Yves Jean - Molecular Orbitals of Transition Metal Complexes (793957), страница 41
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The resemblances betweenthese orbitals are at the heart of the theory of the isolobal analogy,developed by R. Hoffmann, which enables us to build bridges betweenthe electronic structures of inorganic and organic molecules.5.1.1. Fragment orbitals by the valence-bond method3L.
Pauling The Nature of Chemical Bond,3rd edn., Cornell University Press, Ithaca, NY(1960).The orbitals of methane, CH4 , and those of the related fragments CH3 ,CH2 , and CH can be described using the molecular orbital method, aswe have done for all the systems studied so far in this book. But thevalence-bond approach, introduced by L. Pauling,3 can also be used; this isperhaps the simplest way to establish an initial relationship between theelectronic structures of organic and inorganic fragments.In CH4 , the carbon atom is at the centre of a tetrahedron definedby the four hydrogen atoms.
The carbon atom’s four valence orbitals(the 2s orbital and the three 2p orbitals) can be combined to give fourequivalent hybrid orbitals (written sp3 ) that point towards the vertices ofthe tetrahedron. Since carbon has four valence electrons, one electroncan be placed in each hybrid orbital. A 1sH orbital, which is also singlyoccupied, can interact with the sp3 hybrid that points towards it, andin this way we can describe the four equivalent bonds in a tetrahedralarrangement.Using this model, how can we describe the orbital structure of theCH3 , CH2 , and CH fragments that are obtained by homolytic rupture of−H bonds? In the case of CH3 , three of the hybridone, two, or three C−orbitals point towards three hydrogen atoms and interact strongly withthe 1sH orbitals.
But the fourth orbital points in the direction wherethere is no hydrogen atom (5-3a). It is therefore a nonbonding hybridorbital, which contains a single electron (from the homolytic rupture−H bond). In the same way, there are two nonbonding singlyof the C−occupied sp3 hybrid orbitals in CH2 (5-3b), and three in CH (5-3c).HHCCHHCHH5-3a5-3b5-3cThe isolobal analogyWe now turn to an octahedral ML6 complex with a d6 electronicconfiguration, which we shall consider as the starting point for inorganicfragments. This complex obeys the 18-electron rule, just as methaneobeys the octet rule.
To be a little more concrete, though this choice isin no way unique, we shall consider a chromium complex [CrL6 ], withsix neutral L-type ligands (PR 3 , CO, etc.), each of which supplies a pairof electrons to the metal. In this complex, chromium is in the oxidationstate zero, and the electronic configuration is indeed d6 .In the spirit of valence-bond theory, we must construct six hybridorbitals that point towards the vertices of the octahedron.
We musttherefore combine just six of the nine valence orbitals of the metal: itturns out that these are the s orbital, the three p orbitals, and two of thed orbitals (this hybridisation pattern will be written d2 sp3 , see Chapter 2,§ 2.1.2.3). Three d orbitals are therefore not involved in the hybridisation,and they stay unchanged (5-4). The link with MO theory is plain: theseare the three nonbonding orbitals of the octahedral t2g block. In a d6complex, these three non-hybridized orbitals are doubly occupied.pssix d 2sp3 hybridsdthree pure d orbitals5-4LLLLLL5-5With the six metal electrons placed in this way, the hybrid orbitalsare empty. Each of these interacts with the doubly occupied orbital ofthe ligand L towards which it points, thereby forming six bonds in anoctahedral arrangement (5-5).−L bond homolytically, as we did above forWe now break one Cr−methane.
If the ligand is neutral, and of L type (CO, PR 3 , . . .), thishomolytic rupture leaves one of the bonding electrons on the metal,forming the radicals · L+ and [· CrL5 ]− . In the latter (5-6a, right-handside), there are still five d2 sp3 hybrid orbitals that interact strongly withthe orbitals on the five ligands. The sixth orbital points towards thevacant site of the octahedron: it is therefore nonbonding, and it contains−L bond.the electron that came from the homolytic rupture of the Cr−From this viewpoint, the resemblance with CH3 is striking (5-6a): theThe analogy between fragments of octahedral ML6 and of tetrahedral CH4CH3 and [CrL5 ]− fragments are both characterized by the presence of asingly occupied nonbonding orbital which points towards a vacant site,of a tetrahedron for the former, of an octahedron for the latter.LHCrLCHHLL2–Cr5-6bLHL3–LLH5-6aLLHC–L5-6cCrCL4This analogy establishes a link betweenfragments which are neither isostructural norisoelectronic.5T.
A. Albright, J. K. Burdett, M.-H.Whangbo Orbital Interactions in Chemistry,John Wiley & Sons, NY (1985), chapter 21.−L bondIn the same way, the homolytic rupture of a second Cr−2−that leads to the complex [CrL4 ] with a ‘butterfly’ geometry leavestwo singly occupied nonbonding hybrid orbitals on the metal, as in theorganic fragment CH2 (5-6b). And the rupture of a third bond leads tothe fragment [CrL3 ]3− (5-6c), whose electronic structure is similar tothat of the fragment CH with three nonbonding hybrid orbitals eachcontaining one electron.These organic and inorganic fragments, which have the same number of nonbonding hybrid orbitals occupied by the same number ofelectrons, are said to be isolobal analogues.4 The isolobal analogy is represented by a double-headed arrow, underneath which is a symbol thatcan be described either as a small hybrid orbital or as a tear.5CH3[CrL5 ] –CH2[CrL4 ] 2–CH[CrL3 ] 3–The isolobal analogyOur choice of a chromium complex was quite arbitrary.
In each ofthe inorganic fragments above, we may obviously replace chromiumby molybdenum or tungsten, as they have the same number of valenceelectrons. More generally, we may also consider a metal from anothergroup in the periodic table, so long as the number of electrons is notchanged. Thus, all d7 ML5 complexes with a square-based pyramidal(SBP) geometry possess a singly occupied nonbonding hybrid orbital;they are therefore isolobal analogues of the pyramidal fragment CH3 .As examples, we may consider the neutral complexes [Mn(CO)5 ],[Tc(CO)5 ], and [Re(CO)5 ], or the cationic complex [Fe(CO)5 ]+ .In the same way, the complexes [Mn(CO)4 ]− or [Fe(CO)4 ], with a‘butterfly’ geometry, are, like [CrL4 ]2− , complexes with a d8 electronicconfiguration and therefore isolobal analogues of the organic fragmentCH2 .
And pyramidal d9 ML3 complexes ([Cr(CO)3 ]3− , [Mn(CO)3 ]2− ,[Fe(CO)3 ]− , and [Co(CO)3 ], for example) are all isolobal analoguesof CH.6In the isolobal analogy, fragments(organic or inorganic) are considered withgeometries which are not necessarily the moststable. For example, the most stable structurefor [Fe(CO)5 ] is trigonal-bipyramidal (TBP)rather than square-pyramidal.
Similarly, theCH+3 cation is planar.CH3d 7-ML5(SBP)CH2d 8-ML4(butterfly)CHd 9-ML3(pyramidal)The same type of change may also be made on the organic frag+ment, by replacing CH3 with BH−3 or NH3 (still with a pyramidalgeometry). All these fragments are isolobal to d7 ML5 complexes suchas [Mn(CO)5 ]. One can also modify the charge on the organic or inorganic fragment.
Since CH3 is isolobal to [Mn(CO)5 ], CH+3 (pyramidal)to[Fe(CO)],ifallthesecomplexesis isolobal to [Cr(CO)5 ], and CH−536are considered with a SBP geometry. In these three pairs of analogouscompounds, the single nonbonding hybrid orbital contains zero (CH+3and [Cr(CO)5 ]), one (CH3 and [Mn(CO)5 ]) or two electrons (CH−3and [Fe(CO)5 ]).5.1.2. Fragment molecular orbitalsThe analogy between the electronic structures of two isolobal fragmentsis, of course, still present if we consider their molecular orbitals.We start with the organic series CH3 , CH2 , and CH.
Just asthere were one, two, or three nonbonding hybrid orbitals, respectively, in the valence-bond model, the electronic structure in terms ofThe analogy between fragments of octahedral ML6 and of tetrahedral CH4molecular orbitals shows the presence of one, two or three nonbondingor essentially nonbonding MO, respectively (Chapter 1, Figures 1.4–1.6).Moreover, the number of electrons to be placed in these orbitals is thesame as in the nonbonding hybrid orbitals: one for CH3 (5-7a), two forCH2 (5-7b), and three for CH (5-7c). Notice that the electronic occupation of these MO can sometimes be problematical, as the orbital energiesare quite close. For CH2 and CH, we have chosen to place the electronsin the MO so as to create as many pairs as possible.
This electronicoccupation is indeed the ground state of CH, but it is not for methylene, CH2 , for which the ground state is a triplet, with one electron ineach of the two nonbonding orbitals (parallel spins). In fact, this is notimportant when one is using the isolobal analogy. The capacity of afragment to form new bonds depends more on the number of availablenonbonding orbitals and the total number of electrons they contain, thanon the more-or-less arbitrary initial distribution of the electrons in thefragment.Ha1CH35-7aHHHb2HCH25-7bHa1HHHCH5-7cHIn contrast to hybrid orbitals, MO are adapted to molecular symmetry. Several features therefore arise that are new, compared to theprevious description.
First, even though the MO that are considered arealways concentrated in the same region of space as the vacant site(s) ofthe tetrahedron, they do not always point directly towards these sites,except, of course, in the case of CH3 where there is only a single vacantsite. For example, the shapes of the a1 and b2 MO in the CH2 fragmentmean that the two sites of the initial tetrahedron are equivalent for thesetwo MO (5-7b), but neither orbital points along the direction of theThe isolobal analogy−H bonds.
Moreover, in contrast to hybrid orbitals, the MObroken C−do not have the same shape or energy. Still using CH2 as an example, thea1 (a hybrid orbital) and b2 (a pure p orbital) MO have different shapes,and the a1 orbital is lower in energy than the b2 orbital (5-7b). In CH,there is one hybrid orbital with σ symmetry and two pure p orbitalswith π symmetry, the pair of degenerate orbitals (π) being higher inenergy than the σ orbital (5-7c).We shall now consider the inorganic fragments that are the isolobalanalogues of CH3 , CH2 , and CH, that is, the SBP d7 ML5 , ‘butterfly’d8 ML4 and pyramidal d9 ML3 fragments (§ 5.1.1), and compare the MOthat are concentrated around the vacant site(s) following the homolyticrupture of one, two, or three bonds in the initial structure (tetrahedralCH4 or octahedral ML6 ).In the CH3 and d7 ML5 fragments, there is only one orbital ofthis type.
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