M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765), страница 56
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The Oh character table and the representation of the sixhybrid orbitals are given in Table 7-4. The representation reduces to⌫ Oh = A1g + E g + T1uInspection of the Oh character table shows that the only possiblecombination from the available (n–1)d, ns, and np orbitals of themetal is:sp x , p y , pzdx 2 −y 2 , dz 2a1gt1uegThese six orbitals will participate in the hybrid, and the remaining t2gsymmetry orbitals (dxz , dyz , and dxy ) of the metal will be nonbonding.Six ligands approach the six hybrid orbitals of the metal in formingan octahedral complex. These ligands are supposed to be donors, or, inother words, Lewis bases with even numbers of electrons.
Six bonding orbitals and six antibonding ∗ orbitals are formed, with the ligandelectron pairs occupying the bonding orbitals as seen in Figure 7-27.As a consequence of the strong interaction, all six hybrid orbitals ofthe metal are removed from the frontier orbital region, and only theunchanged metal t2g orbitals remain there.We can also deduce the changes that will occur in the five-, four-,and three–ligand fragments as compared to the ideal six-ligand case358Table 7-4. The Oh Character Table and the Representation of the Hybrid Orbitals of the Transition Metal in an ML6 Complexi6S4OhE8C36C26C43C28S63h6d(= C42 )A1gA2gEg11111–11–111111–111111–1x2 + y2 + z22–100220–120(2z2 –x2 –y2 ,x2 –y2 )T1g3300–111–1–1–1331–100–1–1–1111211–11–101–10112–1–1–2–110–1–11–1–1–2–110T2u3300–111–1–1–1–3–3–1100111–1⌫h6002200042T2gA1uA2uEuT1u(Rx , Ry , Rz )(xz, yz, xy)(x, y, z)7 Chemical Reactions7.5.
Isolobal Analogy359Figure 7-27. Molecular orbital construction in an ideal octahedral complex formation. Reproduced by permission [109], copyright (1982) The Nobel Foundation.with the help of Figure 7-27. The situation is illustrated in Figure 7-28.With five ligands, only five of the six metal hybrid orbitals willinteract; the sixth orbital, the one pointing to where no ligand is, willbe unchanged. Consequently, this orbital will remain in the frontierorbital region, together with the t2g orbitals.
With four ligands, two ofthe six hybrid orbitals remain unchanged and with three ligands, three.Always, those metal hybrid orbitals, which point towards the missingligands in the octahedral site, remain unchanged.Figure 7-28. Molecular orbitals in different MLn transition metal-ligand fragments.Adapted with permission [110], copyright (1982) The Nobel Foundation.3607 Chemical ReactionsNow we shall seek analogies between transition metal complexesand simple, well-studied organic molecules or fragments.
In principle,any hydrocarbon can be constructed from methyl groups (CH3 ),methylenes (CH2 ), methynes (CH), and quaternary carbon atoms.They can be imagined as being derived from the methane moleculeitself which has a tetrahedral structure:The essence of the “isolobal analogy” concept is to establish similarities between these simple organic fragments and the transitionmetal ligand fragments, and then to build up the organometalliccompounds. As defined by Hoffmann, “two fragments are calledisolobal, if the number, symmetry properties, approximate energy andshape of the frontier orbitals and the number of electrons in themare similar—not identical, but similar” [111].
However the moleculesinvolved are not and need not be either isoelectronic or isostructural.The first analogy considered here is a d7 -metal-ligand fragment, forexample, Mn(CO)5 and the methyl radical, CH3 :Though the two fragments belong to different point groups, C4v andC3v , respectively, the orbitals that contain unpaired electron belong7.5. Isolobal Analogy361to the totally symmetric representation in both cases.
Since the threeoccupied t2g orbitals of the ML5 fragment are comparatively lowlying, the frontier orbital pictures of the two fragments should besimilar. If this is so, then they are expected to show some similarity in their chemical behavior, notably in reactions. Indeed, bothof them dimerize, and even the organic and inorganic fragments cancodimerize, giving (CO)5 MnCH3 :Following this analogy the four-ligand d8 -ML4 fragments (e.g.,Fe(CO)4 ) are expected to be comparable with the methylene radical,CH2 :Both fragments belong to the C2v point group, and the representation of the two hybrid orbitals with the unpaired electrons is:C2vEC2⌫20023627 Chemical ReactionsThis reduces to a1 + b2 . Although the energy ordering differs in thetwo fragments, this fact is not important, since both will participatein bonding when they interact with another ligand, and their originalordering will thereby change anyway.Consider the possible dimerization process: two methylene radicals give ethylene, which is a known reaction.
Similarly the mixedproduct, (CO)4 FeCH2 , or at least its derivatives, can be prepared. TheFe2 (CO)8 dimer, however, is unstable; and has only been observed ina matrix; it was prepared by the photolysis of Fe2 (CO)9 at low temperature [112, 113]. Spectroscopic studies [114] as well as computations[115] suggest that there are two isomers of this species, one with twoCO bridges and another with an Fe–Fe bond. The latter, with D2hsymmetry, would be the isolobal analogue of ethylene. However, it isnot clear yet what the symmetry of this species is.
All this illustratesthat the isolobal analogy suggests only the possible consequences ofthe similarity in the electronic structure of two fragments. It saysnothing, however, about the thermodynamic and kinetic stability ofany of the possible reaction products.Although Fe2 (CO)8 is unstable, it can be stabilized by complexation.
The molecule in Figure 7-29a consists of two Fe2 (CO)8 unitsconnected through a tin atom [116]. Using the inorganic/organicanalogy, this molecule can be compared to spiropentane (Figure7-29b).An example of a d 9 -ML3 fragment is Co(CO)3 . This is isolobal toa methyne radical, CH:7.5. Isolobal Analogy363(a)(b)Figure 7-29.
(a) The molecular geometry of Sn[Fe2 (CO)8 ]2 . Reproduced bypermission [117], copyright (1982) The Nobel Foundation; (b) The organic analog:spiropentane.Both have C3v symmetry. The representation of the three hybridorbitals with an unpaired electron is:C4vE2C23σv⌫301It reduces to a1 + e. Again, the ordering is different, but the similarity between their electronic structure is obvious. A series ofmolecules and their similarities are illustrated in Figure 7-30. Thefirst molecule is tetrahedrane and the last one is a cluster with metalmetal bonds which can be considered as being the inorganic analog oftetrahedrane.Only a few examples have been given to illustrate the isolobalanalogy.
Hoffmann and his co-workers have extended this conceptto other metal–ligand fragment compositions with various d orbitalparticipations. Some of these analogies are summarized in Table 7-5.Hoffmann’s Nobel lecture [119] contained several of them, and manymore can be found in the references given therein and in later works.Just to mention one example: recent computational studies, basedon the isolobal analogy, suggest that by substituting CH groups bytheir isolobal large-metal fragments (such as Os(PH3 )3 ), the activation3647 Chemical ReactionsFigure 7-30.
Molecular geometries from tetrahedrane to its inorganic analog.Adapted with permission [118], copyright (1982) The Nobel Foundation.Table 7-5. Isolobal AnalogiesTransition metal coordination numberOrganicfragmentCH3CH2CH9876d1 –ML8d2 –ML7d3 –ML6d3 –ML7d4 –ML6d5 –ML5d5 –ML6d6 –ML5d7 –ML4d7 –ML5d8 –ML4d9 –ML35d9 –ML4d10 –ML3barrier of a reaction may be reduced and thus potentially importantnew molecules could be prepared [120].References1. A.
L. Mackay, A Dictionary of Scientific Quotations, Adam Hilger, Bristol,1991, p. 57/85.2. E. Wigner, E. E. Witmer, “Über die Struktur der zweiatomigen Molekelspektren nach der Quantenmechanik.” Z. Phys. 1928, 51, 859–886.3. A. Dick, Emmy Noether: 1882–1935, Birkhauser, Boston, 1989.4. I. Hargittai, M. Hargittai, In Our Own Image: Personal Symmetry inDiscovery, Kluwer-Plenum, 2000, pp. 200–201.5. R. B.
Woodward, R. Hoffmann, The Conservation of Orbital Symmetry,Verlag Chemie, Weinheim, 1970.References3656. R. B. Woodward, R. Hoffmann, “The Conservation of Orbital Symmetry.”Angew. Chem. Int. Ed. Engl. 1969, 8, 781–853.7. K. Fukui, Theory of Orientation and Stereoselection, Springer-Verlag, Berlin,1975; Top. Curr. Chem. 1970, 15, 1.8. K. Fukui, in Molecular Orbitals in Chemistry, Physics and Biology, P.
O.Löwdin and B. Pullmann, eds., Academic Press, New York, 1964.9. R. F. W. Bader, “Vibrationally Induced Perturbations in Molecular ElectronDistributions.” Can. J. Chem. 1962, 40, 1164–1175.10. R. F. W. Bader, P. L. A. Popelier, T. A. Keith, “Theoretical Definition of aFunctional Group and the Molecular Orbital Paradigm.” Angew. Chem. Int.Ed. Engl.
1994, 33, 620–631.11. R. G. Pearson, Symmetry Rules for Chemical Reactions, Orbital Topologyand Elementary Processes, Wiley-Interscience, New York, 1976; R. G.Pearson, “Symmetry Rules for Chemical Reactions.” In I. Hargittai, ed.,Symmetry: Unifying Human Understanding, Pergamon Press, Oxford, 1986,pp. 229–236.12. E. A. Halevi, Orbital Symmetry and Reaction Mechanisms: The OCAMS View,Springer-Verlag, Berlin, 1992.13. E. A. Halevi, “Orbital Correspondence Analysis in Maximum Symmetry.”Helv. Chim. Acta 1975, 58, 2136–2151.14.
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