Yves Jean - Molecular Orbitals of Transition Metal Complexes (793957), страница 15
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The antibonding character ofthe yz orbital is thereby reduced, so that in fact it becomes a weaklyantibonding orbital which can be occupied in stable complexes.The xz orbital behaves in just the same way as yz, but the roles ofthe ligands (L1 , L3 ) and (L2 , L4 ) are interchanged (2-49). It is now themixture with the px orbital which polarizes xz in the direction opposedto the ligands L2 and L4 .
For any value of the angle θ, the xz and yzorbitals are related to each other by a rotation of 90◦ around the z-axis:they are degenerate by symmetry (e symmetry in the C4v point group).The z2 orbital, which had antibonding interactions with all the ligands, is affected by the movement of the four basal ligands towards itsnodal cone. If the angle θ is close to 125◦ , these ligands are even inthis cone,5 leading to zero overlap between the ligand orbitals and the z2orbital of the d block. For this latter orbital, the deformation that we areSquare-based pyramidal ML5 complexesxzpolarized xz2-49studying therefore produces a decrease, even perhaps an elimination, ofthe antibonding contributions on the basal ligands (2-50).
The energyof this orbital is therefore lowered, though it remains higher than that ofthe nonbonding orbital xy, since there is still an antibonding interactionwith the apical ligand L5 .z22-50We turn last to the case of the antibonding orbital x 2 −y2 (2-51). Anincrease in the angle θ decreases the antibonding interactions with theorbitals on the four basal ligands, since these are no longer located inthe regions where the amplitude of this orbital is greatest.
As a result,the x 2−y2 orbital is stabilized, by an amount which increases with theangle θ. However, this orbital remains the least stable of all the five inthe d block.x2–y22-51In Figure 2.8 we present a schematic correlation diagram, whichshows the changes to the shape and the energy of the d-block orbitalsduring this geometrical deformation, as the angle θ varies from 90◦ toabout 110◦ .CommentIt must be noted that a crossing between the energy levels of the orbitals thatare destabilized (xz and yz), and the z2 orbital that is stabilized, can occurif θ becomes sufficiently large.
Since these sets of orbitals have differentsymmetries (e and a1 , respectively), they cannot interact even if their energies are very similar or even equal (an ‘allowed’ energy-level crossing). ThePrincipal ligand fields: σ interactionsx2–y2b1z2a1yz, xzeb2xyFigure 2.8. Correlation diagram for thed-block orbitals of an ML5 complex with anSBP geometry where the angle between theapical and the basal bonds varies from 90◦ toabout 110◦ . = 90° = 110°value of the angle θ for which this crossing occurs depends on the exactnature of the metal and the ligands.2.3.3. Electronic structure and geometry2.3.3.1. d8 or d6 diamagnetic complexesIn the d block of ML5 complexes which adopt an SBP geometry, there isonly one strongly antibonding orbital, x 2 −y2 (Figure 2.8).
The four nonbonding or weakly antibonding orbitals (xy, xz, yz, and z2 ) are thereforelikely to be doubly occupied, leading to diamagnetic complexes with a d8electronic configuration (e.g. [Co(H)5 ]4− , [Ni(CN)5 ]3− , [Mn(CO)5 ]− ,[Co(NCPh)5 ]+ , or [PtI(PMe3 )4 ]+ ). Including the ten electrons associated with the five bonds, these are 18-electron complexes. There are alsodiamagnetic complexes whose electronic configuration is d6 (16-electroncomplexes), such as [M(CO)5 ] (M=Cr, Mo, W) or [W(CO)4 (CS)].
Thepresence of an empty low-energy orbital in the d block (the z2 orbital,Figure 2.8) confers special properties on these complexes. They haveonly been isolated in rare-gas matrices, at very low temperatures, andthey can easily bind a sixth ligand of the L type to give an octahedral18-electron complex.2.3.3.2. Other casesComplexes with an intermediate electronic configuration, d7 , arealso known, such as [Mn(CO)5 ], [Re(CO)5 ], [Cr(CO)5 ]− , and[Co(CN)5 ]3− . These are radical complexes with 17 electrons; theunpaired electron occupies the z2 orbital. They can therefore dimerize, just like organic radicals, to form bimetallic complexes such as[Mn2 (CO)10 ], [Re2 (CO)10 ], or [Re2 (CN)10 ]6− , etc. For some electronicSquare-based pyramidal ML5 complexescounts, the presence of four orbitals with similar energies can favourthe existence of high-spin complexes.
For example, the ground-stateelectronic configuration of the complex [MnCl5 ]2− (d4 ) correspondsto the occupation of each of the orbitals (xy), (xz), (yz), and (z2 ) bya single electron, with their spins parallel. High-spin complexes witha d6 or d8 electronic configuration are also known, which impliesthat the antibonding x 2−y2 orbital is singly occupied. This can onlyhappen for weak-field complexes. Deoxyhaemoglobin is a well-knownexample: it is a d6 iron complex, whose electronic configuration is(xy)2 (xz)1 (yz)1 (z2 )1 (x 2−y2 )1 . We remark in closing this section thatthere are a few complexes, such as [VOF4 ]− or [Nb(NMe2 )5 ], in whichthe d block is empty (d0 configuration).
As for the octahedral complexes,these very electron-deficient systems are only observed when the ligandspossess lone pairs.2.3.3.3. Electronic count and geometryCorrelation diagrams for the d-block orbitals, of the type shown inFigure 2.8, are often used to interpret the changes in the structures ofcomplexes as a function of their electronic configuration dn . In orderto use them, one adopts the hypothesis, which in most cases is verifieda posteriori, that the geometry of the complex is controlled by the energychanges of the highest-occupied molecular orbital (the HOMO rule). ML5complexes with an SBP geometry provide an interesting illustration ofthis rule.CommentThe structures observed for complexes whose electronic configuration isd0 (d-block empty) are characterized by values of the angle θ greater than90◦ (metal above the basal plane).
This preference, which is caused bybonding orbitals in the complex, can, as we shall see, be either modified ormaintained when there are electrons in the d block.We consider first a diamagnetic d6 complex. In the structure withθ = 90◦ , three nonbonding orbitals (xy, xz, and yz) are doubly occupied (Figure 2.8). An increase in the value of θ above 90◦ leads to adestabilization of two of these orbitals (xz and yz), which is energeticallyunfavourable (Figure 2.8). We may therefore predict that these complexes will adopt a structure in which the metal stays in the basal plane(θ = 90◦ ). Experimental values for these complexes are indeed close to90◦ (91–94◦ for the [M(CO)5 ] complexes if M=Cr, W).
But in a d8 diamagnetic complex, the two additional electrons occupy the z2 orbital,which is stabilized when θ increases above 90◦ (Figure 2.8). Applicationof the HOMO rule leads to the prediction that in these complexes, thePrincipal ligand fields: σ interactionsmetal will be located above the basal plane. This change in geometrydue to the number of d electrons is indeed observed: the angle θ is 101.0◦in [Ni(CN)5 ]3− and 102.6◦ in [Mn(CO)5 ]− .In the light of this analysis, we present the energy levels and orbitaloccupations for the d block of d6 and d8 diamagnetic complexes inScheme 2-52.z2z2yzxzxyxzyzxyd6d82-52We can extend this analysis to other electron counts.
In d7 complexes, the z2 orbital is singly occupied. We may therefore expect to findthat θ is larger than 90◦ , but not as large as in the low-spin d8 complexesin which this orbital is doubly occupied. The values of θ for d7 complexesare indeed often intermediate between those found for low-spin d6 andd8 complexes: about 95◦ for [Mn(CO)5 ], [Re(CO)5 ], or [Cr(CO)5 ]− ,97.6◦ for [Co(CN)5 ]3− .For a given number of electrons, the change from a low-spin toa high-spin complex can also lead to a change in geometry, since theHOMO is different. In a diamagnetic d6 complex, whose electronic configuration is (xy)2 (xz)2 (yz)2 , we have seen that the angle θ is close to90◦ .
However, in a high-spin d6 complex, whose electronic configurationis (xy)2 (xz)1 (yz)1 (z2 )1 (x 2−y2 )1 , the HOMO, x 2−y2 , is strongly stabilized by an increase in θ (Figure 2.8), thereby favouring a displacementof the metal out of the basal plane. This is exactly what is observed indeoxyhaemoglobin (a high-spin complex of Fe(II)), where the iron atomis placed well above the plane (θ = 110◦ ) defined by the porphyrin ring(a ligand of L2 X2 type).2.4.
Tetrahedral ML4 complexesIn a complex of this type, the metal is placed at the centre of a tetrahedronwhose vertices are occupied by the four ligands. There are at least twoways to derive the d-block orbitals for a tetrahedral complex. In the‘direct’ method, we allow the d orbitals of the metal to interact with thesymmetry-adapted combination of ligand orbitals (Chapter 6, § 6.6.2.2Tetrahedral ML4 complexesand Exercise 2.11), taking account of their symmetry properties in the Tdgroup.
We may also start from the d orbitals of a square-planar complexand study their changes as the ligands are moved towards the tetrahedralgeometry. We shall use the second approach here, as it not only givesus the d-block structure for a tetrahedral complex, but it also yields theorbital correlation diagram linking the two geometries most frequentlyfound for ML4 complexes.zL1ML2L4yxL3L1L3L2 L42-53The change from one structure to the other is studied following themechanism described in Scheme 2-53, where the ligands L1 and L3 moveupwards in the yz plane, and the ligands L2 and L4 downwards in thexz plane.
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