Yves Jean - Molecular Orbitals of Transition Metal Complexes (793957), страница 25
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These are two equivalentinteractions, since they involve orbitals which are related by a rotationof 90◦ : (xz, yz) on the one hand and (πx∗ , πy∗ ) on the other. Theytherefore lead to the formation of two degenerate bonding MO andtwo antibonding MO that are also degenerate. As shown in § 3.2.3, thebonding MO (xz+λπx∗ and yz+λπy∗ ), which are mainly concentrated onthe metal, are the orbitals which belong to the d block of the [ML5 CO]complex. The presence of a CO ligand therefore lifts the degeneracy ofπ -acceptor ligands: general properties*x –xz*y –xzx2 – y2, z2x2 – y2, z2*x,*ynew d blockxz, yzxyFigure 3.5. Interaction diagram showing theperturbation of the d block of an octahedralcomplex (left-hand side, σ interactions only)∗ orbitals of a carbonyl ligandby the two πCO(right-hand side). The electronic occupationshown corresponds to a complex with a d6electronic configuration.xyxz + *xyz + *ythe three orbitals in the original t2g block of the octahedron, stabilizingtwo of them but leaving the third (xy) unchanged.
The two remainingorbitals in the d block (x 2−y2 and z2 ) are identical to the original MOderived for σ interactions only, since they are not affected by the πinteractions. Finally, the two highest-energy MO (πx∗ −λxz and πy∗ −λyz)are mainly concentrated on the carbonyl ligand. The occupation of thed block clearly depends on the exact nature of the [ML5 CO] complex;Figure 3.5 corresponds to a complex with a d6 electronic configuration.Before the interaction, the four electrons stabilized by the π interactionsoccupied pure metal d orbitals (xz and yz). After the interaction, theseorbitals are partially delocalized onto the carbonyl ligand, showing theπ -acceptor character of this species.CommentThe relative position of the σ -antibonding (x 2−y2 , z2 ) and theπ-antibonding (πx∗ − λxz and πy∗ − λyz) orbitals may be inverted withrespect to that shown in Figure 3.5.
It depends among other things on theenergy gap between the nonbonding (xy, xz, and yz) and the antibonding(x 2−y2 , z2 ) orbitals created by the σ interactions.3.2.4.2. The metal–carbonyl bond: donation andback-donation interactionsThe σ bond between the carbonyl ligand and the metal centre is formedby the σC orbital that characterizes the lone pair on the carbon atom(Figure 3.3) and by a d orbital on the metal (z2 in the orientation shownπ -type interactionsin 3-15). This interaction, which leads to a transfer of electrons from theligand to the metal, is called the donation interaction (3-17a). The π interactions described in Figure 3.5 produce a transfer of electrons in theopposite direction, from the metal to the ligand. These are back-donationinteractions (3-17b). The carbonyl ligand is therefore simultaneously aσ -donor and a π-acceptor.OCe–e–3-17a Donatione–3-17b Back donationThe π interactions reinforce the metal–carbon bond (bonding interactions M−C) but weaken the CO bond (antibonding interactions C−O)(3-17b).
This electronic reorganization can be represented by the Lewisstructures shown in 3-18.MCMOCO3-18Experimentally, the metal–carbon bond is observed to be substantially shorter than the value that would be expected for a σ -only bond,by some 0.2–0.3 Å. The result for the CO bond is less clear, as the distances measured for carbonyl complexes fall in the very narrow rangeof 1.14–1.15 Å. These values are only slightly longer than that foundfor the free ligand (1.13 Å).
The equilibrium CO distance is thereforealmost insensitive to the transfer of electrons, an observation that canat least partially be explained by the fact that the difference in lengthbetween a triple and a double bond is also relatively small (1.13 and1.23 Å, respectively). Infrared spectroscopy (IR) provides a far betterprobe, from the value of the IR absorption frequency associated withthe stretching of the CO bond (νCO ). This frequency is related to thestrength of the bond and is very sensitive to the electronic population in∗ orbitals. For example, for the isolated ligand it decreases fromthe πCO2143 to 1489 cm−1 on passing from the ground state to the excited electronic state in which an electron has been excited from the nonbonding∗ orbital (Figure 3.3). This is thereforeσC orbital to the antibonding πCOa very sensitive indicator which enables the transfer of metal π electrons to one or several carbonyl ligands to be demonstrated.
Thus, νCOdecreases from 2143 cm−1 in isolated CO to 2000 cm−1 in [Cr(CO)6 ],a complex with a d6 electronic configuration, and even to 1860 cm−1in [V(CO)6 ]− , another d6 complex which, due to its anionic nature, isComplexes with several π-donor or π-acceptor ligandsparticularly effective for the transfer of electron density to π -acceptorligands.3.3. Complexes with several π -donor orπ -acceptor ligandsIn the first example that we considered, there was only a single ligandable to perturb the d block of the complex through π interactions.When several ligands of this type are present, their individual effects areadded, destabilizing the d orbitals in the case of π-donors (antibondingmixing in the d block) or stabilizing them in the case of π-acceptors(mixing of a bonding type in the d block).
However, as we shall see inthe following examples, the effect produced by n ligands of a given typeis not necessarily n times larger than that produced by a single ligand.The symmetry properties of the complex may prevent some orbitals,either occupied for π donors or empty for π acceptors, from interactingwith the d-block orbitals.3.3.1. The trans-[ML4 Cl2 ] octahedral complexP2P1ClMLLClzLxLyConsider an octahedral complex of the type [ML4 Cl2 ], with two doubleface π -donor ligands (Cl) in trans positions and four other ligands whichonly have σ interactions with the metal. Three of the symmetry elements in the complex are shown in 3-19: the planes P1 (xz) and P2 (yz)and the inversion centre i, located on the central atom.3.3.1.1. π -type orbitals on the ligandsi3-19Four lone pairs of π-type are available, described by the px and pyorbitals on each chlorine atom.
It must be noticed that the two Cl ligandsare equivalent by symmetry, that is, they are interchanged by at least onesymmetry element (e.g. the horizontal plane xy or the inversion centre i).x *xy*y3-20Rather than consider each of the px and py orbitals individually, it is therefore preferable to use linear combinations of these orbitals that properlyπ -type interactions7The bonding or antibonding character isweak, due to the large separation between thetwo chlorine atoms. It is perhaps better toreplace ‘bonding/antibonding’ by‘in-phase/out-of-phase’, to emphasize onlythe way in which the initial atomic orbitals arecombined.reflect the symmetry of the complex (Chapter 6, § 6.4). In the case oftwo equivalent atoms, these are simply ‘bonding’ and ‘antibonding’7combinations of the initial orbitals. These are usually indicated by (πx ,πy ) and (πx∗ , πy∗ ), respectively (3-20), making reference to the nature ofthe overlap (π ) and the orientation of the orbitals (x- or y-axes).Electronically speaking, these four orbitals are doubly occupied,since they are formed from atomic orbitals that describe π-type lonepairs on each of the chloride ligands.
They therefore provide a delocalizeddescription of these lone pairs, which is adapted to the symmetry of thecomplex.Before constructing the diagram for the interaction between theπ orbitals on the ligands and the d orbitals on the metal centre, we mustanalyse the symmetry properties of these orbitals. We shall describe twomethods, in which we use either some selected symmetry elements, orthe full set of these elements and the machinery of group theory.3.3.1.2.
Taking symmetry into account: initial analysisTo characterize orbital symmetry, we may, as in the examples alreadytreated (§ 3.1.4 and 3.2.4), use the planes P1 and P2 (3-19). But wemust add a third element to enable us to distinguish the symmetry ofthe bonding and antibonding combinations that we have constructedabove. This additional element might be the xy plane, or it might be theinversion centre i. With respect to this latter element, the πx,y orbitals∗ orbitals are symmetric (S) (see 3-21are antisymmetric (A) but the πx,y∗for the πy and πy orbitals).Aiy–yiS *y *y3-21When we take all three of these elements into account (P1 , P2 , and i),the symmetry labels are SAA for πx , ASA for πy , SAS for πx∗ , and ASSComplexes with several π-donor or π-acceptor ligandsfor πy∗ ; on the metal, they are AAS for xy, SAS for xz, ASS for yz, andSSS for both x 2−y2 and z2 (3-22).This initial analysis of the symmetry properties shows us that two ofthe four lone pairs of the chloride ligands, those described by the bondingcombinations πx and πy , cannot interact with the d-block orbitals, due totheir different symmetry properties (S = 0).
In the same way, the xy,x 2−y2 , and z2 orbitals on the metal cannot, by symmetry, interact withthe ligand orbitals. The only interactions that are possible (S = 0) occurbetween πx∗ and xz on the one hand (symmetry SAS), and between πy∗and yz on the other (symmetry ASS). x (SAA)x2–y2 (SSS) y (ASA)z 2 (SSS)xy (AAS) *x (SAS) *y (ASS)xz (SAS)yz (ASS)3-223.3.1.3.
Taking symmetry into account: the use of group theoryRather than select only some symmetry elements present in the systembeing studied, one can consider all of them by using group theory. This isthe most rigorous method—there is no danger of forgetting a symmetryelement that might be important for a particular interaction—and itallows us, particularly in high-symmetry systems, to anticipate certainspecial properties such as the existence of orbitals that are degenerateby symmetry. The symmetry elements of the complex studied here arecharacteristic of the D4h point group (Chapter 6, § 6.2.2 and 6.6.1).If we consider the two π ∗ antibonding combinations of the lonepairs, we notice that they are related by a rotation of 90◦ about thez-axis, which is a symmetry element of the system (a C4 -axis).
The sameapplies for the two π-bonding combinations, and also for the xz and yzorbitals on the metal. These are pairs of orbitals that are degenerate bysymmetry in the D4h point group. If we consult the character table forπ -type interactionsTable 3.1. Character table for the D4h point groupD4hE2C4A1gA2gB1gB2gEgA1uA2uB1uB2uEu111121111211−1−1011−1−10C21111−21111−22C2′2C2′′1−11−101−11−101−1−1101−1−110i11112−1−1−1−1−22S411−1−10−1−1110σh1111−2−1−1−1−122σv2σd1−11−10−11−1101−1−110−111−10x 2 + y2 , z2x 2 − y2xy(xz, yz)z(x, y)this group (Table 3.1), we notice that it contains two two-dimensionalrepresentations, referred to as Eu and Eg , which differ by their behaviourwith respect to the inversion centre of the complex (i, located on thecentral metal): Eg is symmetric (its character in the i column is positive),but Eu is antisymmetric (a negative character).
The bonding combinations (πx , πy ), which are antisymmetric with respect to the inversioncentre (3-21), have eu symmetry, but the antibonding combinations (πx∗ ,πy∗ ), which are symmetric with respect to the inversion centre, haveeg symmetry. The character table also gives us the symmetries of thed orbitals on the metal centre, in the last column: a1g for z2 , b1g forx 2−y2 , b2g for xy, and eg for (xz, yz).In the case being examined, we therefore come to the same conclusion as that established in the preceding section from a limited numberof symmetry elements: the only interactions that occur concern the(πx∗ , πy∗ ) orbitals on the ligands, and (xz, yz) on the metal centre, whichconstitute two degenerate pairs of orbitals with eg symmetry in the D4hpoint group.3.3.1.4.
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