Octahedral bond orbitals

It is found on analysis of the problem that when only two d orbitals are available for combination with the s and p orbitals six equivalent bond orbital- of strength 2.923 (nearly as great as the maximum 3 for the best spd hybrid) can be formed, and that these six orbitals have their bond directions toward the corners of a regular octahedron. We accordingly conclude that complexes such as [CoCNHs ], [PdClc]—, and [PtCle] — should be octahedral in configuration. This conclusion is of course identical with the postulate made by Werner to account for isomerism in complexes with different substituent groups,1 and verified also by the x-ray examination of Co(NH8)el3, (NHOaPdCU, (NH4)2 PtCl , and other crystals (see Fig. 5-1). 

1 There is only one form of a monosubstituted octahedral complex MAiB. A disubstituted complex MA4B2 can exist in two isomeric forms, cis and trans  

Optically active stereoisomers can be obtained of a complex such as MfCsO s, containing oxalate groups which occupy two adjacent octahedral corners  

It is interesting to note, as was pointed out to me some years ago by J. L. Hoard, that these considerations lead to an explanation of the difference in stability of cobalt (II) and cobalt (I JI) as compared with iron (II) and iron (III) in covalent octahedral complexes. The formation of covalent complexes does not change the equilibrium between bipositive and tripositive iron very much, as is seen from the values of the oxida- 

—The angular dependence of an octahedral d p bond orbital with bond direction along the x axis. 

---

A polar graph of an octahedral bond orbital is shown in Figure 5-2, from which its great concentration in the bond direction, leading to large overlapping and the formation of a very strong bond, can be seen. 

For elements adjacent to the noble gases the principal orbitals used in bond formation are those formed by hybridisation of the s and p orbitals. For the transition elements there are nine stable orbitals to be taken into consideration, which in general are hybrids of five d orbitals, one s orbital, and three p orbitals. An especially important set of six bond orbitals, directed toward the comers of a regular octahedron, are the d2sps orbitals, which are involved in most of the Werner octahedral complexes formed by the transition elements. 

The crystal and molecular structure of (PPh3)2(CO)(H)Ir(/u3-B3H7) have been reported.5 The structure is interpreted as a capped octahedral, 7-orbital, 18-electron d4, Irv complex in which the metal-borane bonding occurs predominantly via three two-electron, two-center Ir—B bonds. 

A persistent feature of qualitative models of transition-metal bonding is the supposed importance of p orbitals in the skeletal hybridization.76 Pauling originally envisioned dsp2 hybrids for square-planar or d2sp3 hybrids for octahedral bonding, both of 50% p character. Moreover, the 18-electron rule for transition-metal complexes seems to require participation of nine metal orbitals, presumably the five d, one s, and three p orbitals of the outermost [( — l)d]5[ s]1[ p]3 quantum shell. 

RuC1(CO)2(PBu 2P-To1)]2 0.047 Ru—Ru distance is much shorter than other Ru or Ru° polymers. This fact, together with nonplanarity of Cl bridge system, suggests a bent Ru—Ru bond (formed by overlap of essentially octahedral hybrid orbitals). 1... 

The Fe-Fe interactions vary sensitively with the ratio of the radial extension of the n-bonding orbitals to the Fe-Fe separation. This ratio is significantly greater for the minority-spin electron at an Fe " ion than for the majority-spin electrons because the minority-spin electron of a high-spin 3 d configuration is more weakly bound to the iron nucleus (by some 3 eV for octahedral-site iron in rutile) than are the 3 d majority-spin electrons of the same symmetry. Therefore Fe-Fe interactions are strongest for the couple. 

The number of available bonding orbitals on Co(Ni) could vary with conditions (i) the CN could change from 5 to 6 (ii) at CN = 6 the complex could be either octahedral or trigonal bipyramidal (iii) the number of vacant orbitals may vary if equilibrium adsorption is rapid and competitive between the sulfur compound and other ligands, such as H2S (see Fig. 22b), where one orbital is occupied by a coordinated H2S molecule. 

The effect is so pronounced that covalent compounds of cobalt(II) can decompose water with liberation of hydrogen, whereas the cobalt(III) ion decomposes water with liberation of oxygen, being one of the most powerful oxidizing agents know. The explanation is contained in Figure 6-3. In the ions CO++, Co+++, Fe++, and Fe H+ there is room for all unshared electrons in the 3d orbitals and inner orbitals. When octahedral bonds are formed in the covalent complexes, with use of two of the 3d orbitals, only three 3d orbitals are left for occupancy by unshared electrons. These are enough for bipositive and tripositive iron and for tripositive cobalt, but they can hold only six of the seven outer unshared electrons of bipositive cobalt. The seventh electron must... 

The five d orbitals described in Equation 5-2 are related in a simple way to the six octahedral directions x, y, and z, as may be seen by converting the angular functions to functions of x/r, y/r, and z/r. It is seen that dyt, and d vanish in these six directions, and hence their incorporation in bond orbitals in these directions would decrease the strength of the orbitals. It is the other two d orbitals, d and that can be used effectively in forming single bonds in the octahedral directions. 

CrF forms a cubic crystal containing regular octahedral CrFe groups, each fluorine atom forming a joint corner of two octahedra the Cr—F bonds all have length 1.90 A. The regularity of these octahedra is expected the three unpaired 3d electrons use only three of the 3d orbitals, leaving two available for formation of d sjfi octahedral bonds. 

It is interesting that the difference between the effective radius of manganese in Mnll and the single-bond metallic radius, 0.260 A, is nearly as great as that between the anomalous octahedral manganese radius and the d2 p octahedral radius (Sec. 7-9). It is likely that in MnH the 3d orbitals of the manganese atom are all occupied by electrons and that the bond orbital has very little d character. 

---