Hyperfine enhancement

The 14N hf and quadrupole parameters observed in Co(acacen) by Rudin et al.59 are the first magnetic data reported on equatorial nitrogen ligand nuclei in a low-spin Co(II) complex. Only two of the four predicted AmN = 1 ENDOR transitions (3.9) were observed for each nitrogen nucleus. A numerical calculation of the transition probabilities shows that the corresponding transitions in the other ms-state are at least ten times less intense (hyperfine enhancement). 

The change of the nuclear transition probability due to the electron spin is usually called hyperfine enhancement s and has first been discussed by Abragam The hyper-fine enhancement may be considered classically as originating from the modulation of the magnetic field Be produced by the electron at the nucleus. The size of Be is determined by the hf interaction between the electron and the corresponding nucleus. The field B " which induces nuclear transitions, is then given by the vector sum of B2 and the component of Be which oscillates with the same frequency as the applied field. 

The improved resolution in ENDOR spectra makes it possible not only to measure the hyperfine couplings with high accuracy, but also to observe splittings that are not resolved by ESR. An example is shown in Fig. 2.5 for the malonic acid radical, HCc (COOH)2 [24]. The ESR spectrum is a main doublet due to hyperfine coupling with the H at the Ca position. The resolution is limited by the line-width and the occurrence of forbidden and so-called spin flip lines discussed in Chapter 4. The ENDOR lines denoted V(t and Va are narrower than the ESR lines by more than an order of magnitude. As in the liquid state the intensities between the pair differ due to hyperfine enhancement and relaxation factors. The additional lines in the ENDOR spectrum were examined using the ENDOR Induced ESR (EIE) method described... 

Fig. 2.5 ENDOR spectrum of the malonic acid radical, HC(COOH)2 in a single crystal of malonic acid. The vj lines corresponding to ms = /2 for the H nucleus differ in intensity due to hyperfine enhancement and relaxation factors. Additional hnes A, B and C are attributed to other species that are not apparent in the ESR spectrum, while the overlapping features 2- 5 represent weak couplings due to H at neighbour molecules based on the EIE spectra to the right. The line marked by a square is an instrumental artifact. The ENDOR spectrum was recorded at a magnetic field value marked by in the ESR spectrum. The figure is reproduced fl om [24] with permission from the American Chemical Society.

Several factors unique for ENDOR affect the intensities, i.e. magnetic relaxation, hyperfine enhancement, and angular selection. The two first effects also affect spectra of liquid and crystalline samples, while the third is typical for powder spectra of species with anisotropic g-values. Methods that take the two latter effects into account have been developed and are usually incorporated in software developed for the simulation of ENDOR spectra in the solid state. Simulations that take magnetic relaxation effects into account have been employed only to analyse ENDOR spectra in the liquid state [2]. It is possible that the commonly observed poor agreement between experimental and simulated intensities in the solid state is at least in part due to relaxation effects that are not taken into account in any software we are aware of. 

Powder ENDOR lines are usually broadened by the anisotropy of the hyperfine couplings. The parameters of well resolved spectra can be extracted by a visual analysis analogous to that applied in ESR. The principle is indicated in Fig. 3.25 for an 5 = V2 species with anisotropic H hyperfine structure, where the hyperfine coupling tensor of axial symmetry is analysed under the assumption that 0 < A < Aj. < 2 vh- The lines for electronic quantum numbers ms = V2 and -Vi, centered at the nuclear frequency vh 14.4 MHz at X-band, are separated by distances equal to the principal values of the hyperfine coupling tensor as indicated in the figure. Absorption-like peaks separated by A in the 1st derivative spectrum occur due to the step-wise increase of the amplitude in the absorption spectrum, like in powder ESR spectra (Section 3.4.1). The difference in amplitude commonly observed between the ms = /2 branches is caused by the hyperfine enhancement effect on the ENDOR intensities first explained by Whiffen [45a]. The effect of hyperfine enhancement is apparent in Figs. 3.25 and 3.26. 

The principal values and even the orientation of the principal axes of the Na hyperfine coupling tensor with respect to axes of the g tensor could be determined from Mims and Davies pulsed ENDOR spectra, refer to Section 2.3.3 in Chapter 2. The values Axx( Na) = Ayy( Na) = 6.3 and Azz( Na) = 10.9 MHz were obtained by simulation taking angular selection into account. The so-called hyperfine enhancement of ENDOR intensities due to the interaction between the radio frequency field and the electron spin could lead to pronounced differences in the ENDOR intensities between signals from different rris electron spin states in experiments at conventional MW frequencies such as in X-band, but also at the W-band. The Na (I = 3/2) nuclear quadrupole tensor is almost coaxial to the A tensor, 2zz = 0.48 MHz, Qyy = -0.07 MHz, and Qxx = -0.41 MHz. Simulation of orientation-selective ENDOR spectra as described in [26, 33] serves to refine the principal values of the hyperfine coupling tensors estimated from experiment. In... 

TmES Tm NMR 1.5-4.2 single crystal hyperfine enhancement factor Teplov (1%9)... 

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