Field Splittings

In order to determine into how many Stark terms a given energy level splits when put into a ligand field without making a detailed calculation of the values, the group-theoretical methods of Bethe (66) are convenient. In this method it is noted that the spherical harmonics transform according to the Ith irreducible repre- 

Character Table for the Cubic Croup with Its Five Classes 

Oi contains the identity operation k2 contains three 180° rotations about x, y, z axes, respectively k3 contains six 90° rotations (+ and —) about the x, yt z axes k4 contains six 180° rotations about the six (110) axes k6 contains eight 120° rotations (4- and —) about the four (111) axes. The d wave functions are even and therefore operations involving inversion provide a redundant set. The degeneracy within a representation is given by ci. The Bethe (66) and Mulliken (457a) notations are compared.] 

A number of interesting facts emerge from this treatment. It is seen that P states remain threefold degenerate in cubic fields, but are split by a tetragonal distortion into a twofold and singlefold degenerate state. For a D state, or one d electron outside of closed 

Character of Classes of Cubic Symmetry in the (2L + 1)-Dimensional Representation DL of the Continuous Rotation Group and Their Resolution into Irreducible Representations of Cubic Symmetry 

---

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

When Cr202 is introduced as an impurity into the a-Al202 lattice, as occurs in the semiprecious mineral mby, the color is red rather than the normal green. This color anomaly is the result of ligand field splitting of the Cr(III) ion (51,52). Chromium (ITT) also colors other minerals (53). 

In an ociiihcOraJ field (he free-ion ground F lerm of a d ion is split into an A and two T terms which, along with the excited T(P) term (Fig. A), give rise to the possibility of three spin-allowed d-d transitions of which (he one of lowest eneigy is a direct measure of the ciystal field splitting, A or 10 Dq ... 

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. 

Tetrahedral complexes arc also common, being formed more readily with cobali(II) than with the cation of any other truly transitional element (i.e. excluding Zn ). This is consistent with the CFSEs of the two stereochemistries (Table 26.6). Quantitative comparisons between the values given for CFSE(oct) and CFSE(let) are not possible because of course tbc crystal field splittings, Ao and A, differ. Nor is the CFSE by any means the most important factor in determining the stability of a complex. Nevertheless, where other factors are comparable, it can have a decisive effect and it is apparent that no configuration is more favourable than d to the adoption of a tetrahedral as opposed to... 

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... 

MnFe2- has a crystal field splitting energy, A , of 2.60 X 102 kj/mol. What is the wavelength responsible for this energy ... 

Energy A property of a system which can be altered only by exchanging heat or work with the surroundings activation, 298-300,302 balance, 218-219 crystal field splitting, 418 electrical, 496 exercise and, 219t factor, 452 metabolic, 218 minimum, 165... 

The zero Field splitting (ZFS) parameters D and of the triplet exciton are ... 

These mixed-valence compounds have magnetic moments around 4/tB, indicating an S = 3/2 (quartet) ground state, in keeping with their ESR spectra, which resemble those of Cr3+ compounds with a big zero-field splitting (gj = 4, g = 2) [99]. 

Ligand field splittings in copper(II) compounds. D. W. Smith, Struct. Bonding (Berlin), 1972, 12, 49-112 (220). 

Crystal field splitting parameter, 2, 309 Crystal field theory, 1, 215-221 angular overlap model, 1, 228 calculations, 1, 220 generality, 1,219 low symmetry, 1,220 /-orbital, 1, 231 Crystal hydrates, 2, 305,306 bond distances, 2, 307 Crystals... 

Magnetic exchange, 1,257, 267 polymetallic complexes, 1,138 Magnetic moment, 1, 259 Magnetic properties atomic systems, 1,260 cubic field systems, 1,263 free-atom states and terms, I, 260 lower symmetry, 1, 264 zero-field splitting, 1,262 Magnetic susceptibility, 1,256, 259 Magnetism... 

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... 

The poor data on PuF6 are probably best interpreted as a very small TIP of about 150 x 10-6 emu indicating a singlet ground state and a large crystal field splitting of the octahedral compound ( 5). 

Prediction of the energy level structure for Pu2+ (5f ) is of particular interest since no spectra for this valence state of Pu have been reported. On the basis of what is known of the spectra of Am2+ (26), Cf2" (27), and Es2+ (28), there appears to be evidence for a very small crystal-field splitting of the free-ion levels. Such evidence encourages use of a free-ion calculation in this particular case. The parameter values selected are indicated in Table V. Based on the systematics given by Brewer (19), the first f- d transition should occur near 11000 cm-, so the f- -f transitions at higher energies would be expected to be at least partially obscured. A... 

The complex Ti(H20)6]3+ absorbs light of wavelength 510. nm. What is the ligand field splitting in the complex in kilojoules per mole (kj-mol ) ... 

Ligand field splittings are normally reported as a molar energy, and so we need to multiply this expression by Avogadro s constant ... 

What is the value (in kilojoules per mole) of the ligand field splitting ... 

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. 

---