Yves Jean - Molecular Orbitals of Transition Metal Complexes (793957), страница 16
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In this way, we change from a square-planar (D4h symmetry)to a tetrahedral complex (Td symmetry), maintaining D2d symmetry atintermediate points.CommentThis is not the only way to move from one structure to the other. Onecan, for example, rotate one ML2 unit by 90◦ with respect to the other,progressively adjusting the values of the bond angles (D2 symmetry isconserved).2.4.1. Characterization of the d blockWe shall consider each of the five d orbitals of a square-planar complexas they are presented in Figure 2.6 (right-hand side). On moving to thetetrahedral structure, the xy orbital stays unchanged in both shape andenergy (2-54a), as the four ligands move in one or other of the twonodal planes of this orbital (L2 and L4 in xz, L1 and L3 in yz). Theyz and xz orbitals behave in just the same way as they do when themetal moves out of the basal plane in SBP ML5 complexes (§ 2.3.2).
Onpassing from the square plane to the tetrahedron, two ligands move inthe plane where the amplitude of the orbital is greatest, but the othertwo ligands stay in one of the nodal planes. As a result, the yz orbital isdestabilized by antibonding interactions with the ligands L1 and L3 , butit has no interaction with L2 and L4 which are still located in the nodalplane xz (2-54b). In the same way, the xz orbital is destabilized by aninteraction with the ligands L2 and L4 (2-54c).
These two orbitals, yzPrincipal ligand fields: σ interactionsand xz, which were nonbonding in a square-planar complex, thereforebecome antibonding in a tetrahedral complex, while staying degenerate.However, just as in ML5 complexes (§ 2.3.2), the antibonding interactions are reduced by mixing with a p orbital on the metal (py in the caseof yz, px for xz) which polarizes the d orbital in the direction oppositeto that of the two ligands with which it is interacting (2-54b) and seealso Appendix A).
The z2 orbital becomes rigorously nonbonding (zerocoefficients on the ligands, 2-54d), and thus at the same energy as the xyorbital, since the four ligands in the tetrahedral structure are moved precisely on to its nodal cone (whose angle is exactly equal to 109.5◦ ). Thelast orbital, x 2−y2 , is strongly stabilized since the four ligands leave thex- and y-axes on which they were located. The antibonding interactionsare decreased but not eliminated, since in the tetrahedral structure, theligands are not in the nodal planes of the x 2−y2 orbital (2-54e).xy(a)yz(b)xz(c)z2(d)x2–y2(e)2-54This analysis enables us to describe fully the structure of the d blockof a tetrahedral complex: there are two degenerate nonbonding orbitals(xy and z2 ), two degenerate antibonding orbitals (xz and yz), and a thirdantibonding orbital, x 2−y2 .
The only remaining uncertainty concernsthe relative energies of the (xz, yz) and x 2−y2 antibonding orbitals. Theanswer to this question is found in the character table for the tetrahedralpoint group, Td (Table 2.2).Tetrahedral ML4 complexesTable 2.2. Character table for the Td group (tetrahedral ML4 complex)Td E 8C33C26S46σdA1A2ET1T2112−1−11−101−11−10−1111112 −13030x 2 + y2 + z2(2z2 − x 2 − y2 , x 2 − y2 )(x, y, z)(xy, xz, yz)Inspection of the last column shows that the five d orbitals are foundin two groups of degenerate orbitals, of e (doubly degenerate) and t2(triply degenerate) symmetry, respectively.
As we have already shownthat there are just two nonbonding orbitals, it is clear that they must havee symmetry. The antibonding orbitals therefore have t2 symmetry, andall three are degenerate by symmetry. The d block of the tetrahedrontherefore contains two nonbonding degenerate orbitals (e) and threeantibonding orbitals that constitute another degenerate set (t2 ).CommentWe note that the roles of xy and x 2−y2 orbitals are interchanged in a tetrahedral complex, depending on whether we adopt the analysis developedabove (xy nonbonding (2-54a), x 2−y2 antibonding (2-54e)), or the charactertable (x 2−y2 degenerate with z2 , therefore nonbonding, xy degenerate withxz and yz, therefore antibonding).
This arises simply from a different definition of the axes (a rotation of 45◦ around the z-axis) which interchangesthe role of the xy and x 2−y2 orbitals, as we have already seen in the case ofthe octahedron (Figures 2.3 and 2.4) or the square-planar complex plan (seeExercise 2.4).We can now sketch the correlation diagram linking the d-blockorbitals of a square-planar complex to those of a tetrahedron (Figure 2.9),following the deformation shown in 2-53.b1gt2a1gFigure 2.9. Correlation diagram linking thed-block orbitals of a square-planar ML4complex and those of a tetrahedral ML4complex, following the deformation shown in2-53.egeb2gPrincipal ligand fields: σ interactions2.4.2. Electronic structure2.4.2.1.
d10 diamagnetic complexest2ed102-55The separation between the e and t2 levels of the d block is sufficientlysmall (the t2 orbitals are only weakly antibonding) that all five orbitalscan be occupied. Diamagnetic complexes with a d10 electronic configuration are thus obtained (2-55), such as [Ni(H)4 ]4− , [Ni(CO)4 ],[M(PF3 )4 ] (M=Ni, Pd), [Pt(dppe)2] (dppe=diphenylphosphinoethane), [Ni(CN)4 ]4− , [Co(CO)4 ]− , [Fe(CO)4 ]2− , [Cu(CN)4 ]3− ,[Cu(PMe3 )4 ]+ , [Ag(PPh3 )4 ]+ , or [Zn(Cl)4 ]2− . These are 18-electroncomplexes, since eight additional electrons are associated with the fourmetal–ligand bonds.2.4.2.2.
Other casesML4 complexes whose d block is empty (d0 electronic configuration),such as [TiCl4 ] and [MnO4 ]− , also adopt a tetrahedral geometry. As inthe examples of d0 complexes already mentioned (§ 2.1.3.2 and 2.3.3.2),the ligands have lone pairs which play an important role in the stabilization of these species that apparently are strongly electron-deficient(formally, only eight electrons around the metal!). We may also mention tetrahedral d8 complexes, such as [NiCl4 ]2− , [Ni(PPh2 Et)2 Br2 ], or[CoBr(PR 3 )3 ]. The structure of the d block, with the three t2 degenerateorbitals, leads to a paramagnetic ground state (e4 t24 ), with two unpairedelectrons in the t2 orbitals (a high-spin tetrahedral complex, right-handside of 2-57).2.4.3. ML4 complexes: square-planar or tetrahedral?Not all ML4 complexes have a square-planar or tetrahedral structure.
‘Intermediate’ geometries, of lower symmetry, can be observed(e.g. [Fe(CO)4 ] is a high-spin d8 complex with C2v symmetry, see § 2.8.3).However, a large number of ML4 complexes adopt, either exactly or withonly small deviations, one or other of these high-symmetry geometries.In this paragraph, we shall show how a knowledge of the d block for eachtype of structure (§ 2.2.1 and 2.4.1) enables us to establish a link betweenthe dn electronic configuration of the complex and the geometry that isobserved experimentally.
We shall concentrate our attention on the d10and d8 electronic configurations, which are the most common for ML4complexes.It is straightforward to understand the structural preference for10d complexes: in the tetrahedral geometry, all five d orbitals arelow in energy and can thus receive ten electrons, whereas thereare only four low-energy d orbitals in the square-planar geometryTetrahedral ML4 complexes6The tetrahedral geometry is alsofavoured by the bonding MO, lower in energythan the d block, as shown by theexperimental structures of d0 complexes(§ 2.4.2.2) which have tetrahedral geometries.(Figure 2.9). Complexes with a d10 electronic configuration thereforeadopt a tetrahedral structure (§ 2.4.2.1).6In diamagnetic d8 complexes (low-spin), four d orbitals must bedoubly occupied.
This count is ideal for the square-planar geometry,characterized by four low-energy d orbitals (three strictly nonbonding, one very weakly antibonding (2-56, left-hand side)), well separatedfrom the fifth which is strongly antibonding. The situation is lessfavourable for the tetrahedral geometry: first, there are only four nonbonding electrons instead of six, and second, the distribution of fourelectrons in three orbitals (2-56, right-hand side) is energetically unfavourable since it does not obey Hund’s rule (two electrons shouldoccupy two different orbitals, with parallel spins). In summary, thed-block of a tetrahedral complex is not well suited to accomodatefour pairs of electrons, and in fact diamagnetic d8 complexes adopt asquare-planar geometry ([Ni(CN)4 ]2− , [Pd(NH3 )4 ]2+ , [RhCl(PPh3 )3 ],or [Ir(CO)(Cl)(PPh3 )2 ], for example).Square-planar (d 8 low-spin)Tetrahedral (d 8 low-spin)2-56This leads us naturally to consider the case of paramagnetic d8 complexes (high-spin), that have two unpaired electrons with parallel spin.The situation is now favourable for the tetrahedral geometry: Hund’srule is obeyed, and the occupied d orbitals are either nonbonding oronly weakly antibonding (2-57, right-hand side).
In contrast, in thesquare-planar geometry, an electron must be placed in the stronglyantibonding orbital of the d block (2-57, left-hand side). The tetrahedralstructure is therefore favoured for high-spin d8 complexes (§ 2.4.2.2).As a consequence, the low-spin → high-spin change in d8 ML4 complexes is accompanied with a change in geometry, from square-planarto tetrahedral.It is more difficult to predict whether a given complex with a d8electronic configuration will be low-spin, with a square-planar structure, or high-spin, with a tetrahedral structure.
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