The Crystal Field

FIGURE 1.1 The effect on the d orbitals of bringing up six ligands along the jc, y, and z directions. In this figure, shading represents the symmetry (not the occupation) of the d orbitals shaded parts have the same sign of tj.  

FIGURE 1,2 In a d metal ion, both low- and high-spin complexes are possible depending on the value of A. A high A leads to the low-spin form. 

In an octahedral ion we are obliged to place one electron in the higher-energy (less stable) d level to give the configuration and this will 

FIGURE 13 A d octahedral imi is paramagnetic even in the low-spin form. 

For a given geometry and ligand set, metal ions tend to have different values of A. For example, first-row metals and metals in a low oxidation state tend to have low A, while second- and third-row metals and metals in a high oxidation state tend to have high A. The trend is illustrated by the spectrochenucal series of metal ions in order of increasing A. 

TABLE LI Hard and Soft Adds and Bases Some Formation Constants  

The Hg +/I soft-soft combination is therefore a very good one—by far the best in the table—and dominated by covalent bonding. HI, a mismatched pairing, produces a strong add (pA -9.5). 

Soft bases either have lone pairs on atoms of the second or later row of the periodic table (e.g.. Cl, Br , and PPhs) or have double or triple bonds (e.g., CN , C2H4, and benzene) directly adjacent to the donor atom. Soft acids can come from the second or later row of the periodic table (e.g., Hg +) or contain atoms that are relatively electropositive (e.g., BH3) or are metals in a low ( 2) oxidation state (e.g., Ni(0), Re(I), Pt(II), andTi(II)). Organometallic chemistry is dominated by soft-soft interactions, as in metal carbonyl, alkene, and arene chemistry, while traditional coordination chemistry involves harder metals and ligands. 

FIGURE 1.3 A cf octahedral ion is paramagnetic in both the low-spin (left) and high-spin (right) forms. 

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Orgel diagrams Simple graphs showing the relation between the energies of various electronic slates and the crystal field splitting. 

The and 72 states are broadened as a result of slight variations in the crystal field. The 72 and E states are sharper but the E state is split into two components, 29 cm apart, because of the slight distortion of the octahedral field. Population inversion and... 

The arc and spark spectra of the individual lanthanides are exceedingly complex. Thousands of emission lines are observed. For the trivalent rare-earth ions in soUds, the absorption spectra are much better understood. However, the crystal fields of the neighboring atoms remove the degeneracy of some states and several levels exist where only one did before. Many of these crystal field levels exist very close to a base level. As the soUd is heated, a number of the lower levels become occupied. Some physical properties of rare-earth metals are thus very sensitive to temperature (7). 

The effect of the CFSE is expected to be even more marked in the case of the heavier elements because for them the crystal field splittings are much greater. As a result the +3 state is the most important one for both Rh and Ir and [M(H20)6] are the only simple aquo ions formed by these elements. With rr-acceptor ligands the +1 oxidation state is also well known for Rh and Ir. It is noticeable, however, that the similarity of these two heavier elements is less than is the case earlier in the transition series and, although rhodium resembles iridium more than cobalt, nevertheless there are significant differences. One example is provided by the +4 oxidation state which occurs to an appreciable extent in iridium but not in rhodium. (The ease with which Ir, Ir sometimes occurs... 

Data for some typical complexes are given in Table 26.5. The assignments are made, producing values of the inter-electronic repulsion parameter B as well as of the crystal-field splitting, 0Dq. 

Electronic absorption spectra are produced when electromagnetic radiation promotes the ions from their ground state to excited states. For the lanthanides the most common of such transitions involve excited states which are either components of the ground term or else belong to excited terms which arise from the same 4f" configuration as the ground term. In either case the transitions therefore involve only a redistribution of electrons within the 4f orbitals (i.e. f—>f transitions) and so are orbitally forbidden just like d—>d transitions. In the case of the latter the rule is partially relaxed by a mechanism which depends on the effect of the crystal field in distorting the symmetry of the metal ion. However, it has already been pointed out that crystal field effects are very much smaller in the case of ions and they... 

We will discuss the crystal field model here. It assumes that the bonding between metal "Crystal field" isn t a very descriptive term,... 

Most coordination compounds are brilliantly colored, a property that can be explained by the crystal field model. 

The difference in energy between the two groups is called the crystal field splitting energy and given the symbol A, (the subscript o stands for octahedral ). 

From the color (absorption spectrum) of a complex ion, it is sometimes possible to deduce the value of AOJ the crystal field splitting energy. The situation is particularly simple in 22Ti3+, which contains only one 3d electron. Consider, for example, the Ti(H20)63+ ion, which has an intense purple color. This ion absorbs at 510 nm, in the green region. The... 

Kamenskaya [221] and Konstantinov [37] investigated the concentration field adjacent to the KF - NbF5 side of the ternary interconnected system K+, Nb5+//Q2, F. Fig. 55 shows the projection of the crystallization fields. 

Two symmetry parameterizations of the angular overlap model of the ligand field. Relation to the crystal field model. C. E. Schaffer, Struct. Bonding (Berlin), 1973,14, 69-110 (33). 

Crystal field effects are of the order of the free ion interaction thus they cannot be treated as a small perturbation as in the lanthanides. Whereas the crystal field splitting in the oxidation state +3 is comparable to that for the lanthanides, it is significantly increased in the progression... 

Due to the intermediate coupling the sign of the crystal field matrix element 6 is reversed compared to the pure Russell-Saunders state. Thus for 8-fold cubic coordination a F7 ground state was found. From EPR measurements on Pu3"1" diluted in fluorite host lattices, a magnetic moment at T=0 K can be calculated, ranging from li ff = 1.333 (in Ce02) to y ff = 0.942 (in SrCl2) (24,... 

The electrostatic and spin-orbit parameters for Pu + which we have deduced are similar to those proposed by Conway some years ago (32). However, inclusion of the crystal-field interaction in the computation of the energy level structure, which was not done earlier, significantly modifies previous predictions. As an approximation, we have chosen to use the crystal-field parameters derived for CS2UCI6 (33), Table VII, which together with the free-ion parameters lead to the prediction of a distinct group of levels near 1100 cm-. Of course a weaker field would lead to crystal-field levels intermediate between 0 and 1000 cm-1. Similar model calculations have been indicated in Fig. 8 for Nplt+, Pu1 "1 and Amlt+ compared to the solution spectra of the ions. For Am t+ the reference is Am4" in 15 M NHhF solution (34). 

FIGURE 16.24 In the crystal field theory of complexes, the lone pairs of electrons that serve as the Lewis base sites on the ligands (a) are treated as equivalent to point negative charges (b). 

Crystal-field theory (CFT) was constructed as the first theoretical model to account for these spectral differences. Its central idea is simple in the extreme. In free atoms and ions, all electrons, but for our interests particularly the outer or non-core electrons, are subject to three main energetic constraints a) they possess kinetic energy, b) they are attracted to the nucleus and c) they repel one another. (We shall put that a little more exactly, and symbolically, later). Within the environment of other ions, as for example within the lattice of a crystal, those electrons are expected to be subject also to one further constraint. Namely, they will be affected by the non-spherical electric field established by the surrounding ions. That electric field was called the crystalline field , but we now simply call it the crystal field . Since we are almost exclusively concerned with the spectral and other properties of positively charged transition-metal ions surrounded by anions of the lattice, the effect of the crystal field is to repel the electrons. 

Those electrons must not only avoid each other but also the negatively charged anionic environment. In its simplest form, the crystal field is viewed as composed of an array of negative point charges. This simplification is not essential but perfectly adequate for our introduction. We comment upon it later. 

We are concerned with what happens to the (spectral) d electrons of a transition-metal ion surrounded by a group of ligands which, in the crystal-field model, may be represented by point negative charges. The results depend upon the number and spatial arrangements of these charges. For the moment, and because of the very common occurrence of octahedral coordination, we focus exclusively upon an octahedral array of point charges. 

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