Yves Jean - Molecular Orbitals of Transition Metal Complexes (793957), страница 14
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But if we consult thequalitative analysis given in Chapter 1 (§ 1.6.1), it is at first sight surprisingthat the 18-electron rule is not respected in this family of complexes,since the bonding orbitals, the nonbonding, and the weakly antibondingorbital z2 are all doubly occupied. This ‘lack’ of two electrons arisesbecause, despite appearances, there is a nonbonding orbital on the metalthat is empty. It is not an orbital from the d block, but the metal’s pzorbital whose nodal plane contains the four ligands (2-39). Althoughnonbonding, this orbital is never occupied: it is an (n +1)p orbital whoseenergy is substantially higher (several eV) than that of an nd orbital.This aspect of their electronic structure means that these complexesare likely to undergo addition reactions, in which their 18-electron shellis completed by the arrival of new ligands. For example, the addition ofa molecule of dihydrogen H2 to Vaska’s complex leads to the formationof an octahedral complex (2-40).
In this addition product, the oxidationstate of the metal is +3 (a d6 complex), which, when the 12 electronsassociated with the bonds are included, does indeed correspond to an18-electron complex. We also note that this addition reaction is accompanied by a change in the metal’s oxidation state, from +1 in the reactant(d8 ) to +3 in the product (d6 ). This is therefore called an oxidative addition reaction, since the oxidation state of the metal has increased. Thereverse reaction is called reductive elimination (Ir(III) → Ir(I)).OCR3PIrPR3Cl+oxid.
addit.Hred. elim.R3PClH2HIrPR3COIr (III)Ir (I)2-402.3. Square-based pyramidal ML5 complexesIn an ML5 complex which adopts a square-based pyramidal (SBP) geometry, four ligands (L1 –L4 ) are located at the corners of a square whichPrincipal ligand fields: σ interactionsis the base of the pyramid, while the fifth, or apical, ligand (L5 ), is placedon the summit (or apex) of the pyramid (2-41). The metal centre may,depending on the complex, be either in the basal plane (θ = 90◦ ) (2-41a,§ 2.3.1) or above this plane (θ > 90◦ ) (2-41b, § 2.3.2).θ = 90°L1L2L5ML5θ > 90°L4L3L1ML22-41aL3L42-41b2.3.1.
Characterization of the d block (metal in thebasal plane)In the complex shown in 2-41a, all the angles between the apical bondM–L5 and the basal bonds M–L1–4 are equal to 90◦ . This structuremay formally be obtained by removing one of the ligands from anoctahedral complex (L6 , 2-42). We may therefore establish the MO ofthe d block for the SBP by starting from those that we already know foran octahedron, following the method previously used for square-planarcomplexes (§ 2.2.1).L5L1L2L4ML3zxyL5L1L2ML4L3L62-422.3.1.1.
Derivation of the d orbitals from those of theoctahedronIn the octahedral complex, the coefficients of the xy, xz, yz, and x 2−y2orbitals are zero for the ligands located on the z-axis (left-hand side of2-37). The removal of one of these ligands therefore makes no changeto the shape or energy of these four orbitals: in the d block of the SBPML5 complex, we therefore find that the three orbitals xy, xz, and yz arenonbonding, while x 2−y2 is a strongly antibonding orbital.
This result isjust the same as that found when studying the square-planar geometryas a derivative of the octahedron (Figure 2.6). The z2 orbital is stabilizedby the elimination of one of the two antibonding interactions with theligands placed on the z-axis (2-43). But this stabilization is not as largeSquare-based pyramidal ML5 complexesas that observed when passing from an octahedral to a square-planarcomplex, since in this latter case, both the antibonding interactions alongthe z-axis are removed (Figure 2.6).2-43These results are shown in Figure 2.7, with the orbitals’ symmetry(C4v point group).egx2–y2 (b1)z2 (a1)Figure 2.7. Derivation of the d-block orbitalsfor an ML5 complex with an SBP geometry(the metal is in the basal plane) from those ofan octahedral complex ML6 .t2gxy (b2)xz(e)yz2.3.1.2.
Exact form of the z2 orbitalIt appears that the shape of the z2 orbital, as shown in Figure 2.7, issomewhat different from that indicated in 2-43: the two lobes alongthe z-axis have different sizes, and the orbital is polarized towards theempty site of the original octahedron. The shape shown in 2-43 supposesthat the only change from the original z2 orbital of the octahedron isthe removal of an antibonding interaction.
But this is not the wholetruth, as the symmetry is lowered from Oh to C4v . The major changein fact involves the z2 and pz orbitals on the metal. In the octahedralcomplex, these two orbitals have different symmetries: for example, z2is symmetric with respect to the xy plane but pz is antisymmetric (see2-42 for the orientation of the axes). In the ML5 complex, as there is onlya single ligand on the z-axis, the xy plane is not a symmetry element forthe complex. The z2 and pz orbitals therefore have the same symmetry(a1 , the totally symmetric representation of the C4v group), with theresult that they mix, giving a hybrid orbital belonging to the d block andcalled ‘z2 ’.Principal ligand fields: σ interactionszS >0+z2–pzpolarized z22-44The orbital shown in 2-43 is in fact stabilized by a bonding interactionwith the pz orbital (see Appendix A).
In Scheme 2-44 (left-hand side),the two orbitals are shown separated for greater clarity, but one mustof course imagine that they are superposed. The way in which theymust be combined to obtain a bonding mixture (S > 0) is not obvious,since one of the orbitals is delocalized over all the centres. We shallexamine their overlap if the pz orbital is oriented along negative z (2-44).It can be decomposed into three terms: (i) the overlap between theatomic orbitals z2 and pz : this term is zero since the two atomic orbitalsinvolved are located on the same atom; (ii) the overlap between pz andthe orbitals on the ligands that define the base of the SBP complex: thisterm is also zero, since these ligands are placed in the nodal plane (xy)of pz ; (iii) the overlap between pz and the orbital of the axial ligand(placed on the z-axis), which is the only non-zero term.
It is clear thatthe choice adopted in 2-44 for the orientation of pz leads to the overlapbeing positive. But how should this orbital be represented graphically?Where z is negative, the amplitudes of z2 and pz have the same sign,so they add. But where z is positive, they have the opposite sign, sothey tend to cancel each other. The two lobes along the z-axis aretherefore not equivalent, as the one along negative z is ‘larger’ (2-44,right-hand side). The participation of the pz orbital therefore leads to apolarization of the z2 orbital towards the vacant site of the octahedron.From the energetic point of view, this mixing stabilizes the orbital,since the polarization reduces the antibonding interaction with the axialligand, by reducing the size of the lobe of the z2 orbital that pointstowards that ligand.2.3.2.
Characterization of the d block (metal out of thebasal plane)In most SBP complexes, the metal is located above the base of the pyramid (θ > 90◦ , 2-41b). This geometrical deformation of the precedingstructure leads to a displacement, of the same amplitude, of the ligandsL1 and L3 in the yz plane, and of the ligands L2 and L4 in the xz plane(2-45). These movements change the shape and energy of some of theSquare-based pyramidal ML5 complexesorbitals of the d block represented in Figure 2.7. We shall consider eachof these orbitals in turn.yzxzzL5L1L2L4ML3xL5yL1ML2θL4L32-45The xy orbital has its nodes in the xz and yz planes, the two planesin which the movements of the ligands occur. As the ligands remainlocated in the nodal planes, no interaction is possible with the xy orbital(S = 0), whose shape and energy are unchanged (a pure d orbital that isstrictly nonbonding, 2-46).xy2-46No interaction can take place between the yz orbital and the ligandsL2 and L4 that stay in the nodal plane xz for all values of the angleθ.
However, the ligands L1 and L3 leave the nodal plane xy and moveinto the yz plane in which that d orbital is mainly concentrated. As aresult, the orbitals on the ligands L1 and L3 can interact with the yzorbital when θ is greater than 90◦ . The bonding combination is a lowenergy orbital (an MO that represents a bond), but the antibondingcombination is the new d-block orbital (2-47). The yz orbital, which isnonbonding if θ = 90◦ , is therefore destabilized if θ is larger than 90◦ ,its energy rising as the overlap with the ligand orbitals increases. Thegreatest destabilization occurs when θ = 135◦ , the value for which theligands L1 and L3 are in the region where the amplitude of the yz orbitalis largest.yz2-47Principal ligand fields: σ interactionsBut this destabilization of the yz orbital is reduced by a bondingmixture with the py metal orbital, in a way that is exactly analogous tothat described in § 2.3.1.2 for the z2 orbital (see Appendix A).
As theoverlap between the yz and py orbitals on the metal is zero, a bondinginteraction is obtained if the overlap between py and the orbitals onligands L1 and L3 is positive. The appropriate combination is shown in2-48. If we imagine the superposition of the two orbitals representedin the left-hand part of this sketch, the grey lobe of py points towardsthe orbital on L3 (grey lobe directed towards the metal) and the whitelobe towards the orbital on L1 (white lobe pointing towards the metal).This mixture with py leads to a change in the amplitude of the lobesof the d orbital (2-48). If we consider first the right-hand part of theyz orbital (grey lobe towards the top, white lobe towards the bottom),we must add the grey lobe py to it (2-48). As a result, the grey lobe ofyz is enlarged (the amplitudes add) but the white lobe decreases in size(the amplitudes tend to cancel).
On the left-hand side of the orbital, theopposite effect is observed: the amplitude of the white lobe increases insize, as it is added to that of the py orbital (white lobe pointing towardsthe left), while the amplitude of the grey lobe is diminished.zxy+yzpypolarized yz2-485Since the angle of the nodal cone for z2 is109.5◦ , the corresponding value of θ is125.25◦ . However, this is only an approximatevalue in the present situation, as the z2 orbitalis polarized by the pz orbital.The polarization of the yz orbital by py therefore leads to a reductionin the size of the lobes pointing towards ligands L1 and L3 , but anincrease in the opposite direction (2-48).
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