Spin-dependent properties

The above experimental developments represent powerful tools for the exploration of molecular structure and dynamics complementary to other techniques. However, as is often the case for spectroscopic techniques, only interactions with effective and reliable computational models allow interpretation in structural and dynamical terms. The tools needed by EPR spectroscopists are from the world of quantum mechanics (QM), as far as the parameters of the spin Hamiltonian are concerned, and from the world of molecular dynamics (MD) and statistical thermodynamics for the simulation of spectral line shapes. The introduction of methods rooted into the Density Functional Theory (DFT) represents a turning point for the calculations of spin-dependent properties [7],... 

The results reported here use the Xa exchange-correlation function, which has historical interest and can be compared to past calculations. Within the local density approximation, parametrizations that include the correlation effects found in a uniform electron gas often give a better account of spin-dependent properties (19). Since correlation effects generally stabilize low spin species more than high-spin states (20), one would expect correlation effects to increase J over the values reported here, and this was indeed found in our earlier studies of oxidized three-iron clusters (9). Calculations on the reduced species using improved exchange-correlation potentials are in progress. 

The electronic and structural properties of a molecule may change when it is being exposed to external electrostatic fields. In some sense, the problem of calculating these responses is complementary to those discussed above for the spin-dependent properties. The DC field leads to an extra term in the Kohn-Sham equations... 

Because electrons interact only in pairs (i.e. there are no specifically many-body effects), there is no need to consider distribution functions higher than the pair function Pz. or> if spin-dependent properties are... 

However, there also exists a third possibility. By using a famous relation due to Dirac, the relativistic effects can be (in a nonunique way) divided into spin-independent and spin-dependent terms. The former are collectively called scalar relativistic effects and the latter are subsumed under the name spin-orbit coupling (SOC). The scalar relativistic effects can be straightforwardly included in the one-electron Hamiltonian operator h. Unless the investigated elements are very heavy, this recovers the major part of the distortion of the orbitals due to relativity. The SOC terms may be treated in a second step by perturbation theory. This is the preferred way of approaching molecular properties and only breaks down in the presence of very heavy elements or near degeneracy of the investigated electronic state. 

The anisotropy of the overall tumbling will result in the dependence of spin-relaxation properties of a given 15N nucleus on the orientation of the NH-bond in the molecule. This orientational dependence is caused by differences in the apparent tumbling rates sensed by various internuclear vectors in an anisotropically tumbling molecule. Assume we have a molecule with the principal components of the overall rotational diffusion tensor Dx, Dy, and l)z (x, y, and z denote the principal axes of the diffusion tensor), and let Dx< Dy< Dz. 

Properties of the selective pulses are used therefore twofold in such experiments. Firstly, a selective pulse selectively perturbs the selected spin and the perturbation is distributed in the course of the experiment among the coupled spins, depending on the type of coupling (scalar, dipolar) and depending on the type of exchange mechanism (polarization transfer, cross polarization or cross relaxation). Secondly, the phase (selective 90° pulse) or the frequency (selective 180° pulse) of the selective pulse serve to label the response of both the selected and the residual coupled spins as positive or negative. 

Nevertheless, calculation of such properties as spin-dependent electronic densities near nuclei, hyperfine constants, P,T-parity nonconservation effects, chemical shifts etc. with the help of the two-component pseudospinors smoothed in cores is impossible. We should notice, however, that the above core properties (and the majority of other properties of practical interest which are described by the operators heavily concentrated within inner cores or on nuclei) are mainly determined by electronic densities of the valence and outer core shells near to, or on, nuclei. The valence shells can be open or easily perturbed by external fields, chemical bonding etc., whereas outer core shells are noticeably polarized (relaxed) in contrast to the inner core shells. Therefore, accurate calculation of electronic structure in the valence and outer core region is of primary interest for such properties. 

The last term of Vpp in Eq. (3.90) is introduced so that the driving potential satisfies AVpp = 0. The term proportional to in Eq. (3.88) was omitted because it affects only the spatially uniform phase of the wave function. Thus, the wave function of the intermediate state has a spin-dependent phase factor exy)[iARmcngsJ qK)] added to the phase displayed in Eq. (3.17), and this property can be used to control relative phase between different spin states. It is possible to design the time dependence of R so that the last term of Vpp in Eq. (3.90) does not cause unwanted excitation after the rotation. Although the last term of Vpp compresses the wave function in the z-direction during the rotation around the z-axis, at the final time the wave function Ppp becomes that of the desired rotated state without compression or oscillation in the z-direction. 

Note that the Breit-type operators are often neglected in quantum chemistry because they yield small energy contributions in comparison to the instantaneous Coulomb interaction. However, the effects may not be negligible in highly accurate quantum chemical calculations or for spin- or magnetic-field-dependent properties such as those measured by magnetic resonance spectroscopies. 

In the solid state, II, III, and IV show 1 Ai ST2 spin equilibrium, while I is low-spin. In solution, II and III retain the spin equilibrium property, whereas IV is fully high-spin and I is low-spin over a temperature range of approximately 200 degrees. From the electronic spectra the critical field strength (crossover point) has been estimated to lie near 11700 cm-1. No solvent dependence has been observed. 

Some of the polycrystalline spin crossover systems of iron(II) described above retain their spin equilibrium property upon dissolution in appropriate solvents. The Evans NMR method of measuring the change of the paramagnetic shift with temperature is the most common technique to study the magnetic behaviour of such systems. The spin transition characteristics has been observed to depend on various chemical modi-... 

Electrically detected magnetic resonance (EDMR) is conceptually similar to ODMR, i.e. the magnetic resonance is observed through spin-dependent electrical rather than optical properties of a sample. Virtually all of the EDMR in GaN-based materials reported to date has bear performed on LEDs and so the device type will serve as a basis for the organisation of this section. Three basic device types have been studied m-i-n-n+ diodes, double heterostructures (DHs) and single quantum wells (SQWs). Some details on these structures can be found elsewhere in this volume [35] and in the original work. 

---