Yves Jean - Molecular Orbitals of Transition Metal Complexes (793957), страница 22
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A threeorbital interaction scheme is therefore appropriate for these two orbitalsand the ligand orbital l with the same symmetry (Figure 2.A4), givingthree MO, 1σg , 2σg , and 3σg .As in the preceding example, mixing between z2 and s reinforcesthe bonding character of the 1σg MO and the antibonding characterof the 3σg MO. The orbital with intermediate energy, 2σg , is the onlyone of these three that belongs to the d block. In this orbital, thereis antibonding mixing between z2 and l, but mixing of bonding typebetween s and l (2.A8). The s contribution decreases the amplitude of z2along the z-axis but increases it in the xy plane. The polarization of thez2 orbital therefore reduces the antibonding metal–ligand interactions.zFigure 2.A4. Fragment orbitals (metal andligands) with σg symmetry in a linear ML2complex.z2slAppendix A: polarization of the d orbitalsS>0++=polarized z2 (2g)S<02.A8Without this polarization, the energy of a z2 orbital that is antibonding with the ligands located on the z-axis is very high.
Polarization of theorbital in the xy plane, which does not contain any ligands, lowers itsenergy sufficiently for it to be occupied in stable linear ML2 complexes(d10 complexes, § 2.7.2).2.A4. Polarization by the s orbital and by a p orbital: SBPML5 complexesIn some cases, it is possible for a d orbital to be polarized by the s orbitaland simultaneously by a p orbital.
This happens, for example, to thez2 orbital in ML5 complexes with an SBP geometry (§ 2.3.1.2). Thisorbital does indeed have the same symmetry as the s and pz orbitals(a1 in the C4v point group). The z2 orbital of the d block has antibondinginteractions with the ligands (z2 − l, 2.A9); the s and p contributions mixin so that:(1) the contribution from pz is bonding with the apical ligand (locatedon the z-axis);.(2) the contribution from s is bonding with the basal ligands (located ina plane perpendicular to the z-axis) (2.A9).++pz=z2 – lspolarized z22.A9Notice that we had simplified the problem in § 2.3.1.2, by onlyconsidering mixing with the pz orbital. It is indeed this latter which isPrincipal ligand fields: σ interactionsresponsible for the polarization towards the vacant site of the octahedron that is the most important feature of the z2 orbital in SBP ML5complexes.Appendix B: orbital energiesWhen deriving the d block associated with different ligand fields, weobtained nonbonding, ‘weakly’ antibonding, or ‘strongly’ antibondingorbitals.
These ideas can be made more precise by undertaking calculations which yield numerical values for orbital energies. We have usedthe extended Hückel method for model complexes of the MHn type,the MHn distance being fixed at 1.7 Å. The values obtained are given ineV; while they should only be considered as indications, they can help togive an idea of the energy-level splittings with respect to the initial nonbonding level (εd ) in the main ligand fields. Information on the shapesof the orbitals may be obtained from the figures indicated in Chapter 2.eg –6.02CrCrt2g –11.22Octahedral complex CrH6εd (Cr) = −11.22 eV(see Figure 2.3)b1ga1–9.41(b2, e) –11.22–8.60Nia1g–12.62(b2g, eg) –12.99–6.02SBP complex CrH5(metal in the basal plane)εd (Cr) = −11.22 eV(see Figure 2.7)NiSquare-planar complex NiH4εd (Ni) = −12.99 eV(see Figure 2.6)b1t2 –11.48e –12.99Tetrahedral complex NiH4εd (Ni) = −12.99 eV(see Figure 2.9)Appendix B: orbital energiesa1 –7.06a1 –10.77 = 105°Fee –12.14b2 –12.70SBP complex FeH5(metal out of the basal plane)εd (Fe) = −12.70 eV(see Figure 2.8)90°e⬘ –11.26Fee⬙ –12.70TBP complex FeH5εd (Fe) = −12.70 eV(see Figure 2.10)2a1–9.32b2–10.57e⬘ –12.71CuFe(a2, b1, 1a1) –12.70‘Butterfly’ complex FeH4εd (Fe) = −12.70 eV(see Figure 2.15)2a1Trigonal-planar complex CuH3εd (Cu) = −14.00 eV(see Figure 2.11)–9.73CuFe1a1a1 –13.83e⬙ –14.00g–13.44(g, g) –14.00–12.34(a2, b1, b2) –12.70‘T-shaped’ complex FeH3εd (Fe) = −12.70 eV(see Figure 2.14)Linear complex CuH2εd (Cu) = −14.00 eV(see Figure 2.12)This page intentionally left blank π-type interactionsIn the preceding chapter, we derived the structure of the d block forseveral different MLn complexes in which the ligands were assumed touse only a single orbital to form the metal–ligand bond.
This orbitalwas either nonbonding or essentially so, and oriented towards the metalcentre. Since the overlap between this ligand orbital and a d orbital onthe metal is of the axial type, their interaction leads to the formationof a molecular orbital (MO) which characterizes a σ bond. As we havealready seen in Chapter 1 (§ 1.5.2), some ligands have another orbital(or even two) that can in principle contribute to the bonding with themetal. The orientation of this orbital is usually perpendicular to the axisdefined by the σ bond, so the resulting overlap with a d orbital on themetal is lateral, and the interaction of π type.
Two examples are shownbelow (3-1), in which the ligand orbitals are pure p atomic orbitals.Among the ligands that can in principle have a π interaction with ametal centre, it is important to distinguish two types, depending on theelectronic occupation of the orbital that is concerned on the ligand:3-1• if it is doubly occupied, the ligand is said to be a π-donor• if it is empty, then the ligand is a π-acceptor.This nomenclature is of course linked to the capacity of the ligand togive or receive electrons through the π interaction with the metal.CommentThe notation ‘π’ that is used here is almost never strictly correct accordingto group theory, where it reserved for doubly degenerate orbitals in linearmolecules (Chapter 6).
It is, however, widely used to refer to local symmetry;the expression ‘π interaction’ is used when the two orbitals share a commonnodal plane and have lateral overlap (3-1).The examples treated in this chapter involve octahedral complexes.However, the procedure we have used is general and can be applied toall ligand fields. Several illustrations may be found in the exercises at theend of the chapter.π -type interactions3.1.
π -donor ligands: general properties3.1.1. The nature of the π orbital on the ligandA π-type orbital on a ligand can be doubly occupied only if it issufficiently low in energy. We may therefore be concerned with:1. A nonbonding p orbital on a very electronegative atom. Althoughnonbonding, this orbital is very low in energy and characterizes alone pair on the atom linked to the metal. For example, consider thep lone pair on the nitrogen atom of an amido group that can interactwith one of the metal d orbitals (Scheme 3-2 where the geometryaround nitrogen is assumed to be planar).HHNMHHlone pair3-22. A bonding orbital that characterizes a π bond between two atoms ofthe ligand, as in the case of the imino ligand (3-3) with the doublyoccupied πNC orbital.
Notice that a π -bonding orbital on the ligandis automatically accompanied by the corresponding π ∗ -antibondingorbital. A ligand of this type can therefore act simultaneously as aπ -donor, with its bonding orbital, and as a π-acceptor, thanks toits empty π ∗ orbital. It is categorized as a π-donor if the formerinteraction is dominant. A heteronuclear bond provides a favourablecase, if, as in the imino ligand (3-3), the more electronegative atomis bonded to the metal. The π orbital in such cases is mainly concentrated on the atom bonded to the metal (large overlap), whereas theπ ∗ orbital is mainly concentrated on the more distant centre (smalloverlap, see Chapter 1, § 1.3.2).HHMNHCHH bond3-3Hπ-donor ligands: general properties3.1.2.
‘Single-face’ and ‘double-face’ π-donorsSome ligands possess a single nonbonding doubly occupied p orbital,such as the amino ligand (3-2), or a single π-bonding orbital near tothe metal centre, such as the imino ligand (3-3). These are said to be‘single-face’ π-donors.p lone pairsMMM lone pairMX3-41The polarization of this orbital, in thedirection opposite to the metal, significantlyweakens its σ -type overlap with the orbitals ofthe same symmetry on the metal.
This orbitaltherefore has a negligible influence on theshapes and energies of the MO of thecomplex, as it remains localized on the ligand.MXMX3-5Other ligands, however, possess two orbitals of this type, in perpendicular planes: these are ‘double-face’ π-donors. The halogens are themost common example (F, Cl, Br, I). These are X-type ligands, withseven valence electrons. Formation of the σ bond involves the unpairedelectron on the halogen and a metal electron; as a result, the oxidationstate of the metal is increased by one (Chapter 1, § 1.1.1.2). There aretherefore three lone pairs which remain on the halogen bonded to themetal (Chapter 1, § 1.5.2.3): a σ -type lone pair for which the M–X internuclear axis is a symmetry axis, and two lone pairs characterized bynonbonding p orbitals which ‘point’ perpendicular to the internuclearaxis (more strictly, their axes of revolution are perpendicular to this axis,3-4). Due to its symmetry, the σ lone pair cannot participate in a π-typeinteraction.1 However, the p lone pairs interact with the metal d orbitals through two π-type interactions which take place in perpendicularplanes (3-5).
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