Yves Jean - Molecular Orbitals of Transition Metal Complexes (793957), страница 17
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From a purely electronicpoint of view, the square-planar geometry seems to be favoured, withsix nonbonding and two weakly antibonding electrons, instead of fournonbonding and four more strongly antibonding electrons in the tetrahedron (2-58). However, in this latter structure, the exchange energydue to the two unpaired electrons is a favourable factor. Steric factorsPrincipal ligand fields: σ interactionsSquare-planar (d 8 high-spin)Tetrahedral (d 8 high-spin)2-57 Square planar (d8 high-spin) Tetrahedral (d8 high-spin)also play an important role, since they favour the tetrahedral structure,with bond angles of 109.5◦ rather than the square-planar arrangementwith 90◦ bond angles. So complexes with very bulky ligands (triphenylphosphine, PPh3 , for example), are usually high-spin and tetrahedral.But the balance between all these factors seems to be quite subtle, sincethe complex [Ni(PPh2 Et)2 Br2 ] has been isolated in both forms, squareplanar and tetrahedral; they are found to be in equilibrium in solutionand are thus very close in energy.Square-planar (d 8 low-spin)Tetrahedral (d 8 high-spin)2-58 Square planar (d8 low-spin) Tetrahedral (d8 low-spin)7S.
Keinan and D. Avnir Inorg. Chem. 40,318 (2001).As we have already remarked at the beginning of this section, notall ML4 complexes adopt such high-symmetry structures. In this context, d9 complexes, whose electronic configuration is ‘intermediate’between one which favours a square-planar geometry (diamagnetic d8complexes) and others which favour a tetrahedral geometry (paramagnetic d8 or diamagnetic complexes d10 ), are particularly interesting.
Thetwo structural types are indeed found in the family of d9 ML4 complexes:for example, square-planar for [M(py)4 ]2+ (M=Cu, Ag) (py=pyridine)but quasi-tetrahedral for [Co(CN)4 ]4− , [Co(PMe3 )4 ], and [Ni(PR 3 )3 X](X=Cl, Br, I). A given complex can even adopt very different geometries depending on its environment. For example, 131 structures of the[CuCl4 ]2− anion have been published,7 which differ in the nature ofthe associated cation. The whole range of geometries has in fact beenobserved, from the square plane to an almost ideal tetrahedron!Trigonal-bipyramidal ML5 complexes2.5. Trigonal-bipyramidal ML5 complexesL4L3L2z90°L1M120°L5yx2-598For this geometrical parameter, thedifference appears to be so small that it candepend on the environment! For example, inthe solid-state structure of [Fe(CO)5 ]determined by X-ray diffraction, the axialbonds are slightly longer than the equatiorial,by about 0.008 Å (D.
Braga, F. Grepioni, andG. Orpen Organometallics 12, 1481 (1993)). Buta study of the structure in the gas phase, byelectron diffraction, gives the opposite result,with the equatorial bonds being longer by0.01–0.03 Å (B. W. McClelland, A. G. Robiette,L. Hedberg, and K. Hedberg Inorg.
Chem. 40,1358 (2001)).In an ML5 complex which adopts a trigonal-bipyramidal (TBP) geometry, we distinguish the equatorial ligands (L1 , L2 , and L3 ) from thosein axial positions (L4 and L5 , 2-59). The former are located at the verticesof the triangular base of the bipyramid, and they define the equatorialplane of the complex (the xy plane in 2-59), while the axial ligands arelocated at the vertices of the bipyramid. The angles between equatorialbonds are 120◦ (trigonal base), but those between an equatorial and anaxial bond are 90◦ .CommentThe equatorial and axial ligands are not equivalent by symmetry, since nosymmetry operation of the complex’s point group (D3h ) interchanges anequatorial ligand with an axial. Nor are they equivalent from a chemicalpoint of view, and as a consequence, the M–Leq and M–Lax bond lengthscan differ, even when all the ligands L are identical.82.5.1. Characterization of the d blockWith the orientation of the axes chosen in 2-59, the equatorial ligandsare located in the xy plane and the axial ligands on the z-axis, that is, atthe intersection of the xz and yz planes.The five ligands are thus placed in one or other of the nodal planes ofthe xz (nodal planes xy and yz) and yz (nodal planes xy and xz) orbitals.
Asa result, there cannot be any σ interaction between the ligands and thesetwo orbitals which stay nonbonding in the d-block of a TBP complex(2-60). By consulting the character table for the D3h point group, we findthat these two degenerate orbitals have e′′ symmetry.xzyz2-60z22-61A third orbital in the d block may readily be characterized.
The z2orbital is destabilized by antibonding interactions with all five ligands.This is the highest-energy orbital in the d block, with the strongestantibonding interactions involving the axial ligands along the z-axis(2-61).Principal ligand fields: σ interactionsThe xy and x 2−y2 orbitals have not yet been considered. The firstis destabilized by antibonding interactions with the ligands L2 and L3(2-62). No interaction is possible with the three other ligands whichare located in the nodal plane yz. For the x 2−y2 orbital, its two nodalplanes bisect the x- and y-axes and they contain the z-axis.
It thereforecannot interact with the axial ligands placed on this axis, but antibondinginteractions will develop with the three equatorial ligands, as none ofthem is located in either of the nodal planes. Two representations canbe given for this orbital (2-63). In the first (2-63a), the orientation ofthe axes is the same as that used previously, whereas in the second(2-63b), the plane of the page is chosen as the equatorial plane (xy). Thissecond representation allows us to understand more easily the sign ofthe coefficients for the orbitals on the ligands L2 and L3 if the interactionwith x 2 −y2 is to be antibonding (the sign for the orbital σ1 , on the ligandL1 , is obvious since it points along the y-axis).
It is clear from 2-63b thatthe overlap between the orbitals σ2 and σ3 and the part of the x 2−y2orbital concentrated along the horizontal axis (y) is positive, whereaswith the part of the orbital concentrated along the vertical axis (x) it isnegative. Now since the angle L2 –M–L3 is 120◦ , the M–L2 and M–L3bonds are closer to the x-axis than to the y-axis. The representation givenin 2-63 therefore does indeed correspond to a negative value of the totaloverlap between the orbitals on the ligands L2 and L3 and the x 2 − y2orbital on the metal centre, and thus to an antibonding interaction.3L4L4L1ory1x9The linear combinations of the ligandorbitals with which they interact also have e′symmetry, of course (see Chapter 6, § 6.6.4).L5xyL52-622-63a2x2–y22-63bIt should be noted that the antibonding M–Li character in this orbitalis not equivalent for the three ligands.
L1 is situated on the y-axis andtherefore has a larger axial overlap than do the ligands L2 and L3 , whichare placed between the x- and y-axes. Moreover, the coefficient for σ1is twice as large as those for σ2 or σ3 (Chapter 6, § 6.6.4.2). Thesetwo factors lead to the x 2−y2 orbital being antibonding mainly withthe ligand L1 , but xy is antibonding only with the ligands L2 and L3(2-62).
While this analysis enables us to deduce that the xy and x 2−y2orbitals are both antibonding in the d block, an important additionalpiece of information is provided by examination of the character tablefor the D3h group (Table 2.3). From the last column, we learn thatthe xy and x 2−y2 orbitals are degenerate by symmetry (e′ symmetry).9Trigonal-bipyramidal ML5 complexesTable 2.3. Character table for the D3h groupD3hE2C33C2σh2S33σvA1′A2′E′A1′′A2′′E′′11211211−111−11−101−10112−1−1−211−1−1−111−10−110x 2 + y2 , z2(x, y)(x 2 − y2 , xy)z(xz, yz)The orbitals shown in 2-62 and 2-63 therefore make up a set of twodegenerate orbitals, of e′ symmetry. Their energy is of course higherthan that of the e′′ orbitals (xz and yz), since these latter are strictlynonbonding.The character table also shows that the px and py orbitals on the central atom, like xy and x 2−y2 , have e′ symmetry (penultimate column).They can therefore lead to the formation of polarized degenerate e′ orbitals in the d block, as their contribution polarizes the xy and x 2 −y2 orbitals.A more accurate shape of these orbitals can be obtained by adding a pxcontribution to xy (2-64) and py to x 2−y2 (2-65), so that the overlap ofthe p orbital with the ligand orbitals is positive (see Appendix A, § 2.2).The addition of px to the xy orbital polarizes this orbital in the directionaway from the ligands L2 and L3 , thereby decreasing the antibondinginteractions with these ligands (2-64).
For x 2−y2 , the polarization by pydecreases the amplitude of the orbital in the direction away from the ligand L1 (2-65) with which the antibonding interaction was the strongest.As in the examples that we have already studied (see § 2.3.1.2 and 2.3.2for SBP ML5 complexes), the participation of the p orbitals leads to areduction of the antibonding character of the d-block orbitals.+=pxxypolarized xy2-64=+x2–y2–pypolarized x2–y22-65Principal ligand fields: σ interactionsThe d block of an ML5 complex with a TBP geometry is thereforemade up of two degenerate nonbonding orbitals (xz and yz, with e′′symmetry), two degenerate orbitals that are fairly weakly antibonding(xy and x 2−y2 , with e′ symmetry) and one very strongly antibondingorbital (z2 , with a1′ symmetry).These results are illustrated in Figure 2.10 for two different orientations of the bipyramid, the equatorial plane (xy) being eitherperpendicular to the plane of the page (left-hand side) or in this plane(right-hand side).a1z2z2e⬘x2–y2xyxyx2–y2yzxze⬙xzFigure 2.10.
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