reactivity of functional groups (e.g. Cl, Br, OH, OR, OCOR, NH2, SH) at the atoms of silicon, aluminum, titanium, phoshorus and other elements in comparison with their reactivity binded with oxygen. This is due to the fact that the silicon atom is one and a half times bigger than the carbon atom it has a covalent radius of 0.117 nm, whereas the radius of the carbon atom is only 0.077 nm. It follows that functional groups of the Si atom are much more distanced from each other than... 

The atomic covalent radius (one half of the M-M distance) has been used for a long time for estimates of the nature of chemical bonds. Its magnitude correlates with the M—M bond energy. The notion of the van der Waals radius of an atom is ambiguous3. The sum of van der Waals radii of two atoms is defined in crystallography as the minimum distance at which they can approach each other. 

The covalent radii of transition elements are subject to two additional effects that influence the values of ionic radii also. A large covalent radius for a given atom is favored by both a low oxidation number and a high coordination number. These two effects are independent neither of each other nor of bond order effects however, an adequate unified treatment of the interrelationships between bond number, coordination number, oxidation number, and bond distances for compounds of the transition metals is best postponed to a more advanced text. 

Table 12-3). It should be noted that the van der Waals radius is the maximum nonbonded radius of an atom, the distance between the nucleus and the effective outside of the atom at a point directly opposite the site of bonding. It is the radius of the atom as set off by a line forming an angle of 180 degrees with the bond direction the atomic radius set off by a line through the nucleus at any other angle must be greater than the covalent radius but less than the van der Waals radius. This may be seen from Figure 9-1, which shows two of the C—Br bonds in a compound...

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