Zeeman electronic effect

This is called the Zeeman electronic effect and the energy difference, AE, is given by ... 

Fig. 4.25 Under an applied magnetic field, Bq, the interaction between an unpaired electron and the magnetic field results in a splitting of the energy levels (the Zeeman electronic effect).

This splitting in the energy level is similar to the Zeeman effect that causes separation of electronic states in a magnetic field. It is sometimes referred to in NMR as the Zeeman nuclear effect. 

Low-spin Fe(iii) porphyrins have been the subject of a number of studies. (638-650) The favourably short electronic spin-lattice relaxation time and appreciable anisotropic magnetic properties of low-spin Fe(iii) make it highly suited for NMR studies. Horrocks and Greenberg (638) have shown that both contact and dipolar shifts vary linearly with inverse temperature and have assessed the importance of second-order Zeeman (SOZ) effects and thermal population of excited states when evaluating the dipolar shifts in such systems. Estimation of dipolar shifts directly from g-tensor anisotropy without allowing for SOZ effects can lead to errors of up to 30% in either direction. Appreciable population of the excited orbital state(s) produces temperature dependent hyperfine splitting parameters. Such an explanation has been used to explain deviations between the measured and calculated shifts in bis-(l-methylimidazole) (641) and pyridine complexes (642) of ferriporphyrins. In the former complexes the contact shifts are considered to involve directly delocalized 7r-spin density... 

Dean et al [7] measured the Zeeman splitting of a luminescence line involving the 2p donor state, obtaining the electron effective mass m t=(0.24 0.01)mo and m /m, =0.36 0.01 for n-type cubic crystals. Measurements of infrared Faraday rotation due to free carriers were made by Ellis and Moss [8] at room temperature in a number of n-type hexagonal specimens belonging to the 6H and 15R polytypes of silicon carbide. One component of the total density-of-states effective mass was explicitly determined by this method. A value for the... 

More direct determination of electron effective masses was first performed by Kaplan et al [16] using electron cyclotron resonance (ECR) in n-type 3C-SiC epitaxially grown onto a silicon substrate. They obtained transverse effective mass m t = (0.247 0.011) n, and longitudinal effective mass m, = (0.667 0.015) m0. The effective masses derived from cyclotron resonance agree, within experimental error, with the values obtained from Zeeman luminescence studies [7] of small bulk crystals. An average effective mass of an electron, given by the equation me = (m t2m, )l/3, is 0.344m0. Recently, similar ECR measurements were made by Kono et al [17]. 

Not only can electronic wavefiinctions tell us about the average values of all the physical properties for any particular state (i.e. above), but they also allow us to tell us how a specific perturbation (e.g. an electric field in the Stark effect, a magnetic field in the Zeeman effect and light s electromagnetic fields in spectroscopy) can alter the specific state of interest. For example, the perturbation arising from the electric field of a photon interacting with the electrons in a molecule is given within die so-called electric dipole approximation [12] by ... 

From accurate measurements of the Stark effect when electrostatic fields are applied, information regarding the electron distribution is obtained. Further Information on this point is obtained from nuclear quadrupole coupling effects and Zeeman effects (74PMH(6)53). 

Another legacy of the late nineteenth century was identification of the electron by an appropriate interpretation of the Pieter Zeeman effect in 1896, and more especially by J. J. Thomson s experiments the... 

The number of energy levels found to date, with the aid of the Zeeman effect and the isotope shift data, is 605 even and 586 odd levels for Pu I and 252 even and 746 odd for Pu II. The quantum number J has been determined for all these levels, the Lande g-factor for most of them, and the isotope shift for almost all of the Pu I levels and for half of those of Pu II. Over 31000 lines have been observed of which 52% have been classified as transitions between pairs of the above levels. These represent 23 distinct electron configurations. 

If the electric quadrupole splitting of the 7 = 3/2 nuclear state of Fe is larger than the magnetic perturbation, as shown in Fig. 4.13, the nij = l/2) and 3/2) states can be treated as independent doublets and their Zeeman splitting can be described independently by effective nuclear g factors and two effective spins 7 = 1/2, one for each doublet [67]. The approach corresponds exactly to the spin-Hamiltonian concept for electronic spins (see Sect. 4.7.1). The nuclear spin Hamiltonian for each of the two Kramers doublets of the Fe nucleus is ... 

Energy level splitting in a magnetic field is called the Zeeman effect, and the Hamiltonian of eqn (1.1) is sometimes referred to as the electron Zeeman Hamiltonian. Technically, the energy of a... 

An exception to this rule arises in the ESR spectra of radicals with small hyperfine parameters in solids. In that case the interplay between the Zeeman and anisotropic hyperfine interaction may give rise to satellite peaks for some radical orientations (S. M. Blinder, J. Chem. Phys., 1960, 33, 748 H. Sternlicht,./. Chem. Phys., 1960, 33, 1128). Such effects have been observed in organic free radicals (H. M. McConnell, C. Heller, T. Cole and R. W. Fessenden, J. Am. Chem. Soc., 1959, 82, 766) but are assumed to be negligible for the analysis of powder spectra (see Chapter 4) where A is often large or the resolution is insufficient to reveal subtle spectral features. The nuclear Zeeman interaction does, however, play a central role in electron-nuclear double resonance experiments and related methods [Appendix 2 and Section 2.6 (Chapter 2)]. 

We can now extend the spin Hamiltonians by making combinations of T, with B, and/or S, and/or I, and since we are interested in the effect of strain on the g-value from the electronic Zeeman interaction (B S), the combination of interest here is T B S. 

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