Yves Jean - Molecular Orbitals of Transition Metal Complexes (793957), страница 21
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In these complexes, we distinguish the basal ligands (Lb ) from theapical one (La ). Starting from the knowledge that the M–La bondis either a little shorter than or roughly equal in length to theM–Lb bonds for low-spin d6 complexes, rationalize the followingexperimental results for the different electronic configurations:yx(a) In the low-spin complex [Co(CN)5 ]3− , on the other hand, wefind Co–(CN)a = 2.01 Å but Co–(CN)b = 1.90 Å.(b) This trend is reinforced in the low-spin complex [Ni(CN)5 ]3− ,where Ni–(CN)a = 2.17 Å but Ni−(CN)b = 1.85 Å.3. Which is the longer bond (Mn–Cla or Mn–Clb ) in the high-spincomplex [MnCl5 ]2− ?4. What differences may be anticipated between a low-spin and ahigh-spin d8 complex?Bond lengths in d8 –ML4 complexes2.81.
Indicate the splitting of the d block in an ML4 complex whosegeometry is(i) square-planar;(ii) tetrahedral.2. What is the most stable electronic configuration for a d8 complexin each geometry?3. It is observed experimentally that typical metal–ligand bondlengths for d8 complexes are larger in tetrahedral complexes (seetable below: units are Å).Ni–PNi–SNi–BrSquare-planarTetrahedral2.142.152.302.282.282.36Suggest a rationalization.Principal ligand fields: σ interactions2.91. Derive the d-block orbitals for a butterfly ML4 complex from thoseof a TBP ML5 complex.zL3L2120°L1xML5L3yL2ML1L4L42.
Are these different from the orbitals derived in § 2.8.3 starting froman octahedral complex (consider only the four lowest-energy dorbitals)?2.10Derive the d orbitals for the bent ML2 fragment from those of asquare-planar ML4 complex. Compare them with those obtained in§ 2.8.4.Use of group theory2.111. Construct all the MO of a tetrahedral complex, making use ofsymmetry-adapted combinations of ligand orbitals and the data inthe character table for the Td group (Chapter 6, § 6.6.2), followingthe procedure adopted in Figure 2.2 for an octahedral complex.2. Indicate the orbitals associated with the σ bonds, the d-blockorbitals, and the σ ∗ antibonding orbitals.2.12Repeat the questions in 2.11 for a trigonal-planar ML3 complex (usethe data in Chapter 6, § 6.6.3).Orbital polarization (Appendix A)2.131.
In a square-planar ML4 complex, which metal orbital of s or p typecan polarize the z2 orbital in the d block?2. What are the consequences of this polarization for the shape ofthe orbital and for the metal–ligand interactions?Appendix A: polarization of the d orbitalsAppendix A: polarization of the d orbitalsIn many complexes, some of the antibonding orbitals in the dblock are polarized by mixing, either with a p orbital or with thes orbital of the metal (e.g. see 2-64 and 2-65 for d–p mixing and2-71 for d–s mixing). The purpose of this appendix is to study theorbital interaction scheme that produces these polarizations in greaterdetail.When an orbital in the d block results simply from the antibondinginteraction between a metal d orbital and an orbital of the same symmetry located on the ligands (ℓ) (two-orbital interaction scheme, 2.A1), thed orbital is not polarized.
However, polarization does occur if there is ap (or s) orbital on the metal that has the same symmetry as the d andl orbitals, which leads to a three-orbital interaction scheme (2.A2). In thiscase, while the d and p (or s) orbitals are of course orthogonal (S = 0),since they are located on the same atom, the overlaps between the lorbital on the ligands and each of the metal orbitals are non-zero (Sl−dand Sl−p , 2.A2).dSl–dl2.A1p2.A1.
Three-orbital interaction diagramS=0S l–pdS l–dl2.A214Y. Jean and F. Volatron ‘An Introduction toMolecular Orbitals’, Oxford University Press,NY (1993), chapter 6.3p2We consider the case where two orbitals on the metal, for example,d and p, have the same symmetry as an orbital l on the ligands. Inthe interaction diagram (Figure 2.A1), the latter is placed at lowerenergy than the metal orbitals, due to the greater electronegativityof the ligands. The interaction between these three atomic orbitals leads to the formation of three MO (φ1 , φ2 , and φ3 ). Whenwe consider their energies, φ1 is lower than l and φ3 higher thanp.
The orbital φ2 ends up at an intermediate energy level, a littlehigher than the d orbital with this combination of initial orbitalenergies.14Each MO is a linear combination of the three orbitals l, d, and p.When we examine their shapes, we find that the interactions between land d, and between l and p, are both bonding in the lowest-energy MOφ1 and both antibonding in the highest-energy MO φ3 . In the orbital φ2 ,there is an antibonding overlap (l − d) but also a bonding overlap (l − p)(2.A3).ppdl1Figure 2.A1.
Three-orbital interactiondiagram, with two on the metal (d and p) andone on the ligands (l).S>0pS>0S<0ddS>01ldS<02lS<0l32.A3Principal ligand fields: σ interactions2.A2. Polarization by a p orbital: TBP ML5 complexes15The analysis that follows is alsoapplicable to ML3 complexes with atrigonal-planar geometry.The d block of an ML5 complex with a TBP geometry contains twostrictly nonbonding orbitals with e′′ symmetry (xz, yz), one stronglyantibonding orbital with a1 symmetry (z2 ), and two weakly antibondingorbitals with e′ symmetry (xy, x 2−y2 ) (see § 2.5.1, Figure 2.10).
We shallexamine these last two in greater detail.In the D3h point group appropriate for this complex, the px and pyorbitals have the same symmetry (e′ ) as xy and x 2−y2 (see Table 2.3,§ 2.5.1). Two combinations of orbitals on the equatorial ligands, lx andly , also have this symmetry (Chapter 6, § 6.6.4.2). These six orbitals areshown in Figure 2.A2, where the plane of the page is the equatorialplane (xy).15 Notice that it is possible to separate each pair of degenerateorbitals into an ex′ component, which is antisymmetric with respect tothe yz plane, and an ey′ component which is symmetric with respectto this plane. The first group includes the xy, px , and lx orbitals, whilethe x 2−y2 , py , and ly orbitals belong to the second.
No interaction ispossible between orbitals that belong to different groups, since theyhave different symmetry properties with respect to the yz plane.xy (e⬘x)px (e⬘x)lx (e⬘x)xyFigure 2.A2. Fragment orbitals (metal orligands) with e’ symmetry in a TBP ML5complex. The equatorial ligands are in theplane of the page (xy), and the axial ligands areomitted for greater clarity.x2–y2 (e⬘y)py (e⬘y)ly (e⬘y)The interactions between orbitals with e′ symmetry therefore givetwo equivalent blocks, one involving the three ex′ orbitals, the other thethree ey′ orbitals (Figure 2.A3). The MO 1ex′ , 2ex′ , and 3ex′ , are in the first,and 1ey′ , 2ey′ , and 3ey′ are in the second.Application of the rules presented in § 2.A1 leads to the followingorbital combinations in the 1ex′ (2.A4), 2ex′ (2.A5), and 3ex′ (2.A6) MO.The 1ex′ orbital (2.A4) belongs to the group of bonding MO in theML5 complex, characterized by (i) bonding metal–ligand interactions,reinforced here by the polarization of the d orbital; (ii) a lower energythan that of the ligand orbitals; and (iii) larger coefficients on the ligands than on the metal.
This orbital does not belong to the d block ofthe complex. The 3ex′ orbital (2.A6) is one of the antibonding MO inAppendix A: polarization of the d orbitals3e⬘x, 3e⬘y(px, py)2e⬘x, 2e⬘y(xy, x2–y2)(lx, ly)Figure 2.A3. Interaction diagram for orbitalswith e′ symmetry in a TBP ML5 complex.le⬘x, le⬘ythe complex, and the d–p mixing in the metal reinforces its antibonding character.
This is the highest-energy MO (Figure 2.A3); it is moreconcentrated on the px metal orbital than on xy and is also not part ofthe d block. Among the three MO that we are considering, the one thatbelongs to the d block is therefore the one with intermediate energy, 2ex′(2.A5), since it is mainly concentrated on the initial orbital with intermediate energy, xy. The contribution of the px orbital to this MO leadsto its overlap with the ligand lx orbital being bonding (a result that wehad always assumed in Chapter 2).
As a result, the xy orbital is polarizedin the direction opposite to the ligands, and its antibonding character isreduced. A similar analysis of the interactions of the ey′ orbitals showsthat the second d-block orbital with e′ symmetry is the 2ey′ orbital, whichis degenerate with 2ex′ , and in which the ly ligand orbital mixes in anantibonding way with x 2−y2 , but in a bonding way with py (2.A7).S>0++=1e⬘xS>02.A4S>0++=2e⬘xS<02.A5Principal ligand fields: σ interactionsS<0++=3e⬘xS<02.A6S>0++=2e⬘yS<02.A72.A3. Polarization by the s orbital: linear ML2 complexesIt is possible for a d orbital to have the same symmetry as the metal sorbital. In particular, this happens for linear ML2 complexes, in whichboth the z2 and the (higher-energy) s orbitals have σg symmetry.
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