Tetrahedral complexes orbitals

Thc Crystal l-ield Siabili2ation Energy (CFSl ) is the additional stability which accrues to an ion in a complex, as compared to the free ion, because its d-orbitals are split In an octahedral complex a l2 electron increases the stability by 2/5Ao and an Cf, electron decreases it by 3/5Ao- In a tetrahedral complex the orbital splitting is reversed and an e electron therefore increases the stability by 3/5At whereas a t2 electron decreases it by 2/5Ai. 

The subscript g is not used to label the orbitals in a tetrahedral complex because there is no center of symmetry. 

In octahedral complexes, the e -orbitals (dz< and dx2 -yi) lie higher in energy than the t2 -orbitals (dxy, dyz, and dzx). The opposite is true in a tetrahedral complex, for which the ligand field splitting is smaller. 

FIGURE 16.28 Tbe energy levels of the d-orbitals in a tetrahedral complex with the ligand field splitting A,. Each box (that is, orbital) can hold two electrons. The subscript g is not used to label the orbitals in a tetrahedral complex. 

Consider now spin-allowed transitions. The parity and angular momentum selection rules forbid pure d d transitions. Once again the rule is absolute. It is our description of the wavefunctions that is at fault. Suppose we enquire about a d-d transition in a tetrahedral complex. It might be supposed that the parity rule is inoperative here, since the tetrahedron has no centre of inversion to which the d orbitals and the light operator can be symmetry classified. But, this is not at all true for two reasons, one being empirical (which is more of an observation than a reason) and one theoretical. The empirical reason is that if the parity rule were irrelevant, the intensities of d-d bands in tetrahedral molecules could be fully allowed and as strong as those we observe in dyes, for example. In fact, the d-d bands in tetrahedral species are perhaps two or three orders of magnitude weaker than many fully allowed transitions. 

A mistake often made by those new to the subject is to say that The Laporte rule is irrelevant for tetrahedral complexes (say) because they lack a centre of symmetry and so the concept of parity is without meaning . This is incorrect because the light operates not upon the nuclear coordninates but upon the electron coordinates which, for pure d ox p wavefunctions, for example, have well-defined parity. The lack of a molecular inversion centre allows the mixing together of pure d and p ox f) orbitals the result is the mixed parity of the orbitals and consequent non-zero transition moments. Furthermore, had the original statement been correct, we would have expected intensities of tetrahedral d-d transitions to be fully allowed, which they are not. 

The ligands of a tetrahedral complex occupy the comers of a tetrahedron rather than the comers of a square. The symmetry relationships between the d orbitals and these ligands are not easy to visualize, but the splitting pattern of the d orbitals can be determined using geometry. The result is the opposite of the pattern found in octahedral... 

The crystal field energy level diagram for tetrahedral complexes. The d orbitals are split into two sets, with three orbitals destabilized relative to the two others. 

Although the effect on the d orbitals produced by a field of octahedral symmetry has been described, we must remember that not all complexes are octahedral or even have six ligands bonded to the metal ion. For example, many complexes have tetrahedral symmetry, so we need to determine the effect of a tetrahedral field on the d orbitals. Figure 17.5 shows a tetrahedral complex that is circumscribed in a cube. Also shown are lobes of the dz- orbital and two lobes (those lying along the x-axis) of the dx> y> orbital. 

FIGURE 17.5 A tetrahedral complex shown with the coordinate system. Two lobes of the d/ orbital are shown along thez-axis and two lobes of the df-f orbital ate shown along they axis. 

FIGURE 17.18 A qualitative molecular orbital diagram for a tetrahedral complex. 

From a consideration of the combination of ligand and metal orbitals, it should be apparent that the overlap is much more effective in an octahedral complex (in which orbitals are directed at ligands) than in a tetrahedral complex (where orbitals are directed between ligands). The result is that the energy difference between the e and t2 orbitals in a tetrahedral complex is much smaller than that between the t2g and eg orbitals in an octahedral complex. As we saw when considering the two types of complexes by means of ligand field theory, At is only about half as large as A0 in most cases. 

Make a sketch of a cubic complex (start with a tetrahedral complex and add four ligands). Analyze the repulsion of each of the d orbitals and sketch the splitting pattern that would exist in a cubic field. 

A splitting of magnitude A6 is produced and it depends on the nature of both the metal ion and the ligand. In the case of the octahedral field each electron placed in one of the t2g orbitals is stabilized by a total of -2/5A, while electrons placed in the higher energy eg orbitals are destabilized by a total of 3/5A. The splitting for a tetrahedral complex, Atet is less than that for an octahedral one and algebraic analysis shows that Atet is about 4/9A. ... 

The situation is quite different with tetrahedral complexes of Ni(0), Pd(0) and Pt(0). We might anticipate that an associative mechanism would be deterred, because of strong mutual repulsion of the entering nucleophile and the filled d orbitals of the d system. Thus a first-order rate law for substitution in Ni(0) carbonyls, and M (P(OC2H5)3)4M = Ni, (Sec. 1.4.1) Pd and Pt, as well as a positive volume of activation ( + 8 cm mol ) for the reaction of Ni(CO)4 with P(OEt)3 in heptane support an associative mechanism. 

Complexes of class a metals are more ionic, while those of the class b metals are more covalent. Generally, the metals that form tetrahedral complexes by using sp hybrid orbitals are class a types. Those forming square planar complexes by using dsp hybrid orbitals are normally class b types. 

The extension to non-octahedral complexes is possible, but must be carried out with great care The orbitals chosen can be expressed as a linear combination of the usual orbitals for an octahedron, and electron-electron repulsions can then be calculated from those for the octahedral case. It is not necessarily adequate for tetrahedral complexes of the first row transition elements, to use ligand field theory in the strong field limit, even for powerful ligands in V(mesityl)4 the ligand field splitting is only 9250 cm ... 

It has been shown, however, that the orbital degeneracy of the 3Ti(F) state would be lifted by spin-orbit coupling 142). In this case there is no longer any need for Jahn-Teller distortion, and when the four ligands are identical the tetrahedral complexes may be quite regular. 

Ligand-field theory predicted (10, 22) that tetrahedral nickel(II) complexes should be unstable with respect to octahedral ones, at least so long as the two extra ligands were available. This arises because, if one accepts the d-orbital center of gravity as an energy-zero (a point which should be raised more often), the crystal-field stabilization of an octahedral complex works out to be 0.84 A greater than that of a tetrahedral complex with... 

Splitting of the energy levels. Both an octahedral complex (two electrons in orbitals) and a tetrahedral complex (four electrons in orbitals) are less favorable in this case. 

In tetrahedral symmetry, the d9 configuration has three orbital levels lowest as does d1 in octahedral symmetry. The similarity between the g values for tetrahedral and distorted octahedral symmetry indicates that the distortion in tetrahedral complexes of Cu2+ is large and leaves the unpaired electron in the (x2 — y2) orbital. In tetrahedral symmetry, 4p orbitals have the same symmetry as the d orbitals, and thus there can be a mixing of 4p and 3d orbitals. Sharnoff (281) has estimated from the spin Hamiltonian of CuClJ- that the unpaired electron is in an orbital that is 70 per cent 3d9 12 per cent 4p, 17 per cent 3p of Cl, and 1.3 per cent 3s of Cl. 

In order to find out the relative energies of the e and t2 orbitals, let us place our tetrahedral complex in a set of coordinate axes as shown in Figure 9.10. Once more, we can make a comparison between either of the e orbitals and any one of the t2 orbitals, and perhaps the best selection in order to visualize the relative electrostatic energies is again the pair dxy and dxi.y The difference here is much less striking than in the octahedral case, but it can be seen that qualitatively an electron in the dxy orbital will have a higher... 

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