The tetrahedral crystal field

Since Atet is significantly smaller than Aoct, tetrahedral complexes are high-spin. Also, since smaller amounts of energy are needed for ti e transitions (tetrahedral) than for eg tjg transitions (octahedral), corresponding octahedral and tetrahedral complexes often have different colours. (The notation for electronic transitions is given in Section 4.7.) 

Tetrahedral complexes are almost invariably high-spin. 

Jahn-Teller effects in tetrahedral complexes are illustrated by distortions in d (e.g. [CuCy ) and high-spin complexes. A particularly strong structural distortion is observed in [Fe04] (see structure 21.33). 

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The splitting pattern of the 4f orbitals in a tetrahedral crystal field can be deduced in a similar manner. If we adopt the coordinate system shown in Fig. 8.11.4, we can obtain the splitting pattern shown in the same figure. As expected the 1 3 3 pattern for the tetrahedral crystal field is just the reverse of the 3 3 1 pattern of the octahedral field. Also, the symmetry classification of the orbitals in a tetrahedral complex can be readily obtained from the character table of the Td group. 

The geometries of the octahedral and tetrahedral coordination sites shown in figs 2.3 and 2.6a suggest that the value of the tetrahedral crystal field splitting parameter, A, will be smaller than the octahedral parameter, A0, for each transition metal ion. It may be shown by simple electrostatic arguments and by group theory that... 

So far we have restricted the discussion to octahedral complexes we now turn to the tetrahedral crystal field. 

Why do tetrahedral complex ions have a different crystal field diagram than octahedral complex ions What is the tetrahedral crystal field diagram Why are virtually all tetrahedral complex ions "high spin" ... 

So far we have restricted the discussion to octahedral complexes. We now turn to the tetrahedral crystal field. Figure 21.7 shows a convenient way of relating a tetrahedron to a Cartesian axis set. With the complex in this orientation, none of the metal d orbitals points exactly at the ligands, but... 

We have considered the distortions to octahedral structure that result from the presence of d electrons. Tetrahedral structures are also observed in metal complexes however, they are less common than octahedral and distorted octahedral configurations. If four ligands surround a metal atom, a tetrahedral structure is expected. Two exceptions must be noted. As we have seen, four-coordinated low-spin (f complexes are square planar, as are many four-coordinated (f and high-spin d complexes. Tetrahedral cf, d, cf, and (f systems should exhibit marked Jahn Teller distortions however, very few examples of this type of eompound exist. Low-spin tetrahedral complexes need not be discussed, sinee there are no examples of such complexes. The tetrahedral crystal field splitting (A,) is apparently too small to cause spin pairing. 

The tetrahedral crystal field is more difficult to visualize than the octahedral and related square planar cases. One way to simplify the tetrahedral case is to consider its relationship to a cubic field. Figure 4.7 shows a cubic field—that is, a field of eight ligands at the corners of a cube containing the metal ion at the center. As illustrated, the cube can be thought of as the sum of two tetrahedra. (One tetrahedron of ligands is depicted in bold print for clarity.) By convention, the Cartesian coordinates are shown coming out of the center of each of the six cube faces. 

The details of the ground state of the Cuzn acceptor in ZnO have been established from the EPR and infrared absorption studies [107]. The low-temperature absorption spectrum of the Cu-doped ZnO contained two sharp lines at 717 and 722 meV. The details of the absorption spectra, the Zeeman splitting in magnetic field, and the EPR data allowed Dietz et al. [107] to construct the following model of Cuz in ZnO. The free ion term D of the Cu ion is split by the tetrahedral crystal field into the E (D)... 

The three p orbitals are directed along the three cartesian axes and so, in an octahedral crystal field, suffer equal repulsion from point charges sited on those axes. The energies of the three p orbitals, therefore, remain degenerate. Similarly, a free-ion P term remains unsplit in octahedral or tetrahedral crystal fields and is labelled Tig or Ti respectively. 

A low-spin to high-spin transition relates to the crystal field splitting of the d-orbitals in an octahedral or tetrahedral crystal field. However, even in cases where the energy difference between two spin states is much larger, electronic transitions are observed. An atom with total spin quantum number S has (22 + 1) orientations. In a magnetic field the atom will have a number of discrete energy levels with... 

At an early stage in the development of ligand field theory, it was found that A the splitting parameter for tetrahedral MX4, should be equal to (4/9) of A0, the splitting parameter for octahedral MX6, and experimental data are in good agreement with this prediction. However, this takes no account of the fact that the M—X distance in tetrahedral MX4 is usually some 8—10% shorter than in octahedral MX6. In the pointcharge crystal field model, A is proportional to R-5, so that if the difference in R between MX4 and MX6 is taken into account, we predict (At/A0) to be 0.6—0.7, compared with the experimental value of about 0.5. An AOM treatment (131) leads to better results, since here we find ... 

Figure 29.2 (a) Octahedral and (b) tetrahedral crystal fields represented as point charges around a central ion. Arrows show the effect of a tetrahedral distortion to the crystal field, (c) d-Orbital energy level diagrams for octahedral crystal field and octahedral crystal field with tetragonal distortion, and (d) tetrahedral crystal field and tetrahedral crystal field with tetragonal distortion. 

Figure 1-6. The splitting of the d orbitals in a tetrahedral crystal field. The total splitting is given by the quantity A,et (which is approximately Aoct).

We may use exactly similar arguments to obtain total CFSE terms for the various d electron configurations within a tetrahedral crystal field. It is quite possible to construct crystal field splitting diagrams for any of the other geometries commonly adopted in transition-metal complexes, and to calculate the appropriate CFSE terms. 

A 3) and two small negative peaks (-0.6 e A-3) are located in the directions of four C3 axes at 0.40 A from the Co nucleus. This arrangement of positive and negative peaks is just opposite to that observed for the transition metal ions in an octahedral environment. A simple crystal field model can also be applied to this case, because of the highly ionic character of this crystal (Section IV,B). In a tetrahedral crystal field, a fivefold degenerate 3d level splits into a lower doublet e and a higher triplet f2 as follows ... 

To conclude this chapter, we discuss the shapes of the 4f orbitals as well as their splitting patterns in octahedral and tetrahedral crystal fields. The results are of use in studying the complexes of the rare-earth elements. 

For systems of cubic symmetry, it is convenient to choose an alternative set of combinations known as the cubic set. Their abbreviated Cartesian labels and symmetry species in point group Oh arexyz(A2u) x3, y3, z3 (Tiu) z(x2 - y2), x(z2 — y2), y(z2 — x2) (Tin). These functions are particularly useful when octahedral and tetrahedral crystal field splitting patterns are considered. The... 

Splitting pattern of the 4f orbitals in a tetrahedral crystal field. 

Figure 3.10 Partial energy level diagram for the Fe3+ or Mn2+ ions with 3tfi configurations in high-spin states in an octahedral crystal field. Only sextet and quartet spectroscopic terms and crystal field states are shown. Note that the same energy level diagram applies to the cations in tetrahedral crystal fields (with g subscripts omitted from the state symbols for the acentric coordination site).

MO diagram for the tetrahedral [FeOJ cluster The molecular orbitals calculated for Fe3+ in the tetrahedral cluster [FeOJ-5 indicate that the antibonding e and t2 molecular orbitals, corresponding to the iron 3 d orbitals in a tetrahedral crystal field, are mostly localized on the iron atom (Sherman, 1985a). Furthermore, although allowed by symmetry, there appears to be little Fe 4p character in these orbitals, casting some doubt on the intensification mechanism of absorption bands in crystal field spectra of tetra-hedrally coordinated cations ( 3.7.1). 

The first-order JT effect is important in complexes of transition metal cations that contain nonuniformly filled degenerate orbitals, if the mechanism is not quenched by spin-orbit (Russell-Saunders) coupling. Thus, the JT effect can be expected with octahedrally coordinated and high spin d cations, and tetrahedrally coordinated and d cations. The low-spin state is not observed in tetrahedral geometry because of the small crystal field splitting. Also, spin-orbit coupling is usually the dominant effect in T states so that the JT effect is not observed with tetrahedrally coordinated d, d , d, and d ions. 

Many of the results obtained for the octahedral crystal-field calculation can be used for the description of the magnetic properties of ions in tetrahedral environments. If an 5 4 axis of the tetrahedron is taken as the axis of quantization (being collinear with the C4 axis of quantization of the octahedron), and the C3 axes of the tetrahedron are collinear with the C3 axes of the octahedron, then the crystal-field potential energy... 

Figure 6.8 The effect of cubic and tetrahedral crystal fields on the energies of d orbitals...

The character table for the tetrahedral group 7rf is shown below. Referring to Section 10.6, verify that the five -orbitals in a tetrahedral crystal field transform according to the E and T2 representations. 

FIGURE 8.26 Energy-level structures of the 3d orbitals in square-planar and tetrahedral crystal fields. 

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