Allowed ESR transition

Use of (1.244) shows that the allowed ESR transitions are between levels 1 and 3 and between levels 2 and 4. The electron s spin flips, while the nuclear spin remains unchanged. The transition frequencies are... 

For an S = 1 system (e.g. a complex of Ni2+) with D = 0 the Zeeman term makes the energy levels equally spaced. The two allowed ESR transitions occur at the same energy... 

For instance, the allowed ESR transition 1(1 4) can be saturated by application of a sufficiently high microwave power (vide infra) so that the levels 1 and 4 are equally populated and consequently no ESR signal is observed. Now, a strong radiofrequecny field is appHed with a frequency, Vjif, given by the energy difference between the levels 3 and 4, i.e. 

Figure 9.14 Quintet state with an external field Bo interacting with one proton (I = 1/2). All allowed ESR transitions (a-d) and NMR transitions (1-5) are shown. By ENDOR, in first order, only the two NMR transitions directly connected to the observed ESR line are detectable [36].

High-field energy levels for a system with electron spin S = 1/2 and magnetic nuclei with I = 1/2 and 1 = 1. On the left are the levels at zero order where only the interaction with the external field is included. On the right are the energy levels according to Equation 12.22, where the spin-spin interactions have been included by first-order perturbation theory. The nuclear spin-spin interaction has been exaggerated relative to typical values in order to show the effect. The vertical lines correspond to the allowed ESR transitions, and below them is a stick representation of the spectrum that corresponds to these transitions. 

FIGURE 3 Schematic of the first-order spin energy levels of a hydrogen atom, showing successive interactions in the spin Hamiltonian, the allowed ESR transitions, and the spin wave functions. 

UV/VIS/NIR spectroscopy and ESR spectroscopy. The UV/VIS/NIR spectrum shows a sharp peak at 983 nm and a broad peak at 846 nm. These two absorbances are attributed to allowed NIR-transitions and these values are consistent with spectra of the cation obtained with other methods [2]. EPR spectroscopy of Cgg-cations, produced by different methods, leads to a broad distribution of measured g-values. These differences are caused by the short lifetime of the cation, the usually low signal-noise ratio and the uncertainty of the purity. The most reliable value imtil now is probably the one obtained by Reed and co-workers for the salt Cgg"(CBiiHgClg)-(g= 2.0022) [2,9] (see also Section 8.5). Ex situ ESR spectroscopy of above-mentioned bulk electrolysis solutions led to a g-value of2.0027 [8], which is very close to that of the salt, whereas the ESR spectra of this electro lyticaUy formed cation shows features not observed earlier. The observed splitting of the ESR signal at lower modulation amplitudes was assigned to a rhombic symmetry of the cation radical at lower temperatures (5-200 K). 

Fig. 7.10 The Zeeman splitting of the triplet states of the two differently-oriented molecules A and B in the naphthalene crystal (see Fig. 7.11) for three different orientations of the applied magnetic field Bq, each parallel to one of the principal axes of the A molecules. There are two allowed Am = 1 ESR transitions for each of the two molecular orientations A and B. (In the term diagram for Bol x/, these transitions are shown for simplicity only for the molecular orientation A).

ENDOR and FT ESEEM spectra differ mainly in the intensities of the lines, which in ESEEM are given by a factor related to the ESR transition probabilities. A necessary prerequisite for modulations in the time domain spectrum is that the allowed Ami = 0 and forbidden Ami = 1 hyperfine lines have appreciable intensities in ESR. The zero ESEEM amplitude thus predicted with the field along the principal axes of the hyperfine coupling tensor is of relevance for the analysis of powder spectra. Analytical expressions describing the modulations have been obtained for nuclear spins I = V2 and / = 1 [54, 57] by quantum mechanical treatments that take into account the mixing of nuclear states under those conditions. Formulae are reproduced in Appendix A3.4. 

Allowed and forbidden ESR transitions can also occur by the nuclear quadrupole interaction for / > V2. Analytical formulas are applicable when the quadrupole energy is small compared to the combined effect of hyperfine and nuclear Zeeman interactions [57]. Numerical solutions have been applied when this approximation does not hold [58]. Systems with S > Vi require special treatments [59, 60]. 

Considering the resolution of the nuclear frequency spectrum, this two-pulse echo experiment is not optimal. The nuclear frequencies are here measured as differences of frequencies of the ESR transitions, so that the line widths correspond to those of ESR transitions. The nuclear transitions have longer transverse relaxation times Tin and thus smaller line widths. In fact, if the second mw pulse is changed from a n pulse to a Ji/2 pulse, coherence is transferred to nuclear transitions instead of forbidden electron transitions. This coherence then evolves for a variable time T and thus acquires phase v r or vpT. Nuclear coherence cannot be detected directly, but can be transferred back to allowed and forbidden electron coherence by another nil pulse. The sequence (jt/2)-x-(Jt/2)-r-(jt/2)-x generates a stimulated echo, whose envelope as a function of T is modulated with the two nuclear frequencies v and vp. The combination frequencies v+ and v are not observed. The modulation depth is also 8 211. The lack of combination lines simplifies the spectrum and the narrower lines lead to better resolution. There is also, however, a disadvantage of this three-pnlse ESEEM experiment. Depending on interpulse delay x the experiment features blind spots. Thus it needs to be repeated at several x values. 

Electron Spin Resonance Spectroscopy. Several ESR studies have been reported for adsorption systems [85-90]. ESR signals are strong enough to allow the detection of quite small amounts of unpaired electrons, and the shape of the signal can, in the case of adsorbed transition metal ions, give an indication of the geometry of the adsorption site. Ref. 91 provides a contemporary example of the use of ESR and of electron spin echo modulation (ESEM) to locate the environment of Cu(II) relative to in a microporous aluminophosphate molecular sieve. 

UV-vis spectra of matrix-isolated intermediates are not so informative as matrix IR spectra. As a rule, an assignment of the UV spectrum to any intermediate follows after the identification of the latter by IR or esr spectroscopy. However, UV-vis spectra may sometimes be especially useful. It is well known, for example, that the energy of electronic transitions in singlet ground-state carbenes differs from that of the triplet species. In this way UV spectroscopy allows one to identify the ground state of the intermediate stabilized in the matrix in particular cases. This will be exemplified below. 

Spectroscopic techniques such as electron spin resonance (ESR) offer the possibility to "probe" the chemical environment of the interlayer regions. With the ESR technique, an appropriate paramagnetic ion or molecule is allowed to penetrate the interlayer, and chemical information is deduced from the ESR spectrum. Transition metal ions, such as Cu2+, and nitroxide radical cations, such as TEMPAMINE (4-amino-2,2,6,6-tetramethylpiperidine N-oxide) have been used as probes in this manner (6-14). Since ESR is a sensitive and non-destructive method, investigations of small quantities of cations on layer silicate clays at various stages... 

The allowed transition in ESR is diagrammed in Figure 2. The ESR experiment is commonly conducted at a fixed frequency near 9.5 x 109 Hz by scanning through a magnetic field range until absorption of electromagnetic radiation is detected at H0. The value of H0 can then be used to calculate the electron g-factor. 

Figure 3. Spin levels for an electron interacting with the N atom (1=1) in the nitroxide radical. The three allowed transitions generate an ESR spectrum with hyperfine splitting, A.

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