Magnetic resonance electronic Zeeman interaction

For nitroxides in dilute liquid solution, the generally anisotropic spin Hamilton operator is simplified tremendously and, if imresolved proton hyperfine couplings are treated as line broadening, only the electron-Zeeman interaction and the hyperfine coupling to the magnetic nucleus (7 = 1) remain [20]. The g- and hyperfine (4-) tensors are averaged to isotropic values due to fast motion of the spin probe and the resonance condition for the irradiated microwave becomes... 

In Equation (6) ge is the electronic g tensor, yn is the nuclear g factor (dimensionless), fln is the nuclear magneton in erg/G (or J/T), In is the nuclear spin angular momentum operator, An is the electron-nuclear hyperfine tensor in Hz, and Qn (non-zero for fn > 1) is the quadrupole interaction tensor in Hz. The first two terms in the Hamiltonian are the electron and nuclear Zeeman interactions, respectively the third term is the electron-nuclear hyperfine interaction and the last term is the nuclear quadrupole interaction. For the usual systems with an odd number of unpaired electrons, the transition moment is finite only for a magnetic dipole moment operator oriented perpendicular to the static magnetic field direction. In an ESR resonator in which the sample is placed, the microwave magnetic field must be therefore perpendicular to the external static magnetic field. The selection rules for the electron spin transitions are given in Equation (7)... 

The unpaired electron with its spin S = 1/2 in a sample disposed into the resonator of the EPR spectrometer interacts magnetically a) with the external magnetic field H (Zeeman interaction) b) with the nuclear spin of the host atom or metal ion / (hyperfine interaction) c) with other electron spins S existing in the sample (dipole-dipole interaction). In the last case, electrons can be localized either at the same atom or ion (the so called fine interaction), for example in Ni2+, Co2+, Cr3+, high-spin Fe3+, Mn2+, etc., or others. These interac-tions are characterized energetically by the appropriate spin-Hamiltonian... 

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. 

The Zeeman Hamiltonian given in equation (8.322) is sufficient to provide a semi-quantitative description of the magnetic effects but, as was described in our discussion of the magnetic resonance spectrum of H2, it is an approximate form. The local magnetic field experienced by the H and F nuclei is not quite the same as the applied laboratory field because of shielding effects due to the surrounding electrons. In addition the rotational Zeeman interaction should be described not by the single constant... 

The electron Zeeman effect arises from the interaction of unpaired electrons with the external magnetic field and determines the position at which resonance occurs [i.e., the deviation of the g-factor from the free electron value (g = 2.00232)]. Species with axial symmetry, such as Cu2+ and V " " (i.e., with one principal axis of symmetry, conventionally the z-axis, and equivalent x> and y-axes), exhibit two g-values, usually labeled gy = i.e., the g-value along... 

The most important interaction in NMR is the coupling of the nuclear spins to the applied magnetic field. This is the Zeeman interaction (cf. Section 2.2.1). In a strong magnetic field, it determines the value of the resonance frequency in zeroth order. For a more accurate description of the NMR frequency, the chemical shift and the indirect coupling of spins have to be considered in liquids. Both depend on the details of the electron states in the neighbourhood of the nuclei. Therefore, they are used as fingerprints of the chemistry of the material. 

The interaction of the spin magnetic moment with the orbital magnetic moment of the unpaired electron leads to an orientationally dependent shift of the resonance frequency. This effect is normally described by an effective spin operator S and an anisotropic g matrix. The quantimi-mechanical Hamilton operator for the interaction of the electron spin with the external magnetic field Zeeman interaction) can, therefore, be described by... 

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