Zeeman frequencies

In spin relaxation theory (see, e.g., Zweers and Brom[1977]) this quantity is equal to the correlation time of two-level Zeeman system (r,). The states A and E have total spins of protons f and 2, respectively. The diagram of Zeeman splitting of the lowest tunneling AE octet n = 0 is shown in fig. 51. Since the spin wavefunction belongs to the same symmetry group as that of the hindered rotation, the spin and rotational states are fully correlated, and the transitions observed in the NMR spectra Am = + 1 and Am = 2 include, aside from the Zeeman frequencies, sidebands shifted by A. The special technique of dipole-dipole driven low-field NMR in the time and frequency domain [Weitenkamp et al. 1983 Clough et al. 1985] has allowed one to detect these sidebands directly. 

A typical temperature dependence of is shown in fig. 53. Clough et al. [1981] have found a universal correlation between the temperature at which has a minimum, r in, and A, when the measurements are performed at the same Zeeman frequency. This correlation, demonstrated in fig. 54, holds for all molecular solids studied so far, with A covering a range of four orders... 

Fig. 54. Universal correlation between T , and tunneling frequency A. The values of A are given in peV (1 peV 8.066 X 10 cm = 2.42 x 10 Hz). The Zeeman frequency equals 21 MHz. The points correspond to different chemical species.

HYSCORE spectra of zeaxanthin radicals photo-generated on silica-alumina were taken at two different magnetic fields B0=3450G and B0=3422G, respectively. In order to combine the data from the two spectra, the field correction was applied (Dikanov and Bowman 1998). The correction consists of a set of equations that allow transformation of spectra to a common nuclear Zeeman frequency. The set of new frequencies was added to that of the former spectrum and plotted as the squares of the frequencies v2a and v2p. Examples of these plots can be found in Focsan et al. 2008. 

The principle of the ENDOR method is illustrated in Fig. 1. It refers to the most simple spin system with an electron spin S = 1/2 and a nuclear spin I = 1/2 for which an isotropic hf interaction, aiso, is considered. In a steady state ENDOR experiment4, an EPR transition (A, D), called the observer, is partly saturated by microwave radiation of amplitude B while a driving rf field of amplitude B2, called the pump, induces nuclear transitions. At frequencies vj and v2, the rf field tends to equalize the populations within the ms-states. This alters the degree of saturation of the observer so that, in the display of the EPR signal height versus the radio frequency, two ENDOR lines at transition frequencies vj = aiso/2 - vn (A, B) and v2 = ais0/2 + v (C, D) will be observed (v = / NgnBo denotes the nuclear Zeeman frequency for a static field B0). 

In the case of gas lasers the discharge conditions, and therefore also the laser intensity, change with the magnetic field strength, and often the maximum Zeeman frequency shift is not limited by technical considerations (greatest possible magnetic fields) but by the fact that the laser intensity drops to zero f... 

Zeeman frequencies 10.5 and 21 MHz and Tmin located in the range 20-150 K, correspond to rotation barrier heights from 0.65 to 3.4kcal/ mol. 

Zeeman broadening can be reduced by motional averaging providing that the rate at which the atom transverse the trap is large compared to the Zeeman frequency spread. The average linewidth is given by... 

Left ESEEM spectrum of a solution containing triphosphate and vanadyl ions in the ratio 3 1, pH = 5, c(VO +) = 0.7mM, recorded at the nij = — V2 EPR transition and v- are the Zeeman frequencies for and H, respectively. The doublets at 5.3 and 6.7 MHz (superhyperfine coupling constants 1-1.5 MHz) are indicative of direct bonding of phosphate to VO, as represented by the proposed structure (inset).The presence of water/hydroxide in the coordination sphere of vanadium is inferred from the respective HYSCORE spectrum. Reproduced from S. A. Dikanov et at, J. Am. Chem. Soc. 124, 2969-2978. Copyright (2002), with permission from the American Chemical Society. Right section of the structure of hydroxyapatite, with two phosphorus sites arbitrarily replaced by vanadium (full circles). The drawing of the apatite structure was provided by Barbara Albert, Technical University of Darmstadt, Germany. 

The chemical shift range for deuterium, as well as its dipolar and scalar interactions, are of the order of only a few (<5) kHz at 11.7 T. Thus, they can be ignored in view of the dominant quadrupolar coupling constant, which is e Qlh — 167 kHz for aliphatic C— H bonds [19, 21]. Here, e is the elementary charge and eq the largest field gradient. Q = 2.875 x 10 cm is the scalar quadrupole moment for the deuteron, and h is Planck s constant. Since the deuterium quadrupolar frequency is much smaller than the Zeeman frequency difference, the H NMR spectrum can be described by treating the quadrupolar interaction as a first-order perturbation of the Zeeman interaction [1, 19, 21, 60]. 

The action of the external fields like electric or magnetic can be taken into accotmt in a very general way. External fields, as a rule, lift the degeneracy of different magnetic sublevels of the angular momentum state. It means that in the external field magnetic sublevels are split and cause appearance of the nonzero Zeeman frequencies = Em, —Em, )/Ti. For different molecules in different (electric... 

Another way to demonstrate the same chemistry and identify the surface species is to utilize the specific motional averaging of a methyl group as a signature of the ethylidyne. For this example Slichter and coworkers [ 105] chose solid-state NMR. For a static deuteron, the resonance frequency of a given isochromat, relative to the Zeeman frequency is given by the expression... 

Overlap of lines can make analysis difficult when several nuclei contribute in the one-dimensional (ID) two- and three-pulse ESEEM spectra. Eollowing the development in NMR, methods to simplify the analysis involving two-dimensional (2D) techniques have therefore been designed. The Hyperfine Sublevel Correlation Spectroscopy, or HYSCORE method proposed in 1986 [14] is at present the most commonly used 2D ESEEM technique. The HYSCORE experiment has been applied successfully to study single crystals, but is more often applied to orienta-tionally disordered systems. It is a four-pulse experiment (Fig. 2.23(a)) with a k pulse inserted between the second and the third k/2 pulse of the three-pulse stimulated echo sequence. This causes a mixing of the signals due to the two nuclear transitions with m.s = Vi of an 5 = Vi species. For a particular nucleus two lines appear at (v , V ) and (V ", v ) in the 2D spectrum as shown most clearly in the contour map (d) of Fig. 2.23. The lines of a nucleus with a nuclear Zeeman frequency... 

Fig. 2.23 Schematic HYSCORE spectrum showing (a) the HYSCORE sequence, (b) the 2D time-domain modulation signal, (c) the 2D HYSCORE spectrum and (d) the contour plot of a single crystal sample for an 5 = Vi species containing a H nucleus with an axitilly symmetric hyper-fine coupling. The magnetic field is at an angle 0 = 10° with the A axis. The nuclear Zeeman frequency vh 15 MHz is larger than the hyperflne coupling, i.e. Ai I < A < 2 vh...

HYSCORE has a higher sensitivity in the region of low nuclear frequencies than that of ENDOR spectroscopy. Single crystal measurements have therefore been applied to studies of nitrogen-containing paramagnetic species (nuclear Zeeman frequency v( " N) = 1 MHz at X-band) of interest in biochemical and fundamental applications. The local structure around the species may be obtained as discussed below for the radical H3CCHCOO in irradiated /-alanine. 

Cross relaxation Transfer of energy between spins with different Zeeman frequencies... 

Fig. 3.33 Schematic HYSCORE contour plot for an S = Vi single crystal species with an anisotropic hyperfine coupling due to two I = Vi nuclei. The spots symmetrically displaced from the diagonals correspond to nuclear frequencies with electron quantum number ms = 14.The correlation between the nuclear transitions for a particular nucleus is achieved by the Jt pulse inserted between the second and the third tt/2 pulse of the three-pulse stimulated echo sequence. The spots in the right quadrant are due to a nucleus with frequencies (Vd, vpi) for the two nuclear transitions corresponding to ms = 14. The frequencies to the right are small compared to the nuclear Zeeman frequency, while the spots in the left quadrant are for the opposite case with large frequencies (v, vpa)...

---