Crystal field forces

Excitation spectra of Mn " enable us to calculate the crystal field force A and Raka parameters B and C. The relative position of the ground level Aig (S) and excited levels 4Eg G) and Eg(D) does not depend on A. Using the frequencies of electronic transitions from the ground level to those excited levels (ks and k ), parameters B and C may be calculated based on formulas ... 

In many actinide solids, as we shall see, the experimentally determined magnetic properties are explained well by assuming the permanent magnetic moment due to Hund s rules. The f-electrons are considered atomic, and their interaction with the environment is through crystal field forces or weak exchange forces with conduction electrons. Here, the magnetic properties are explained in the atomic limit. 

The rarity of the phenomenon of conformational polymorphism (one of the rare examples of conformational polymorphism is D,L-methionine (30)) is an indication that it is unusual for the crystal field forces to exercise a dominant influence on molecular conformation. It appears that the differences in the lattice sums of the crystal field forces for different conformations are in most cases an order of magnitude too small to induce conformational changes—i.e., tenths of kilocalorie per interaction rather than kilocalories. 

This appears not to be the case. On average, the crystal field forces have a distortion effect. This was realized from some of the earliest analyses of hydrogen-bond lengths [52]. It arises from two factors one is the influence of many-atom effects, such as cooperativity. The second is the fact that all other atom-pair interactions are striving toward the equilibrium minimum. Since hydrogen-bonded functional groups tend to protrude from molecules, this results in an overall distortion. The most obvious example of this difference is that between the values for the H 0 distances of 1.7 to 1.8 A observed in the ices and 2.0 A for the water dimer (see Thble 4.3). Similarly, the distribution for two-center OwH O bonds in the hydrates of small molecules, discussed in Part IV, has a mean value of 1.80 A, in agreement with the ices. 

However, the interpretation of the data was compUcated by the existence of anisotropic crystal field forces, in addition to interchain perturbing forces, and the question remains unresolved. 

Figure 23 (Vogt 1968) shows that in diluted HoSb the magnetization curve and, especially, anisotropy is only governed by the crystal electric field (cf. results for TmSb, for example). The crystal field forces the moments strictly into the <100> direction.

Again, in addition to the expected seven IR-active n.v. of point group Cs , there are other absorptions corresponding to combination bands of n.v. activated by crystal field forces. 

Finally, we should remember that f f transitions are parity-forbidden. However, most of them become partially allowed at the electric dipole order as a result of mixing with other orbitals that have different parity because of a noninversion symmetry crystal field (see Section 5.3). Thus, a proper choice of the crystal host (or the site symmetry) can cause a variety of (RE) + transitions to become forced electric dipole transitions. 

Other structural analyses of crystals in which the bifluoride is present are listed in Table 7. One compound, p-toluidinium fluoride [C7H,oN ][HF2 ], is worthy of further comment. The first X-ray diffraction study reported a symmetrical anion (Denne and MacKay, 1971), but a later analysis showed that the proton was not centred between the two fluorines and 7 f h values were 102.5 and 123.5 pm (Williams and Schneemeyer, 1973). This can be explained not by a double minimum potential energy well but by asymmetry due to other forces, such as secondary hydrogen bonding between one end of the bifluoride anion and the N—H group of the cation. An alternative explanation attributes the asymmetry of the bifluoride hydrogen bond to an unsymmetrical crystal field caused by the cation (Ostlund and Bellenger, 1975). 

The crystal field effect is due primarily to repulsive effects between electron clouds. As we have already seen, the repulsive energy is of opposite sign with respect to coulombic attraction and the dispersive forces that maintain crystal cohesion. An increase in repulsive energy may thus be interpreted as actual destabilization of the compound. 

The crystal field model may also provide a calciflation scheme for the transition probabilities between levels perturbed by the crystal field. It is so called weak crystal field approximation. In this case the crystal field has little effect on the total Hamiltonian and it is regarded as a perturbation of the energy levels of the free ion. Judd and Ofelt, who showed that the odd terms in the crystal field expansion might connect the 4/ configuration with the 5d and 5g configurations, made such calculations. The result of the calculation for the oscillator strength, due to a forced electric dipole transition between the two states makes it possible to calculate the intensities of the lines due to forced electric dipole transitions. 

Figure 4.23 Various degrees of complexity that can arise in JT systems. (After Gehring Gehring, 1975.) CF stands for crystal field. Single circle indicates first-order transition and a double circle indicates a second-order transition. A single circle with a broken circle indicates a transition which is first-order because of the existence of anharmonic forces.

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