Zeeman perturbations

When the Zeeman-perturbation term is applied to these functions, we obtain for the g values... 

Fig. 3 Scheme of the calculation of energy levels in atoms, ions and unimetal complexes. The weak-field path (a) + (b) + (c). The strong-field path (b) + (a) + (c). The multiplet path (a) + (c) + (b). The crystal-field multiplets represent an appropriate basis for involvement of the Zeeman perturbation in the magnetic field... 

The rotational and Zeeman perturbation Hamiltonian (X) to the electronic eigenstates was given in equation (8.105). It did not, however, contain terms which describe the interaction effects arising from nuclear spin. These are of primary importance in molecular beam magnetic resonance studies, so we must now extend our treatment and, in particular, demonstrate the origin of the terms in the effective Hamiltonian already employed to analyse the spectra. Again the treatment will apply to any molecule, but we shall subsequently restrict attention to diatomic systems. 

Matrix Elements of the Zeeman Perturbation W = r(r2 — z2) in the Scaled Hydrogenic Basis"... 

Perturbation Corrections to the Ground-State Energy up to 10th Order for the Zeeman Perturbation"... 

Up to now, we have considered the A — B system in absence of any external perturbation. However the most appropriate methods to study the nature and the relative energies of the low lying states in A - B consist of observing the response of the system to an external magnetic field H. In this case, we have to add to Eq. (2) [or (2) + (3)] a Zeeman perturbation of the form ... 

The Zeeman perturbation is finally expressed as the sum of the local contributions ... 

Since the ground state of the compound is the singlet (vide infra), it is not necessary to introduce local anisotropy or anisotropic interaction terms in Eq. (83). The Zeeman perturbation is ... 

Apparently the zero field splitting within the ground state is very weak since XmT does not exhibit any deviation from the Curie law below 10 K. This is confirmed by the EPR spectrum at 4.2 K where no fine structure is detected. This spectrum exhibits the AMS = 1 allowed transition at g = 1.991 and the AMS = 2, 3 and 4 forbidden transitions of decreasing intensity at half, third and quarter-field respectively. The theoretical expression for the magnetic susceptibility has been established from the spin state structure of Fig. 41 and the Zeeman perturbation expressed as ... 

Let us examine now the consequences of this irregularity as far as the temperature dependence of XmT is concerned, xm being the magnetic susceptibility per AB unit. The Zeeman perturbation to add to Eq. (93) is ... 

Key Words Chlorine-35, Chorine-37, Bromine-79, Bromine-81, Iodine-127, Quadrupolar nuclei, Zeeman-perturbed NQR, Solid-state NMR, Electric field gradient, Magnetic shielding tensor, Chemical shift tensor, Quantum chemical calculations, Ab initio calculations. 

TABLE 16 Bromine-79/81 solid-state NMR data for molecular systems (mainly from Zeeman-perturbed NQR measurements)... 

Subsequently, K. Rao and Murty measured the Br Zeeman-perturbed NQR spectrum, but could not resolve the three sites and assigned all three sites i q = 0.12 0.03. ... 

Zeeman-perturbed NQR on a single crystal. Temperature dependence also studied. 

The only chlorate which has been significantly studied using chlorine SSNMR is sodium chlorate. Many early Zeeman-perturbed chlorine NQR studies feature analyses of this salt. It is not surprising therefore, that one of the early chlortne-35 SSNMR studies was on this material, carried out by Kawamori and in 1963. The authors studied a single crystal and reported the resonance frequency for multiple orientations. Bain and co-workers ° re-examined a single crystal of NaClOa recently to confirm the validity of their theoretical approach for the exact calculation of combined Zeeman and quadrupolar interactions. 

Although this review is aimed at coverirtg high-field NMR experimertts on diamagnetic solids, a great number of studies have been published which serve to highlight the complimentary nature between Zeeman-perturbed NQR and... 

The first reports of Zeeman-perturbed bromine NQR, both using single crystals of NaBrQa, confirmed prior measurements of the Br magnetic dipole moment ° and also highlighted the fact that Kriiger s ° Zeeman-perturbed NQR theory was valid for both bromine isotopes. ... 

Subsequent Zeeman-perturbed NQR experiments were generally used to determine tjq (which is not possible using a pure NQR spectrum of an 7 = 3/2 nucleus), the orientation of the EEG tensor in the crystal frame, and could also be used to determine the bond character for the atoms directly bound to the bromine... 

Doane and Flultsch used a single crystal of NaBrOa to demonstrate the interesting possibility of using the Zeeman-perturbed NQR transitions to modify the signal intensity associated with the Br Zeeman transitions by irradiating the sample at NQR transition frequencies while in a weak magnetic field.This information was subsequently used to determine quadrupolar relaxation transition probabilities. ... 

Zeeman-perturbed NQR was applied by Kehrer et al. to determine the EFG tensor in glycyl-L-alanine hydroiodide monohydrate. Although this is not a typical solid-state NMR study, it is interesting to quote the quadrupolar parameters, Cq( I) = 74.04 MHz and rjQ = 0.776 (at 274.5 K) since the corresponding hydrobromide salt is isomorphous and could be of interest for further study. 

We have seen that the construction of the Zeeman operator matrix for a general triad is a complex task the Zeeman perturbation couples the states of the adjacent total spins and the states of the adjacent intermediate spins. Under certain assumptions, however, it can be considerably simplified. 

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