Yves Jean - Molecular Orbitals of Transition Metal Complexes (793957), страница 31
Текст из файла (страница 31)
By makinguse of the results established in Chapter 6 (§ 6.6.6.2), give the∗ orbitals (thesymmetry-adapted linear combinations of the πCOpoint group is D3h , whose character table is given in Table 6.21).3. Construct the diagram for the interaction of these orbitals withthose in the d block of question 1. Deduce the shapes and relativeenergies of the d-block MO in [Ni(CO)3 ].4.
Try to find these orbitals without using group theory (construction ‘by hand’, § 3.3). Show that some of the information providedby group theory cannot be readily obtained without its use.Appendix C: the carbonyl ligand, a double-faceπ -acceptorIn an octahedral complex with a carbonyl ligand (see § 3.2.2), two metald orbitals (xz and yz, 3C.1) can interact with the π-bonding and π ∗ antibonding MO on the CO ligand: πx and πx∗ with xy, πz and πz∗with yz, following two equivalent three-orbital interaction diagrams(see Appendix A, Chapter 2).
By comparing the strength of the d ↔ πand d ↔ π ∗ interactions, we may deduce whether the carbonyl ligandis a π donor or a π acceptor. These interactions, which involve orbitalsof different energy, are proportional to S2 /ε (Chapter 1, § 1.3.2);they therefore increase in strength with a decrease in the orbital energydifference, but with an increase in the overlap.Appendix C: the carbonyl ligand, a double-face π -acceptorTable 3C.1.
d-orbital energies for the metals of the first transition series, and∗ − d(ε ∗ ) calculated bythe energy differences d − πCO (επ ) and πCOπthe extended Hückel method (eV)ScTiVCrMnFeCoNiCuεd−8.5 −10.8 −11.0 −11.2 −11.7 −12.6 −13.2 −13.5 −14.0επ7.24.94.74.54.03.12.52.21.71.71.92.12.63.54.14.44.9επ ∗ −0.6zxy *z *xzx* COS *xy∆ *yz∆εS COM CO3.C114R. Hoffmann J.
Chem, Phys. 1963, 39,1397. One may also consult Y. Jean and F.Volatron Structure électronique des molécules,volume 2, 3rd edn., chapter 14, Dunod (2003).15These values differ only slightly fromthose in Table 1.4 (Chapter 1) that wereobtained from spectroscopic data:ε3d (Sc) = −7.92 eV and ε3d (Cu) =−13.46 eV.The comparison of επ with επ ∗ is not straightforward, sincethe d-orbital energy depends on the nature of the metal: these metalorbitals become considerably more stable as one moves from left toright in the periodic classification (Chapter 1, Table 1.3).
One can obtainat least a qualitative indication of the relative values of επ and επ ∗by using the extended Hückel method,14 for example, for the metals ofthe first transition series (Table 3C.1). The energy of the d orbitals liesbetween −8.5 eV (Sc) and −14.0 eV (Cu),15 and the energies calculated∗ MO are −15.7 and −9.1 eV, respectively, for a C−Ofor the πCO and πCOdistance of 1.14 Å(the average value in metal carbonyl complexes).If we consider only the energetic criterion, the interaction with the∗ orbitals is stronger than with ππCOCO for all the metals on the left of thetable, up to and including manganese (επ ∗ < επ ), suggesting thatthe carbonyl ligand should behave as a π acceptor.
On the other hand,for the metals furthest to the right, and particularly for Co, Ni, and Cu,the energy separation involving the πCO orbitals is smaller.The second criterion that needs to be examined involves the overlap.The analysis here is simpler, since the Sπ and Sπ ∗ overlaps, for a givenmetal, are proportional to the magnitudes of the coefficients on carbonπ -type interactions∗ MO, respectively (we are neglecting here the overlapin the πCO and πCOwith that part of the MO located on the oxygen atom, since this is somuch further from the metal centre). As a result of the polarization ofthe π orbitals, the coefficient on carbon is far larger in the antibondingorbital (0.66) than in the bonding (0.37). The ratio of the overlaps Sπ ∗ /Sπis therefore 1.78.
Since the interaction depends on the square of theoverlap, we may conclude that the overlap term favours the π-acceptorcharacter of the carbonyl ligand by a factor of about 3.2. For the metalslocated towards the left of the periodic table, the combination of asmaller energy difference and a much larger overlap ensures that the∗ interactions are far stronger than the d ↔ πd ↔ πCOCO interactions, sothe carbonyl ligand behaves as a double-face π -acceptor. For the metalslocated towards the right, the energy difference favours the π -donorcharacter of the carbonyl ligand, but the overlap favours a π-acceptorbehaviour.
If we examine the extreme case of copper, (Table 3.C1), the∗ interaction) is onlyoverlap factor (about 3.2 in favour of the d ↔ πCOslightly different from the energetic factor (about 2.9 in favour of thed ↔ πCO interaction). This is the only case where the π-donor andπ-acceptor characters are roughly balanced, and this arises because thed orbitals on copper are very low in energy, compared to those on theother transition metals.To conclude, an accurate treatment of the π interactions that involve∗ MOthe carbonyl ligand requires both the occupied πCO and empty πCOto be taken into account (a three-orbital interaction scheme, 3.C1). If onenotes that the interactions involving the antibonding MO are dominant,∗ orbitals on theone can simplify the description, by considering only the πCOcarbonyl ligand.
In this simplified model, three MO are considered forthis ligand: the occupied orbital σC , that characterizes the lone pair oncarbon (Chapter 3, Figure 3.3), giving the ligand a σ -donor character,∗ orbitals, which confer a double-face π-acceptorand the two empty πCOcharacter. ApplicationsA detailed knowledge of the electronic structure of transition metalcomplexes, and in particular of the shape and electronic occupation ofthe d-block orbitals, enables several problems related to their structureand reactivity to be studied. The examples discussed in this chapterillustrate a method for analysing these problems that usually relies ona study of orbital interactions between the ligand and the metal centre,and/or on a correlation diagram that links the orbitals of two differentstructures. The answers that one may hope to obtain from this type ofanalysis are qualitative rather than quantitative.
For example, one canoften determine which of two possible conformations of a complex isthe more stable, and why, without being able to deduce the energy difference between them. Once the electronic factors that favour a particularstructure are established, it may well also be possible to predict the typeof changes that will follow from, for example, a change in the nature ofthe ligands. A qualitative interpretation of the structure and reactivityof complexes is exceedingly interesting for chemists, even if studies ofa different type, that depend on accurate calculations, are necessary toprovide theoretical data that may usefully be compared, quantitatively,with experimental results.4.1. Conformational problemsSeveral conformations may sometimes be envisaged for a particularcomplex, depending on the orientation of a ligand with respect to the restof the molecule.
In such circumstances, the analysis for each conformation of the interactions between the ligand orbitals and those on theremaining fragment containing the metal often enables us to understandwhy one particular conformation is energetically favoured.
We shall consider four examples in this section, using this ‘fragment method’, whichinvolve mono- and bis-ethylene complexes and a molecular hydrogencomplex; several other examples are presented at the end of the chapterin the form of exercises.4.1.1. d8 -[ML4 (η2 -C2 H4 )] complexesConsider a trigonal-bipyramidal (TBP) complex in which an ethylene ligand occupies an equatorial site. The d8 electronic configuration, whichApplicationsleads to an 18-electron complex, is the most common for this class ofcompounds (Chapter 2, § 2.5.2) and the complex [Fe(CO)4 (η2 -C2 H4 )]is a well-known example.Two limiting orientations may be envisaged for the ethylene ligand,depending on whether the carbon–carbon bond is perpendicular to theequatorial plane (4-1a) or in that plane (4-1b).
Both structures have C2vsymmetry and we shall use the planes of symmetry P1 and P2 (4-1) toanalyse the symmetry of the most important orbitals.P1P2P1P2M4-1a (perpendicular)SSASMAASA4-2SS4-1b (coplanar)The orbital structure of each conformation may be analysed as theresult of the interaction between the occupied π orbitals and the emptyπ ∗ orbitals on ethylene on one hand, and the orbitals of a d8 ML4 fragment with a ‘butterfly’ geometry (Chapter 2, § 2.8.3) on the other. Forthis latter, we shall consider the four occupied orbitals of the d block(three nonbonding, one weakly antibonding) and the lowest-energyempty orbital, which is an s–p hybrid orbital pointing towards the emptysite of the TBP.
The shapes of these orbitals are presented below (4-2)in the simplest case, where the four ligands are identical and only haveσ interactions with the metal. To simplify matters, the small contributions from the ligands to the two highest orbitals are not shown. Thesymmetries of the orbitals with respect to the planes P1 and P2 are alsoindicated in 4-2.On passing from the perpendicular structure to the coplanarone (4-1), the orientation of the ML4 fragment does notchange. However, there is a rotation of the ethylene ligandby 90◦ , and therefore also of the associated π and π ∗ orbitals. These are shown in 4-3a and b, and their symmetries with respect to the planes P1 and P2 are given for eachSASS4-3a (perpendicular)MASSS4-3b (coplanar)Conformational problems1If the symmetry labels of the C2v groupare used, the symmetries SS, SA, AS, and AAcorrespond to a1 , b1 , b2 , and a2 , respectively.conformation.1 We note already that the symmetry of the π ∗ orbitalchanges from one conformation to the other, and this will prove to becrucial for the conformational preference for the complex.The π orbital on the ethylene ligand, whose symmetry is SS inboth conformations, can interact with (i) the empty orbital and (ii)the occupied nonbonding orbital of the same symmetry on the ML4fragment (4-2).
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
