Anisotropic electronic interactions

An exception to this rule arises in the ESR spectra of radicals with small hyperfine parameters in solids. In that case the interplay between the Zeeman and anisotropic hyperfine interaction may give rise to satellite peaks for some radical orientations (S. M. Blinder, J. Chem. Phys., 1960, 33, 748 H. Sternlicht,./. Chem. Phys., 1960, 33, 1128). Such effects have been observed in organic free radicals (H. M. McConnell, C. Heller, T. Cole and R. W. Fessenden, J. Am. Chem. Soc., 1959, 82, 766) but are assumed to be negligible for the analysis of powder spectra (see Chapter 4) where A is often large or the resolution is insufficient to reveal subtle spectral features. The nuclear Zeeman interaction does, however, play a central role in electron-nuclear double resonance experiments and related methods [Appendix 2 and Section 2.6 (Chapter 2)]. 

An indirect mode of anisotropic hyperfine interaction arises as a result of strong spin-orbit interaction (174)- Nuclear and electron spin magnetic moments are coupled to each other because both are coupled to the orbital magnetic moment. The Hamiltonian is... 

We have shown that redox chromophores organized in LB films with resped to their orientation, alignment, or electronic interactions make very useful and specific photoresponses such as amplified fluorescence quenching, photocurrents controlled at the molecular level, photoinduced anisotropic eledrochromism, and photochemically modulated second harmonic generation. These results may contribute to facilitate the design and construction of novel photonic devices in the near future. 

General relationships between AOM and crystal field parameters are shown in Table 23. Using the AOM one can easily compute the electronic energy levels, inclusive of spin-orbit coupling, without any symmetry assumption or perturbation procedure, and it is also easy to account for the different chemical natures of the ligands and for differences in bond distances. It is also possible to handle anisotropic n interactions, which can be expected to occur with pyridine or pyridine iV-oxide ligands.366,367 General review articles on the AOM and its applications have already appeared.364,368-371... 

The same can be done in the graphite lattice as show in Fig. 2. The bonding force acting between two neighboring atoms can be directly demonstrated as a function of interatomic separation, resulting in anisotropic properties. The bond energy in the c direction is commonly called van der Waals bond or n electron interaction and is estimated to be 17-33 kJ/mol between the planes as compared to 430 kJ/mol of chemical covalent nature or tr-bond within the planes [37]. 

Rotational motion of a nitroxide modulates the anisotropic electron-nuclear magnetic dipolar interaction, giving rise to electron relaxation that affects the EPR spectral line shape. At X-band frequency, the spectra are sensitive to motions with correlation times in the range of 10-11 < rc < 10-7, but also reflect the anisotropy of the motion. Figure 5B shows simulated EPR spectra for isotropic motion in the fast, intermediate, and slow motional regimes and illustrates the high sensitivity of the line shape to motional rate. 

Superhyperfine interactions are rarely observed in the ESR spectrum of the VO + ion because the unpaired electron interacts only weakly with the hgand nuclei, so that often the size of the coupling is less than the ESR bandwidth. This problem has been surmounted through the use of ENDOR spectroscopy. In ENDOR spectroscopy, molecules with their V=0 axes either parallel or perpendicular to the direction of the static magnetic field are selectively irradiated. In this way, the anisotropic superhyperfine coupling constants of H and " N and the " N quadrupolar coupling constants can be obtained. 

The isotropic g and a values are now replaced by two 3x3 matrices representing the g and A tensors and which arise from the anisotropic electron Zeeman and hyperfine interaction. Other energy terms may also be included in the spin Hamiltonian, including the anisotropic fine term D, for electron-electron interactions, and the anisotropic nuclear quadrupolar interaction Q, depending on the nucleus. Usually the quadrupolar interachons are very small, compared to A and D, are generally less than the inherent linewidth of the EPR signal and are therefore invisible by EPR. They are readily detected in hyperfine techniques such as ENDOR and HYSCORE. All these terms (g. A, D) are anisotropic in the solid state, and must therefore be defined in terms of a tensor, which will be explained in this section. 

Since the electron is not localized at one position in space. Equation 1.35 must be averaged over the electron probabihty distribution funcbon. H is averaged to zero when the electron cloud is spherical (as in s orbitals) and comes to a finite value for axially symmetric orbitals. The magnitude of the anisotropic hyperfine interaction then depends on the orientation of the paramagnehc system with respect to the external field. 

At small distances, the two unpaired electrons will experience a strong dipole-dipole interaction analogous to the interaction between electronic and nuclear magnetic dipoles, and this gives rise to anisotropic hyperfine interactions. The electron-electron interaction is described by the spin-spin Hamiltonian given by ... 

Here g and gjL are the electronic g factors for the magnetic field, respectively parallel and perpendicular to the symmetry axis, A is now the isotropic hyperfine interaction constant, and B is the anisotropic hyperfine interaction constant. The dependence on magnetic field orientation is given by the function (3 cos —1), where Oh is the angle between the magnetic field and the symmetry axis. 

Copper NMR was used to gauge the quality of [Ni/Cu] " and [Co/Cu] superlattices synthesized by the ion sputtering method. The authors noted that the shapes of the spectra vary noticeably with the change in angle between the interface planes and the external field. This is a unique feature of superlattice systems, not observed in bulk metals, and which can offer information on the electronic states in the copper layers. A study of CUAI2 by A1 and Cu NMR investigated quadrupole and anisotropic shift interactions between 3 and 40 MHz. 

---