Orbital Interaction Theory of Organic Chemistry

Figure 13.2. Occupied valence orbital energies of the ®rst-row (- - - - - -) and second-row (-- -- -- --) transition metals and adjacent elements (circles): black, d orbitals; gray, s orbitals; white, p orbitals. The e¨ect on d orbital energies of three electronic con®gurations of the metals is shown. The vertical scale on the left is in hartrees. The scale at right is in units of jbj relative to aC.

VALENCE ORBITALS OF REACTIVE METAL COMPLEXES

As the above discussion shows, we will adopt the simple view that an octahedrally hexacoordinated metal complex, ML6, is coordinatively saturated, just as is a tetracoordinated carbon atom. Metal complexes with fewer than six ligands will be treated on the same footing as organic reactive intermediates. The distinction we are making is that direct involvement of the metal center in a reactive process (bond making or breaking) is easy only at coordinatively unsaturated metal centers, just as it is at carbon. Of course, just as at saturated carbon, ligand substitution by association or dissociation can take place, and the presence of the center (C or M) with its array of substituents can in¯uence

180 ORGANOMETALLIC COMPOUNDS

Figure 13.3. Four-orbital interaction forms a s bond to the metal (mostly ligand) and removes one of the metal orbitals from the valence set. The remaining metal orbitals are shown.

the chemistry of the ``ligands'' themselves in hexacoordinated metal complexes. We begin in the same way as in the case of main group fragments, by building up the library of fragment valence orbitals, beginning with a fragment in which the metal is bound to three groups, ML3, and working our way up to pentacoordination, ML5. A discussion of monoand dicoordinated complexes may be found in standard sources [58, 275, 278]. We emphasize here, as earlier, that bonding means s bonding only. If, after we have accommodated all ligands by s bonds, there are valence orbitals and electrons left over, multiple bonding can be considered. The bare (0-coordinated) metal has nine valence orbitals, in ascending order, ®ve d 's, one s, and three p's. Each s bond formed removes one of the metal's valence orbitals. Since a potential ligand always has the opportunity (by symmetry) to interact with one of the d orbitals, the s orbital, and one of the p orbitals, a complex mixing pattern arises from the hybridization of the three. By virtue of relative electronegativities, the usual situation (see below) is that all of the metal orbitals lie to higher energy than the ligand, even if it is a hydrogen or carbon atom. The consequences of this four-orbital interaction are shown in Figure 13.3. As in the case of twoand three-orbital interactions, the orbitals of the four-orbital interaction move apart. The lowest orbital is the s bond to the ligand. If the ligand is highly electronegative, this orbital is highly polarized toward the ligand. Since the ligand also introduced an orbital to the set, this does not count. The highest, most antibonding orbital may be considered to be the s orbital. It is metal centered and counts as the one removed from the valence set. The middle two orbitals, both spd hybrids, are left in the valence set. Both are mostly nonbonding. The upper is chie¯y the pz orbital. The lower is chie¯y the dz2 orbital polarized away from the coordinated atom. The same principle, namely that the middle two orbitals are essentially metal centered nonbonding and polarized away from the s- bonded substituent, applies to metal centers with multiple s bonds.

Intrinsic Interaction Matrix Element, hAB , Between d Orbitals and Orbitals of C and H. The quantities D, the separation of the weakly antibonding d orbital from the nonbonded d orbitals (Figure 13.3), and DeL, the amount of lowering of the bonding orbital, will be of special interest. Here, D is not directly analogous to DeU of earlier orbital interaction diagrams because of the mixing with higher energy orbitals, but its magnitude is governed by the same principles, namely the energy separation of the

ligand orbital from the metal d orbitals and the intrinsic interaction matrix element, which is approximately proportional to the overlap of the two orbitals and the average of their energies [e.g., equation (3.44)]. Judging from Figure 13.2 and parametrizations of extended HuÈckel theory [279], the energies of the d orbitals are similar to the 2p orbital energies of C, N, and O. Hence the principal factor governing the magnitude of hAB, and therefore DeL and D, will be the overlap. Overlap of orbitals decreases with increasing numbers of nodes and mismatch of sizes. For both reasons, both s- and p- type overlap between d orbitals and the orbitals of the ®rst-row elements will be smaller than equivalent overlaps between the ®rst-row elements themselves. As a consequence, one expects smaller DeL and D and weaker bond dissociation energies.

In the octahedral environment, D will be related to DO, the spectroscopically derived octahedral crystal ®eld-splitting parameter [280]. One can gain some insight into the variation of hAB as a function of ligand type and metal by noting how these factors a¨ect DO. Ligands may be ranked according to their e¨ect on DO. Thus DO increases in the series: Iÿ < Brÿ < Clÿ < Fÿ < OHÿ < H2O < NH3 < en < PPh3 < CNÿ < CO [280]. The halogens have the weakest e¨ect on DO while CO has the greatest e¨ect, probably because the ``nonbonded'' orbitals are lowered by in-phase interaction with the pCO. Another e¨ect of ligands, which is also attributed to overlap, namely the trans e¨ect, may be a measure of D (and of hAB) (Figure 13.3). In square planar complexes, the trans e¨ect of a s-bonding ligand, L1, measures the rate enhancement for ligand substitution of another ligand, L2, when L1 is in the trans position in the complex. Presumably, L1 raises the energy of n dz2 (Figure 13.3), thereby decreasing its bonding to L2. Sigmabonding ligands, in order of increasing trans e¨ect in square planar complexes of Pt(II), are OHÿ < NH3 < Clÿ < Brÿ < CNÿ, CO, CHÿ3 < Iÿ < PR3 < Hÿ [280]. We note particularly that Hÿ has the largest trans e¨ect and that CHÿ3 (and other alkyl groups) is also high on the list. Comparing the DO series with the trans e¨ect series reveals that they di¨er principally in the softness or nucleophilicity property which reverses the order of the halogens and of amines and phosphines.

Effect of Formal Oxidation State. Since the valence orbitals are largely localized to the metal, their energies will be sensitive to the net charge of the metal, of which the formal oxidation number will be a good guide provided the ligands are poor s donors, like the halogens or oxygen. It is suggested here that for the purpose of assigning nonbonding d orbital energies, a metal with formal charge ‡m be treated as equivalent to the neutral metal with m higher atomic number; that is, the d orbital energies of Pd(II) will be those of Cd(0) in Figure 13.2. Thus the nonbonding d orbitals drop sharply with increasing oxidation. However, the antibonding hybrid d orbitals drop less since D increases (see below). A good s donor, like H or alkyl, will have a maximum e¨ect in supporting the antibonding d orbitals, especially if it is in the trans position.

In addition to the e¨ects of ligands, DO (and D) depends on the type of metal and its oxidation state [280]:

DO increases with increasing formal oxidation state

DO increases down a group

The dependence on formal oxidation state can be attributed to electrostatic lowering of the metal d orbitals thereby narrowing the gap with ligand orbitals. The e¨ect of principal quantum number may be due to better overlap of the larger 4d and 5d orbitals with ligand orbitals, compared to the more compact 3d orbitals. Thus DO increases in the

182 ORGANOMETALLIC COMPOUNDS

series Mn2‡ < Ni2‡ < Co2‡ < Fe2‡ < V2‡ < Fe3‡ < Co3‡ < Mn4‡ < Mo3‡ < Rh3‡ < Ru3‡ < Pd4‡ < Ir3‡ < Pt2‡ [280]. We will return to these points below as we discuss the valence orbitals of metal fragments which are 3-, 4-, and 5-coordinated.

SIX VALENCE ORBITALS OF TRICOORDINATED METAL

Three distinct geometric con®gurations need to be considered for tricoordination. Only two, a trigonal planar structure and a pyramidal con®guration of C3v symmetry, were available to main group tricoordinated systems. The addition of d orbitals into the valence shell introduces the third possibility, a T-shaped structure with local C2v symmetry. The six valence orbitals of each of the structures in their individual standard orientations are shown in Figure 13.4. In the case of the T-structure, the most convenient orientation has the fragment in the xy plane with the symmetry axis aligned with the x axis. The valence orbitals, in ascending order, are dxz ˆ b1, dyz ˆ a2, dxy ˆ b2, nz2 ˆ a1, nx2 ÿ y2 ˆ a1, and pz ˆ b1.

The standard orientation of the trigonal planar structure has the molecule in the xy plane and the C3 axis coinciding with the z axis. It is derived from the T-structure by movement of the ligands away from the y axis. The resulting valence orbitals and correspondence of the energy levels is shown in Figure 13.4. Two of the T-shaped fragment orbitals are signi®cantly a¨ected by the change in geometry, namely the dxy ˆ b2 orbital, which su¨ers a strongly repulsive interaction and rises in energy, and the nx2 ÿ y2 ˆ a1 orbital, which obtains a relief in repulsion and moves to lower energy. The result is that the quasidegenerate set of three lowest orbitals is broken apart, leaving only two orbitals at low energy. The valence orbitals, in ascending order, are …dxz; dyz† ˆ e00, nz2 ˆ a20 ,

…nxy; nx2 ÿ y2† ˆ e0, and pz ˆ a200.

Movement of all three ligands of the D3h structure symmetrically out of the plane leads to the pyramidal C3v structure. All valence orbitals are a¨ected by the geometry change. The …dxz; dyz† ˆ e00 set can interact with the ligands and are raised in energy. Repulsion is reduced signi®cantly in nz2 ˆ a10 and somewhat in the …nxy; nx2 ÿ y2† ˆ e0 set, and these move to lower energy in a corresponding fashion. The npz ˆ a200 orbital rises. In ascending order, the six valence orbitals of the trigonal pyramidal structure are

occur only in the case of the early transition metals, which have the highest energy valence orbitals. By the same token, late transition metals can only support higher valence occupancies if they are in high formal oxidation states since the high central positive charge lowers the energy of the higher valence orbitals.

FIVE VALENCE ORBITALS OF TETRACOORDINATED METAL

Three distinct structural types are available for a tetracoordinated fragment: a square planar structure of D4h symmetry, a nonplanar square pyramid with C4v symmetry, a nonplanar structure with C2v symmetry (which would result from the removal of two cis ligands from an octahedral ML6), and the tetrahedral structure of symmetry Td . These are shown in Figure 13.5 in the standard orientation. The orbitals of the D4h structure

Figure 13.4. Valence orbitals of a tricoordinated metal; D (longer gray bracket) is analogous to DeU. The splitting of the upper levels (shorter gray bracket) is a measure of the trans e¨ect.

are readily derived from symmetry considerations [58]. In ascending order, they are

…dxz; dyz† ˆ eg, dxy ˆ b2g, n dz2 ˆ a1g, and pz ˆ b1g.

Movement of all four ligands symmetrically to one side of the plane yields the square

orbitals and the latter by relief of repulsion with the ligand orbitals. In ascending order, the ®ve valence orbitals of the C4v structure are dxy ˆ a2, …nxz; nyz† ˆ e; nz2 ˆ a1, and

npz ˆ a1.

Movement of the two opposite ligands of the D4h structure out of the xy plane yields the tetracoordinated C2v fragment. The b1g and a1g orbitals are again stabilized and one of the members of the eg set is destabilized. The position of the orbitals shown is that

184 ORGANOMETALLIC COMPOUNDS

Figure 13.5. Valence orbitals of a tetracoordinated metal; D (long gray bracket) is analogous to

DeU.

expected if the out-of-plane ligand bond angle is reduced to 90 . The orbitals in order of increasing energy are dxy ˆ a2, dyz ˆ b1, nz2 ˆ a1, nxz ˆ b2, and npz ˆ a1.

The C2v structure may be transformed into a tetrahedral structure by movement of the remaining collinear ligands out of the xy plane in the opposite direction. When the structure has Td symmetry or close to it, the bonding pattern shown in Figure 13.5 is obtained. From lower energy to higher, the valence orbitals are …dz2; dx2 ÿ y2† ˆ e and …dxy; dxz; dyz† ˆ t2. Thus the dyz ˆ b1 orbital of the C2v structure is severely destabilized upon deformation toward Td . A tetracoordinated transition metal is also highly unsaturated. Stable fragments occur as follows: 18e …s2d 6†, structure Td , e.g., Ni(CO)4; 16e …s2d 6†, structure C4v or C2v, e.g., Fe(CO)4; 14e …s2d 4†, structure C4v, D4h, or C2v, e.g., 12e …s2d 2†, structure Td , e.g., FeCl4.

186 ORGANOMETALLIC COMPOUNDS

pair, …dxz; dyz† ˆ e, is destabilized and moves to higher energy, approaching the descending nz2 ˆ a1 orbital as the out-of-plane deformation increases.

The natural orientation of the D3h trigonal bipyramidal system requires a reorientation of the coordinate frame relative to that used for the C4v structures. The four valence orbitals resolve themselves into two degenerate groups (in ascending order) …dxz; dyz† ˆ e00 and …dxy; dx2 ÿ y2† ˆ e0. The correspondence to the orbitals of the C4v structures is shown in Figure 13.6.

TRANSITION METALS AND CÐH OR HÐH SIGMA BONDS

Nonpolar s bonds such as CÐH and HÐH are chemically inert to acids and bases under normal circumstances. The primary reason is that the s bonding orbital is very low in energy and not polarized. Both aspects reduce its ability as a s or p donor of electrons. As we have seen in Chapter 4, such s bonds are directly susceptible to attack by only the strongest Lewis acids, such as carbocations. By the same token, the s orbital is very high in energy and also not polarized. Both aspects reduce its ability to act as an electron acceptor. An additional factor which we did not dwell upon in the earlier discussions is that both ends of the CÐH or HÐH bond are of intermediate electronegativity and so are unable to support a substantial positive or negative charge. Donation of electrons in a two-electron, two-orbital interaction in which the CÐC, CÐH, or HÐH bond acts as a donor or as an acceptor necessarily is accompanied by charge transfer and the accumulation of charge on C or H. Only if it were possible to donate and accept at the same time could the build-up of substantial charge be avoided. This is normally not possible in main group chemistry because there are no stable molecular species which simultaneously are at least moderately strong donors and acceptors. An additional requirement is that the system must be a strong acceptor in the sigma sense because the s bond is a nodeless donor. To be able to react with a s bond, the agent must be a p donor (because maximum overlap with the s acceptor orbital requires accommodation of the node across the middle of the bond). Transition metals can satisfy the last requirement because an occupied dxz or dyz orbital has the nodal characteristics to be a p donor if the s bond approaches from the z direction in an edgewise …h2† fashion. At the same time, the metal may also satisfy the requirement of being an e¨ective nodeless s acceptor because advantageous mixing of the s, pz, and dz2 orbitals can take place.

The last requirement to be met is that the metal d orbitals are close enough in energy to the CÐH and HÐH orbitals for e¨ective interaction to take place. This requirement is readily met across most of the ®rst and second transition row series. The energies of the d orbitals sweep a broad range as the atomic number and formal oxidation state are changed, and the size, shape, and energy may be ®nely tuned by the appropriate choice of ligands.

MORE ABOUT C LIGANDS IN TRANSITION METAL COMPLEXES

A tricoordinated carbon center acting as a ligand to a transition metal is a powerful s donor because of the high energy of its valence …spn† orbital, and it is not a p acceptor.

A dicoordinated carbon atom bonded to a metal may vary greatly in its p acceptor ability. If the atom is formally bonded by a p bond to another atom, the p acceptor ability ranges from poor to moderate depending upon whether the other atom is C (i.e.,

vinyl), N (i.e., iminyl), or O (i.e., carbonyl). If the dicoordinated carbon atom is not involved in formal p bonding, then it is considered to be a carbene center and its p acceptor ability ranges from moderate to high, depending upon whether its two substituents are themselves good p donors (N or O) or not (alkyl or H).

Similar considerations apply to a monocoordinated carbon atom which functions as a ligand to a transition metal. The carbon atom may have two formal p bonds to its attached atom, as in acetylides, cyanide anion, or carbon monoxide. Such compounds coordinate in a linear fashion and can accept p electrons equally in the two orthogonal planes. The p acceptor ability ranges from poor to moderate. The electrically neutral carbonyl group may formally donate electrons to one metal and accept electrons from another and therefore bridge the two. If the two metals are similar, the CO molecule acting in this fashion is functionally equivalent to a ketone carbonyl group. Acetylides and cyanide cannot function in the same way because neither the carbon atom nor the nitrogen atom are electronegative enough to support the extra nonbonded electron pair and the negative charge. Substitution by an alkyl group on N or a second alkyl or hydrogen on C permits the carbon atoms of these groups to coordinate to two metals as well. The groups are vinylidene and isonitrile, respectively.

CHELATING LIGANDS

Chelating ligands such as en (ethylenediamine), acac (acetylacetonate), and alkyl separated phoshines can be regarded as the equivalent number of L: and X: groups. Thus en ˆ L2 and acac ˆ LX. The length of the chelating bridge may impose a geometry restriction, however, forcing an interligand bond angle to be less than 90 , for instance.

ORGANIC p-BONDED MOLECULES AS LIGANDS

A simple alkene is just an L:-type ligand, donating 2e in a s fashion from one face of the p bond. It is also a modest p acceptor through its p orbital. Unsaturated molecules with multiple but isolated p bonds, like 1,5-cyclooctadiene, behave as chelating ligands. Conjugated p systems of four or six electrons can donate any number of pairs of electrons up to the maximum. Thus benzene may act as L, L2, or L3 and cyclopentadienyl as X, LX, or L2X. If acting as multiple donors, then they necessarily impose geometry restrictions consistent with the dimensions of their s framework and in this sense behave as chelating ligands. To a much greater extent than is true for simple chelating ligands, however, multiple conjugated p donor ligands can change their donating characteristics in response to the electronic demand of the metal. For instance, a cyclopentadienyl complex in which the cyclopentadiene is acting as a four-electron donor (hapto-3, h3) can readily use the cyclopentadienyl ring to occupy a coordination site vacated by the departure of another ligand. The cyclopentadienyl then assumes the role of a six-electron donor (hapto-5, h5). The ``hapto'' number describes phenomenologically the number of (more or less) equivalent short metal-to-ligand distances, but from it can be inferred the number of donated electrons.

TRANSITION METAL BONDING TO ALKENES: ZEISE'S SALT

Zeise's salt, KPtCl3(h2-C2H4), exempli®es transition metal bonding to unsaturated hydrocarbons. The orbital interaction diagram for the T-shaped metal fragment PtClÿ3 and

188 ORGANOMETALLIC COMPOUNDS

Figure 13.7. Orbital interaction diagram for Zeise's anion, [PtCl3(CH2CH2)]ÿ.

ethylene shown in Figure 13.7 describes the bonding. Construction of the interaction diagram requires one to place the metal fragment orbitals and the alkene orbitals on the same scale. We already know that the p and p orbitals are placed at a ÿ jbj and a ‡ jbj, respectively. The placement of the metal fragment orbitals is accomplished with reference to Figures 13.4 and 13.2. The Cl ligands are poor s donors so Pt(II) will be treated as Pd(II) ˆ Cd(0). The energy scale is adjusted to the jbj scale, as recommended in Figure 13.2. The energies of the p orbitals are not very row dependent. It was recommended above that these be placed at a ‡ 1:5jbj. The nonbonded dxy, dxz, and dyz orbitals will