Spin and multiplicity

FIGURE 10 NMR spectra of the spin quadrupolar nucleus Rb, taken under (top) static, (middie two) magic angle spinning, and (bottom) conditions of magic angle spinning, and multiple quantum coherence (MQMAS). 

To fill out Table 8-1, change the element symbols in the last line to Li, Be, or B and designate the charge and spin multiplicities as 1 1, 2 1, 3 1 in that order. In line 5, the first number is the single positive charge and the second number is the spin multiplicity, 1 for paired electronic spins and 2 for an unpaired election. A... 

To use HyperChem for calculations, you specify the total molecular charge and spin multiplicity (see Charge, Spin, and Excited State on page 119). The calculation selects the appropriate many-electron wave function with the correct number of alpha or beta electrons. You don t need to specify the spin function of each orbital. 

Ebert, H., and Battocletti, M., 1996, Spin and orbital polarized relativistic multiple scattering theory - with applications to Fe, Co, Ni and Fe cCoi- c , Solid State Commun. 98 785. 

SPIN AND ORBITAL POLARIZED RELATIVISTIC MULTIPLE SCATTERING THEORY... 

In other cases, discussed below, the lowest electron-pair-bond structure and the lowest ionic-bond structure do not have the same multiplicity, so that (when the interaction of electron spin and orbital motion is neglected) these two states cannot be combined, and a knowledge of the multiplicity of the normal state of the molecule or complex ion permits a definite statement as to the bond type to be made. 

A term label like for example, is thus no longer strictly meaningful for it implies constant spin- and orbital angular momentum properties (5 = 1, L = 3). One consequence of spin-orbit coupling is a scrambling of the two kinds of angular momentum. So a nominal term may really more properly be described as a mixture of terms of different spin-multiplicity as, for example, in Eq. (4.10). 

To understand how the chemical shift and multiplicity information is separated, we need to reconsider the spin-echo sequence described earlier. 

In tier (1) of the diagram (for the electronic structure of iron(III)), only the total energy of the five metal valence electrons in the potential of the nucleus is considered. Electron-electron repulsion in tier (2) yields the free-ion terms (Russel-Saunders terms) that are usually labeled by term ° symbols (The numbers given in brackets at the energy states indicate the spin- and orbital-multiplicities of these states.)... 

Fig. 2.9.2 Radiofrequency, field gradient and current distributions requires a three-dimen-ionic current pulse sequences for two-dimen- sional imaging sequence [see Figure 2.9.1(a)] sional current density mapping. TE is the Hahn and multiple experiments with the orientation spin-echo time, Tc is the total application time of the sample relative to the magnetic field of ionic currents through the sample. The 180°- incremented until a full 360°-revolution is pulse combined with the z gradient is slice reached. The polarity of the current pulses...

Floquet theory [60] represents a powerful method to analyze and describe NMR experiments including, in the present context, methods for dipolar recoupling. In particular the bimodal variants are promising in the sense that they may handle perturbations/interactions involving multiple time periodicities, as for example induced by combined sample spinning and rf irradiation in the case of dipolar... 

The relationship between different components of orbital angular momentum such as Lz and Lx can be investigated by multiple SG experiments as discussed for electron spin and photon polarization before. The results are in fact no different. This is a consequence of the noncommutativity of the operators Lx and Lz. The two observables cannot be measured simultaneously. While total angular momentum is conserved, the components vary as the applied analyzing field changes. As in the case of spin or polarization, measurement of Lx, for instance, disturbs any previously known value of Lz. The structure of the wave function does not allow Lx to be made definite when Lz has an eigenvalue, and vice versa. 

Table 2.3. Calculated bond lengths and energies of first-row transition metal monofluorides in low-spin and high-spin configurations (an asterisk marks the spin multiplicity of lowest energyj...

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