Spin flip lines

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... 

This type of spectra are frequently observed at X-band for n-electron radicals of the common type H—Ca. The appearance of the spectra is different for weakly coupled nuclei, in which case so-called spin flip lines appear. 

In other applications the presence of forbidden and spin flip lines makes interpretations more difficult, particularly when they occur in the same spectrum as for the malonic acid radical in Fig. 4.20. The early work by McConnell and co-workers to obtain the first ESR single crystal data of this radical, including an interpretation of the forbidden transitions must therefore be considered as an extra-ordinary... 

Fig. 4.20 First-derivative ESR spectra of the radical H<,C(COOH)2 from an X-itradiated single crystal of mtilonic acid recorded at 295 K at (a) low (0.2 mW) and (b) high (100 mW) microwave power. The vtirious resontmce lines have been designated according to their categorization as main lines (m), forbidden trtmsitions (f) due to hyperfine coupling with H<, and spin-flip lines (s) due to hyperfine coupling with distant hydrogen atoms at neighbour molecules. The figure is reproduced from [E. Sagstuen et til. J. Phys. Chem. A 104, 6362 (2000)] with permission from the American Chemical Society...

Fig. 4.21 (a) Schematic X- and Q-band singie crysttil spectra of the hydrazine cation radical, with the magnetic field B Y. The hyperfine stiucture due to accidentally equivtdent 4 H is the expected quintet at X-band, while spin-flip lines occur on the Q-band spectrum, (b) Experimental and simulated X-band spectra with the magnetic field at an angle of 25° with X in the XY-plane. The spectra were adapted from [O. Edlund et al. J. Chem. Phys. 49,749 (1968)] with permission from the American Institute of Physics... 

Anisotropic A, with principal values b Apart from the spin flip lines due to weak dipolar coupling with distant H atoms of the matrix this case is rare at X-band and lower frequencies, but may become of interest for measurements at high microwave frequency bands. The situation is most likely to occur for species with anisotropic hyperfine couplings of moderate size due to nuclei with large nuclear g-factors like or F. The effective field acting on the nucleus is dominated by the applied field, so that a and the normal selection rule Ami = 0 applies. The splitting between the lines is AT = 1 A 1 and A g = 1 Ag 1 for isotropic and anisotropic g-factors, respectively. 

Figure 13.3 shows both the H and the l3C NMR spectra of methyl acetate, CH3CO2CH3. The horizontal axis shows the effective field strength felt by the nuclei, and the vertical axis indicates the intensity of absorption of rf energy. Each peak in the NMR spectrum corresponds to a chemically distinct 1H or 13C nucleus in the molecule. (Note that NMR spectra are formatted with the zero absorption line at the bottom, whereas IR spectra are formatted with the zero absorption line at the top Section 12.5.) Note also that 1H and 13C spectra can t be observed simultaneously on the same spectrometer because different amounts of energy are required to spin-flip the different kinds of nuclei. The two spectra must be recorded separately. 

Here we comment on the shape of certain spin-forbidden bands. Though not strictly part of the intensity story being discussed in this chapter, an understanding of so-called spin-flip transitions depends upon a perusal of correlation diagrams as did our discussion of two-electron jumps. A typical example of a spin-flip transition is shown inFig. 4-7. Unless totally obscured by a spin-allowed band, the spectra of octahedral nickel (ii) complexes display a relatively sharp spike around 13,000 cmThe spike corresponds to a spin-forbidden transition and, on comparing band areas, is not of unusual intensity for such a transition. It is so noticeable because it is so narrow - say 100 cm wide. It is broad compared with the 1-2 cm of free-ion line spectra but very narrow compared with the 2000-3000 cm of spin-allowed crystal-field bands. 

With a laser linewidth of less than IKHz spectroscopy has been carried out on water vapor lines around 1885 cm ( v- 5,3jum) with a resolution never obtained before. Application of the spin-flip laser to P- and Q-Branch absorption of NO with 0.08 cm resolution has been reported by Wood et al... 

Finally, Levchenko and Krylov (2004) have defined spin-flip versions of coupled cluster theories along lines similar to those previously described for SF-CISD. Applications to date have primarily been concerned with the accurate computation of electronically excited states, but the models are equally applicable to computing correlation energies for ground states. 

All three of these problems tend to be resolved when bands due to intraconfigurational transitions are used. In six-coordinate, approximately Oh complexes these are l2g t2g and eg -> eg transitions, quite often accompanied by a spin flip, and therefore forbidden. In contrast to t2g - eg transitions, these are usually numerous, narrow (because the excited state resembles the ground state), and simple each observed narrow line comprises just one component. The relative abundance of these sharp lines (8 for d3 complexes, for example, and as many as 14 for low-spin d4) is deceptive it is because the also numerous t2g —> eg components cluster under broad bands. 

Figure 6. Polarized neutron reflectivities of fN 0 = 5 nm, 20 nm and 60 nm samples during the reversal process. The spin flip (R+, R +) and non spin flip (if4-1", R") reflectivities are simultaneously modeled to obtain the magnetization configuration as shown in the inset. The lines are the computed reflectivities for different scattering cross-sections based on this model.

In order to obtain a Larmor resonance line we have to vary the frequency of the microwave field and count the number of spin flips per unit time. In order to avoid saturation effects the microwave field amplitude was kept low. The resonance curve obtained in the described manner is rather asymmetric. The lineshape can be described using the known spatial configuration of the magnetic field and a thermal distribution of the axial energy. A least squares fit to the data points as shown in Fig. 9 leads to a fractional uncertainty of about 10 and the g factor can be quoted with the same error [9]. 

Three-spin systems can be readily analyzed by inspection only in the first-order cases AX2 and AMX. The second-order AB2 spectrum can contain up to nine peaks—four from spin flips of the A proton alone, four from spin flips of the B protons alone, and one from simultaneous spin flips of both the A and the B protons. The ninth peak is called a combination line and is ordinarily forbidden and of low intensity. Although these patterns may be analyzed by inspection, recourse normally is made to computer programs. The other... 

---