Yves Jean - Molecular Orbitals of Transition Metal Complexes (793957), страница 42
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It is totally symmetric (a1 symmetry) in both cases (C3v forCH3 and C4v for ML5 ) (5-8), it points towards the vacant site (of thetetrahedron or of the octahedron) and of course it has axial symmetrywith respect to the main symmetry axis (C3 and C4 , respectively). Thesetwo orbitals are not identical—the first is an sp3 hybrid orbital, the seconda polarized z2 orbital—but they are very similar. Counting electrons,the nonbonding orbital of the methyl radical is singly occupied (5-7a).In a d7 ML5 fragment, such as [Mn(CO)5 ], six electrons occupy thenonbonding orbitals derived from the t2g block of the octahedron, andthe seventh occupies the polarized z2 orbital (Chapter 2, Figure 2.7).
Inboth fragments, the orbital pointing towards the vacant site is thereforesingly occupied.La1HLLLa1LHHd 7-ML 5 (SBP)CH 35-8The set of all these characteristics—the same number of orbitals tobe considered, similar symmetry properties, and the same number ofelectrons—allows us to establish that two fragments are isolobal in theframework of MO theory.The analogy between fragments of octahedral ML6 and of tetrahedral CH4CommentThe hydrogen atom, with its atomic orbital 1sH singly occupied, is also anisolobal analogue of the d7 ML5 fragment.7This orbital (py ) has b2 symmetry (seethe character table for the C2v point group,Chapter 6, Table 6.5).
If the x- and y-axes areinterchanged (the z-axis stays as the C2 axis),this orbital becomes px , which has b1symmetry (as was noted in Chapter 1,Figure 1.5). The choice is arbitrary. Theimportant point is that this orbital isantisymmetric with respect to the molecularplane. This comment also applies to thepolarized d orbital on the metallic fragment,whose symmetry is either b1 or b2 , dependingon the orientation chosen for the x- and y-axes.The CH2 and d8 ML4 (‘butterfly’) fragments, both with C2 v symmetry, provide a second illustration. Now there are two orbitals toconsider for each fragment. For CH2 , these are the two orbitals shown in5-7b: the first, totally symmetric (a1 ), has of course axial symmetry withrespect to the C2 axis; the second (a pure p orbital with b2 symmetry)7is antisymmetric with respect to the molecular plane. For the metallicfragment, whose orbital structure was established in Chapter 2 (Figure 2.15), there is a polarized d orbital, with b2 symmetry, and the s–phybrid orbital on the metal, with a1 symmetry.
The orbitals involvedin the two fragments have the same symmetries (5-9). Moreover, thesame number of electrons must be placed in these orbitals: two in CH2(5-7b) and also in a d8 ML4 fragment, since there are six electrons in thethree nonbonding d orbitals derived from the t2g block of the octahedron(Chapter 2, Figure 2.15). Notice, however, that the energetic order of theorbitals is inverted (5-9), so that with the chosen electronic occupation(the lowest-energy MO doubly occupied) the electronic configuration isnot the same for the two fragments (a12 in CH2 , b22 in d8 ML4 ).
As long asone is mainly concerned by the fragments’ capacity to form new bonds,this difference is of no real consequence (see § 5.3.1).xzLya1LHHHb2b2a1LLLLLLHd 8-ML4 (‘butterfly’)CH25-9For the CH and pyramidal d9 ML3 fragments, three orbitals mustbe considered. For CH, these are the orbitals shown in 5-7c: one orbitalwith σ symmetry and two degenerate orbitals with π symmetry, withthree electrons in total. In a d9 ML3 complex, such as Co(CO)3 , six electrons occupy the three nonbonding orbitals derived from the t2g blockThe isolobal analogyof the octahedron (Chapter 2, Figure 2.13).
At slightly higher energy, wefind the three orbitals that are concentrated in the region of the vacantsites of the octahedron — a pair of degenerate orbitals (e symmetry inthe C3v point group) and one totally symmetric orbital (a1 )—in whichwe must place the three remaining electrons. If we compare the degenerate MO in the two fragments, we notice that in each case one orbital isantisymmetric with respect to the plane of the paper (py and ey ) but theother is symmetric with respect to this plane (px and ex ). Even thoughthe symmetry labels in the C∞v and C3v point groups are different, thesimilarity between the orbitals in the two fragments is plain: the σorbital in CH corresponds to the a1 orbital in the metallic fragment, andthe degenerate π pair to the degenerate e pair (5-10).
It is true that theenergetic ordering of the degenerate and the totally symmetric orbitalsis inverted, but this detail has no more importance here than in thepreceding example concerning the CH2 and d8 ML4 fragments.xzLLya1HHpyHpx LeLLLLLLCHexeyd 9-ML3 (pyramidal)5-105.2. Other analogous fragmentsAn octahedral d6 ML6 complex, such as [Cr(CO)6 ], is not the only initialstructure that can be used to construct inorganic fragments which areanalogous to the organic fragments CH3 , CH2 , and CH (5-11a and b).Two other structures are often used as starting points.The cyclopentadienyl ligand (Cp) is very widespread in organometallic chemistry. When it is coordinated in the η5 mode, the most commonsituation, it behaves as an L2 X ligand (Chapter 1, § 1.1.1.3).
[CpML3 ]complexes (L = CO, PR 3 , . . .) are therefore pseudo-octahedral complexes of the ML5 X type, which have 18 electrons when their electronicconfiguration is d6 . A d6 [CpML3 ] complex may therefore be used asa new initial structure, very similar to that used previously. Since thepresence of the cyclopentadienyl ligand oxidizes the metal by one unit,a metal with seven valence electrons (M = Mn, Tc, Re) must be usedto obtain a neutral complex. The complex [CpMn(CO)3 ] is therefore aApplicationspossible starting point. Subsequently, the fragments d7 [CpMn(CO)2 ]− ,d8 [CpMn(CO)]2− , and d9 [CpMn]3− are obtained by homolytic rupture−CO bonds.
Neutral metallic fragments can beof one, two, or three Mn−obtained, if the metal is taken from one group further to the right in theperiodic table each time. Starting from the complex d6 [CpMn(CO)3 ],we can thus deduce that the fragments d7 [CpFe(CO)2 ], d8 [CpCo(CO)],and d9 [CpNi] are isolobal to CH3 , CH2 , and CH, respectively (5-11aand c).LHHHLCHLLLLCLFeLLFeLCoLNiLNiLLCoCCoLLLLLLLLFeLLHLLMnCLLLHHMnLLHHHLLCrCuL5-11a5-11b5-11c5-11dAnother starting point is sometimes used, taking a complex whose‘normal’ number of electrons is 16 instead of 18. The most commonexample involves a square-planar complex with a d8 electronic configuration (Chapter 2, § 2.2).
Starting, for example, from [Fe(CO)4 ], and usingthe same method as above, one can show that the fragments [Co(CO)3 ],with a ‘T-shaped’ geometry, bent [Ni(CO)2 ] and [Cu(CO)] are isolobalanalogues of CH3 , CH2 , and CH, respectively (5-11a and d).5.3. Applications5.3.1. Metal–metal bondsSince the CH3 and d7 ML5 fragments have analogous electronic structures, their chemical behaviour is similar in some respects. For example,The isolobal analogydimerization to form ethane (C2 H6 ) is an important property of themethyl radical, as is its initiation of radical-type chain reactions. Similarly, species such as [Mn(CO)5 ] or [Co(CN)5 ]3− , both of which ared7 ML5 systems, have a very rich radical-type chemistry; in particular,they dimerize to form [Mn2 (CO)10 ] and [Co2 (CN)10 ]6− , respectively, (despite the presence, in the latter, of three negative chargeson each monomer!).
These bimetallic complexes are therefore isolobalanalogues of the ethane molecule.C 2H 6[Mn2(CO)10][Mn(CO)5CH3]The main orbital interaction that occurs during the dimerization ofthe fragments (CH3 , [Mn(CO)5 ] or [Co(CN)5 ]3− ) involves in all casesthe singly occupied nonbonding orbital on each monomer. The interaction schemes for the orbitals on the [Mn(CO)5 ] (or [Co(CN)5 ]3− ) andCH3 fragments produce a doubly occupied bonding MO in the dimer,with axial symmetry around the internuclear axis, and the corresponding antibonding orbital which is empty (5-12a and b).
There is thereforea single σ bond between the two metallic centres in the [Mn2 (CO)10 ] or[Co2 (CN)10 ]6− dimers, which implies nearly free rotation around the−C single bond in ethane.metal–metal bond, as there is around the C−The analogy can be extended to mixed inorganic–organic dimers such as[Mn(CO)5 CH3 ], formed by the combination of the metallic fragment[Mn(CO)5 ] and its organic analogue CH3 . In this last example, there isonce again a single σ bond between the metal and the carbon, resulting from the combination of the singly occupied orbitals on the twofragments.CH3CH3C2 H 65-12a[Mn(CO)5 ][Mn(CO) 5 ][Mn 2 (CO)10 ]5-12bAnother example involves the dimerization of the CH2 and ‘butterfly’ d8 -ML4 fragments.
The dimer of CH2 is just simply ethylene,a planar molecule characterized by a double bond between the twocarbon atoms (a σ bond and a π bond). The isolobal analogy linkingthe CH2 and ‘butterfly’ [Fe(CO)4 ] fragments (5-9) shows us that theApplicationsbimetallic complex [Fe2 (CO)8 ], in the conformation shown in 5-13, isan isolobal analogue of ethylene, which implies the existence of a doublebond between the two metallic centres.HCOHCOCOOCCFeCFeCOOCHHCOC 2 H4CO[Fe 2(CO) 8]5-13The similarity in the electronic structures of the two molecules isconfirmed by the interaction diagrams shown in 5-14a for C2 H4 and5-14b for [Fe2 (CO)8 ].* CC*CCHHb2a1b2a1HHHCCH5-14aHH CC*MM*MMLLLa1LLLLLb2a1 MMb2LLLL5-14bLLLLMMThe isolobal analogyIn ethylene, the interaction between the fragment orbitals leads tothe formation of two bonding (σCC and πCC ) and two antibonding∗ and π ∗ ). In the ground electronic state, the former areMO (σCCCCdoubly occupied and characterize the σ and π bonds (5-14a).
In the[Fe2 (CO)8 ] dimer, there are also two bonding MO, one of σ type withaxial symmetry around the internuclear axis, the other of π type witha nodal plane in the plane of the paper, and the two correspondingantibonding MO (5-14b). There are still, in total, four electrons to beplaced in these MO, so in the ground electronic state the two bondingMO (σMM and πMM ) are doubly occupied, just as in ethylene.We noted above that the different orbital occupations in the twoisolated fragments (a12 for CH2 , b22 for [Fe(CO)4 ], 5-9) has no influenceon their capacity to form new bonds and is therefore of little importancefor the isolobal analogy.
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