Electron spin resonance crystal-field theory

Although analytic expressions for the potential constants exist, they are rarely calculated directly. The covalency degree, uncertainties of effective ligand charges and other conceptual drawbacks make such an approach problematic. The potential constants are more often taken as free parameters of the theory which enter the final formulae of electron spectroscopy, electron spin resonance and magnetochemistry. The potential constants in different representations of the crystal field potential obey simple proportionality relationships which can be found in special monographs [10-13]. For example, the potential expressed through the Racah operators... 

Abstract A brief excursion is made into the concept of continuous groups, with an example of the rotation groups. The purpose is to familiarize the reader with the concept of electron spin. The coupling of spins is discussed. Applications are taken from Crystal-Field Theory and Electron Spin Resonance. 

The simplest crystal field theory deals with a purely atomic ion in a static electric field. This ionic model should, however, be regarded as an approximation to the real cases in which there can generally be certain amount of covalency in the bonding between the metal ions and the surrounding anions. The reduction of the Coulomb repulsion energy, expressed by the parameters B and C, and of the spin-orbit interaction constant A implies the wider spread of the orbital functions than the purely atomic d functions " > > (see also Table XXII of ref. 50). The most direct experimental evidence for this covalency is the hyperfine structure due to anion nuclei observed in the electron spin resonance spectra by the metal ions. This phenomenon will be discussed in detail in the next section. 

The most precise measurements of the fine-structure parameters D and E have in fact been carried out using zero-field resonance. Figure 7.6 shows the three zero-field transitions in the Ti state of naphthalene molecules in a biphenyl crystal at T = 83 K. In these experiments, the absorption of the microwaves was detected as a function of their frequency [5]. The lines are inhomogeneously broadened and nevertheless only about 1 MHz wide. Owing to the small hnewidth of the zero-field resonances, the fine-structure constants can be determined with a high precision. This small inhomogeneous broadening is due to the hyperfine interaction with the nuclear spins of the protons (see e.g. [M2] and [M5]). For triplet states in zero field, the hyperfine structure vanishes to first order in perturbation theory, since the expectation value of the electronic spins vanishes in all three zero-field components (cf Sect. 7.2). The hyperfine structure of the zero-field resonances is therefore a second-order effect [5]. 

---