Constants hyperfine

The above-mentioned set of Ki values are deduced from analyses based on the hyperfine constants of mononuclear FeS4 centers. However, we have already stressed that local parameter values are not necessarily transferable from one type of iron—sulfur center to an-... 

It is quite apparent (Figures 3,4) that the hyperfine constants of the central and terminal atoms in the two radicals are strongly influenced by the out-of-plane displacement. For the central atom, the coupling increases with 161 and tms is clearly related to a strong change in hybridization. 

Here, /3 and / are constants known as the Bohr magneton and nuclear magneton, respectively g and gn are the electron and nuclear g factors a is the hyperfine coupling constant H is the external magnetic field while I and S are the nuclear and electron spin operators. The electronic g factor and the hyperfine constant are actually tensors, but for the hydrogen atom they may be treated, to a good approximation, as scalar quantities. 

For the hydrogen atom, two such resonance conditions occur, giving rise to two lines separated by 506 G, which is just the value of a for the hydrogen atom [Eq. (ID)]. The spectrum would look the same for a single crystal or for a polycrystalline sample because the g factor and the hyperfine constant are isotropic. 

The NO2 molecule offers an example which illustrates this point. The spectrum of N02 molecules rigidly held on MgO at —196° is characterized by gxx = 2.005, gyv = 1.991, and gzz = 2.002 (29). If this molecule were rapidly tumbling, one would expect a value of Qa.v — 1 999. The spectrum of NO2 absorbed in a 13X molecular sieve indicates an isotropic gzv = 2.003 (.80), which is within experimental error of the predicted value for NO2 on MgO. The hyperfine constants confirm that NO2 is rapidly tumbling or undergoing a significant libration about some equilibrium position in the molecular sieve (81). 

The spin Hamiltonian for the hydrogen atom will be used to determine the energy levels in the presence of an external magnetic field. As indicated in Section II.A, the treatment may be simplified if it is recognized that the g factor and the hyperfine constant are essentially scalar quantities in this particular example. An additional simplification results if the z direction is defined as the direction of the magnetic field. For this case H = Hz and Hx = Hv = 0 hence,... 

The hyperfine constant a in Eq. (1) was also taken to be a scalar quantity for the hydrogen atom however, it is in general a tensor because of the various directional interactions in a paramagnetic species. The hyperfine term in the spin Hamiltonian is more correctly written as S-a-I, where a is the hyperfine coupling tensor. 

The electron hyperfine interaction thus has important effects on both NMR relaxation and frequency shifts, and can provide valuable information on the incorporation of magnetic ions into semiconductor lattices and the resulting electronic structure as characterized by transferred hyperfine constants. Examples in Sect. 4 will show how the possible incorporation of magnetic ions into semiconductor nanoparticles can be studied by NMR. 

The electron spin resonance (ESR) spectra of free radicals obtained by electrolytic or microsomal reduction of several potential antiprotozoal 1,2,5-oxadiazoles were characterized and analyzed. Ab initio MO calculations were performed to obtain the optimized geometries, and the theoretical hyperfine constant was carried out using Zerner s intermediate neglect of differential overlap (ZINDO) semi-empirical methodology. DFT was used to rationalize the reduction potentials of these compounds <2003SAA69>. 

Besides the hyperfine constants for the muonium impurity itself, one can also investigate the so-called superhyperfine interaction for the neighboring 29Si atoms. These values have also been accurately measured (Kiefl et al., 1988) with level-crossing resonance.For the anisotropic parameters, it is customary to compare b with Aj,ree, which is an average of r 3 determined for the valence p-orbital. The results are given in Table II. Both... 

Using the approach described in the previous section, Van de Walle (1990) also calculated the isotropic hyperfine constant for muonium at T in Si. The calculated value for iK0)]x/ experimental result (0.45) for normal muonium in Si. Motional averaging slightly lowers the theoretical value, bringing it in even closer agreement with experiment. 

The effect of zero-point motion on the hyperfine constant has been the subject of some controversy. Manninen and Meier (1982) argued that motional averaging (over all positions sampled in the vibrational ground... 

The ozonide ion has widely spaced energy levels, and to first order the g values are not influenced by the host lattice or the surface. Thus, the absolute values of the g values are useful in the identification of the ion. These g values, along with the hyperfine coupling constants, are given in Table I. The three sets of hyperfine constants indicate that the oxygen atoms are not equivalent, at least when the ozonide ion is formed according to reaction 2. The geometry of the ion on MgO is believed to be... 

As the TieS lengthen and l/Tie (s ) approaches the size of the electron—nuclear interaction, considerable NMR line broadening can occur, and it may not be possible to acquire high-resolution NMR spectra under these conditions. The effect of Tie on the nuclear relaxation times is discussed in more detail in ref 22. Large hyperfine constants are observed (of many MHz) when the nuclear and electronic spins are on the same atom. For example, a hyperfine constant A/h of —324 MHz was measured by electron... 

The sign (and size) of the hyperfine constant Ac/h (Hz) determines the direction (and size) of the shift... 

So, STOs give "better" overall energies and properties that depend on the shape of the wavefunction near the nuclei (e.g., Fermi contact ESR hyperfine constants) but they are more difficult to use (two-electron integrals are more difficult to evaluate especially the 4-center variety which have to be integrated numerically). GTOs on the other hand are easier to use (more easily integrable) but improperly describe the wavefunction near the nuclear centers because of the so-called cusp condition (they have zero slope at R = 0, whereas Is STOs have non-zero slopes there). 

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. 

In this paper, the main features of the two-step method are presented and PNC calculations are discussed, both those without accounting for correlation effects (PbF and HgF) and those in which electron correlations are taken into account by a combined method of the second-order perturbation theory (PT2) and configuration interaction (Cl), or PT2/CI [100] (for BaF and YbF), by the relativistic coupled cluster (RCC) method [101, 102] (for TIF, PbO, and HI+), and by the spin-orbit direct-CI method [103, 104, 105] (for PbO). In the ab initio calculations discussed here, the best accuracy of any current method has been attained for the hyperfine constants and P,T-odd parameters regarding the molecules containing heavy atoms. 

A similar increase in the values for the hyperfine constants and parameters of the P,T-odd interactions when the correlations with the core shells (primarily, 5s, bp) are taken into account is also observed for the BaF molecule [93], as one can see in Table 3. Of course, the corrections from the 4/-electron excitations are not required for this molecule. The enhancement factor for the P,T-odd effects in BaF is three times smaller than in YbF mainly because of the smaller nuclear charge of Ba. 

The hyperfine constants are measured in an inert gas matrix [124] and the semiempirical Wi values [25] are based on these data. 

The P,T-parity nonconservation parameters and hyperfine constants have been calculated for the particular heavy-atom molecules which are of primary interest for modern experiments to search for PNC effects. It is found that a high level of accounting for electron correlations is necessary for reliable calculation of these properties with the required accuracy. The applied two-step (GRECP/NOCR) scheme of calculation of the properties described by the operators heavily concentrated in atomic cores and on nuclei has proved to be a very efficient way to take account of these correlations with moderate efforts. The results of the two-step calculations for hyperfine constants differ by less than 10% from the corresponding exper-... 

Selected 17 O Hyperfine Constants and Total Spin Densities for Diatomic Oxygen Species with Equivalent Oxygen Nuclei... 

The g tensors and hyperfine constants of the paramagnetic centers observed in irradiated NH4Y zeolites after various activation treatments are given in Table VIII. Despite the abundance of experimental results, many of the structures proposed for these centers should be regarded as suggestive rather than definitive, as previously noted by Kasai and Bishop (264). Neither the axially symmetric g tensor of the V center associated with two aluminum atoms nor the isotropic g tensor of the V center associated with one aluminum atom reported by Vedrine et al. (266) is consistent with the symmetry of the respective models proposed above. 

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