Yves Jean - Molecular Orbitals of Transition Metal Complexes (793957), страница 27
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If we now re-examine thed-block orbitals of the dichloro complex trans-[ML4 Cl2 ] (Figure 3.6), wenotice, but after the event, that we could have obtained them directly byconsidering successively the contributions expected for each of the twoligands, that is, by proceeding in two stages, as shown in 3-24.LLLMCl1Cl1LLCl1LMLLLLCl2LLLMLLCl23-24(1)(1)The interactions of the lone pairs px and py of the first substituentCl1 leave the xy, x 2−y2 , and z2 orbitals unchanged (zero overlaps),Complexes with several π-donor or π-acceptor ligands(1)whereas xz and yz are destabilized by antibonding interactions with px(1)and py , respectively (non-zero overlaps). Analogous observations canbe made for the second substitution by Cl2 , since the same overlaps are(2)(2)involved when we consider the px and py lone pairs.
This two-stagedecomposition of the construction of the d-block orbitals for the trans[ML4 Cl2 ] complex is illustrated in 3-25 for the three initially nonbondingorbitals of the octahedron. The xy orbital which cannot interact withany of the lone pairs is unchanged, whereas the xz and yz orbitals aredestabilized in the same way (two equivalent antibonding interactions).xyxzyzCl1Cl2Cl1Cl2Cl1Cl23-25On can proceed in the same way for the trans-ML4 (CO)2 complex,∗ orbitals occurs inthe only difference being that the mixing with the πCOa bonding sense (π acceptor) (3-26).xyxzyz(CO)1(CO)2(CO)1(CO)2(CO)1(CO)23-26π -type interactions3.3.3.2.
mer-[ML3 (CO)3 ] complexesWe shall now apply this method ‘by stages’ to a new octahedral complexwith three carbonyl ligands and three other ligands that only have σinteractions with the metal. The arrangement chosen for the ligandsis indicated in 3-27. Of the two possible isomers for an [ML3 (CO)3 ]complex, this one is the mer isomer, in contrast to the fac isomer inwhich the carbonyl ligands are placed at the three vertices that make upa face of the octahedron. On the C1 O1 and C3 O3 , carbonyl ligands, theπ ∗ orbitals point parallel to the x- and z-axes, whereas on the centralligand C2 O2 they are parallel to the x- and y-axes (3-27).
We now examinehow each of the octahedral orbitals can overlap with the π ∗ orbitals onthe carbonyl ligands.O2C2O1zLC3 O 3C1LyxL3-27The x 2−y2 and z2 orbitals have zero overlap with all the π ∗ orbitals,as in the preceding complexes. These orbitals (σ antibonding) are therefore not perturbed by the π interactions. It is only the nonbonding xy,xz, and yz orbitals, derived from the t2g block of the regular octahedron,that will be perturbed.∗(1)We consider first the xy orbital (3-28).
Its overlap with πx is non∗(1)zero, but it is zero with πz , located in a nodal plane of xy. As a result,∗(1)xy is stabilized by a bonding interaction with πx . This analysis allows∗(3)us to anticipate an equivalent interaction with the πx orbital on the∗(2)∗(2)symmetry-related ligand C3 O3 . But the two orbitals πx and πyon the central ligand C2 O2 are both located in the nodal planes of xy(xz and yz, respectively), and their overlap with xy is zero (3-28). We∗(1)conclude that xy is stabilized by two bonding interactions, with πx and∗(3)πx (3-31a).x*(2)x*(1)xyS≠0*(1)zxyS=0xyS=03-28y*(2)xyS=0Complexes with several π-donor or π-acceptor ligands∗(1)∗(1)The yz orbital can interact with πz on C1 O1 , but not with πxwhich is located in one of its nodal planes (xy) (3-29).
The same remarksmay be made about the group C3 O3 . On the central carbonyl C2 O2 ,∗(2)πy is the only orbital whose overlap with yz is non-zero. The yz orbital∗(2)∗(1)is therefore stabilized by three bonding interactions, with πz , πy , and∗(3)∗(1)∗(3)πz (3-31b). Notice that the contributions of πz and πz are equal∗(2)in magnitude, by symmetry, but the contribution of πy on the centralcarbonyl C2 O2 may be different, since it is not exchanged with the twoother groups by any symmetry element in the complex.x*(2)yzx*(1)*(1)zS=0y*(2)yzyzyzS≠0S=0S≠03-29The xz orbital cannot interact with any of the orbitals on the C1 O1∗(2)and C3 O3 groups, and can combine only with the πx orbital on thecentral group C2 O2 (3-30).
Therefore, the xz orbital is stabilized by a∗(2)single bonding interaction, with πx (3-31c).x*(2)x*(1)xzS=0*(1)zy*(2)xzS≠0xzS=0xzS=03-30We see, therefore, that the three nonbonding orbitals derived fromthe t2g block of the regular octahedron are perturbed in different waysin the substitution pattern that we have studied (3-31). All the d ↔ π ∗interactions concern the same lateral overlap between a pure d orbital∗ orbital, but the number of interactions changes from oneand a πCOorbital to another.xy3-31ayz3-31bxz3-31cπ -type interactionsAs a consequence, the degeneracy of the three orbitals is lifted inthis substitution pattern. We can anticipate that yz, stabilized by three∗ orbitals, is lower in energy thanbonding interactions with the πCOxy (two bonding interactions), which in turn is lower than xz (only asingle bonding interaction) (3-32). Part of the complete diagram for the∗ orbitals has thereforeinteraction of these three d orbitals and the πCObeen obtained.
Moreover, it is the most important part, since it givesus the three new d orbitals that may be occupied in this strong-fieldoctahedral complex. It is straightforward to derive the missing parts ofthis diagram. Three antibonding combinations, mainly concentratedon the carbonyl groups, correspond to the three bonding combinations∗described in 3-31. We note that three linear combinations of the πCOorbitals have been used in these interactions. Since initially there were∗ orbitals, two per ligand, three other combinations have notsix πCOinteracted; they remain entirely localized on the ligands, at an energy∗ orbital.level close to that of an isolated πCOCOxy, xz, yzOCCOxz (+ 1*CO)xy (+ 2*CO)yz (+ 3*CO)3-323.3.3.3. A rigorous or an approximate method?The method we have used has consisted in analysing successively the possible interactions for each of the ligands with a π system.
This method,which can be applied in the same way to any type of complex with anysubstitution pattern (see Exercises 3.1–3.5), enables us to obtain ratherquickly the shapes of the d orbitals as perturbed by the π interactions, aswell as their relative energies. The use of group theory, which requires usin each case to construct the symmetry-adapted orbitals on the ligands,is more time-consuming. But is there really a fundamental differencebetween the two methods? The application of group theory is basedon the symmetry elements of the complex as a whole; this is the rigorous way to proceed.
However, the construction ‘by hand’ that has beenproposed in the two preceding sections uses local symmetry elementsshared by a d orbital and a particular π ∗ orbital, to deduce whetherinteraction is possible between them (Schemes 3-28–3-30). The twomethods fuse when the symmetry elements of the complex and the localComplexes with several π-donor or π-acceptor ligandssymmetry elements used are identical. This is the case, for example, forthe trans-[ML4 Cl2 ] and trans-[ML4 (CO)2 ] complexes (§ 3.3.3.1) and forthe xy and yz orbitals of the mer-[ML3 (CO)3 ] complex. However, in thislatter case, we used a local symmetry element that is not a symmetryelement of the complex. Use of the horizontal plane xy allows us to show∗(1)that the overlap between πx and xz is zero (3-30, left-hand side), and∗(1)we concluded that πx makes no contribution to the xz orbital (3-31c).This conclusion is not rigorous, since the xy plane is not a symmetryelement for the complex as a whole.
Fortunately, calculations show that∗(3)∗(1)the participation of πx in this orbital is very small (as is that of πx ,∗(1)by symmetry), precisely because the local overlap between πx and xzis zero. The approximate description of the d orbitals given in 3-31 isthus essentially correct.3.3.4. [MCl6 ] and [M(CO)6 ] octahedral complexesWhen the six double-face π -donor or π-acceptor ligands are identical,octahedral symmetry is preserved.
We therefore find the usual splittingpattern in the d block, into two groups of degenerate orbitals, whosesymmetries are t2g and eg . We shall now use the method set out in thepreceding section to determine the shapes of the MO and the energeticconsequences of the π interactions.3.3.4.1. The d block in [MCl6 ] and [M(CO)6 ] complexesIn the [MCl6 ] complex, each orbital in the t2g group (xy, xz, and yz) caninteract with four of the p orbitals that characterize lone pairs on theligands (3-33).
All the interactions are antibonding (π-donor ligands);they destabilize the three orbitals in an equivalent way, so these remaindegenerate.xyxzyz3-33It is easy to verify that the orbitals in the eg group (z2 and x 2−y2 )have zero overlap with all the nonbonding p orbitals on the ligands, sotheir energy and shape remain unchanged. The symmetry propertiesof the octahedral complexes [MCl6 ] therefore allow only three linearcombinations of the nonbonding p orbitals on the chloride ligands, thoseshown in 3-33, to interact with the d-block orbitals.
In other words,π -type interactionsonly three lone pairs out of the twelve (two per ligand) can transferelectron density to the metal centre; we shall return to this point in§ 3.5, Figure 3.10.By an exactly analogous analysis, it can be shown that in the caseof six carbonyl ligands, the three orbitals in the t2g block are stabilized∗ orbitalsto the same extent by four bonding interactions with the πCO(3-34), though the two eg orbitals are not affected.xyxzyz3-343.3.4.2.
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