Spectra powder

In solid-state NMR, it is more usual to deal with a powdered sample, where there is a uniform distribution of molecular orientations over three-dimensional space. The NMR spectrum for a powdered sample, therefore, consists of a superposition of many lines, corresponding to all the possible resonance frequencies. 

4 Simulated static powder spectrum first-order quadrupolar coupling of a spin / = 1 (with added noise) for the anisotropic broaden- nucleus, e. g., H. (Reproduced by permission of ing due either to a dipolar coupling between the SocieU Italiana di Fisica from (5).) an isolated pair of spin / =1/2 nuclei or to the 

If powder spectra of the type shown in Fig. 9.3 and 9.4 can be obtained experimentally, the principal values of the anisotropic interaction in question (though not the orientation of the PAS with respect to a fixed frame) can be obtained by a straightforward lineshape analysis. However, to obtain such spectra, it is necessary that there is only one distinct nucleus, and that one anisotropic interaction dominates. Usually, the static NMR lineshape is a broad featureless hump due to the overlapping of many powder patterns as well as the interplay of the different broadening mechanisms. As an example of this. Fig. 9.5 presents a NMR spectrum of a representative organic sohd, together with, for comparison, the corresponding solution-state spectrum. It is to be noted that the problem in such a case is not a lack of information, but rather there is essentially an overload, such that the net effect is the virtual loss of all information. In the remainder of this article, soHd-state NMR approaches by which this information can be recovered wiU be demonstrated. 

To understand why so-called magic-angle spinning (MAS) is so successful as a means of line narrowing, it is first necessary to recognise that the CSA, dipolar, and first-order quadrupolar interaction all have basically the same orientational dependence for an axially symmetric tensor (this is always the case for the dipolar interaction, and corresponds to a CSA or first-order quadrupolar interaction with a zero asymmetry parameter), the orientationally dependent part of the frequency of a particular crystalHte can be expressed in the form 

To illustrate the effect of MAS, we consider in Fig. 9.7 the specific example of a dipolar coupling between two spins. The four cones represent the range of positions adopted over the course of one rotor period for four different orien- 

A simulation of such a superposition, using the fine-structure constants of the naphthalene molecule (D/hc = 0.100 cm , E/hc = -0.015 cm , and g = ge), and with a linewidth of AB = 1.2 mT for each component is shown in Fig. 7.13a. The discontinuities in the broad Am = 1 ESR spectrum correspond to the principal-axis orientations Bo u u = x,y,z). They occur because of the high density of resonance-field values in the neighbourhood of the principal-axis directions (compare Fig. 7.4). For B = 0, two of these discontinuities occur at the same place. The Am = 2 spectrum is narrow because the anisotropy of the Am = 2 transitions is to first approximation zero. The ESR signal (Fig. 7.13b) is - as usual in ESR due to the method of measurement - the first derivative of the spectrum (absorption vs. frequency or field strength. Fig. 7.13a). Even with a powder or a glass sample. 

---

At low rotation rates, less than the chemical shifts anisotropy, however, the powder spectra contained disturbing side bands dispersed among the isotropic chemical shifts. In order to discriminate between sidebands and isotropic resonances two spectra obtained at different spinning speeds were multiplied together or the differentiation was made by visual inspection. 

Fig. 8. Calculated solid echo 2H NMR powder spectra for jumps between two sites related by the tetrahedral angle for ij =0, i.e. true absorption spectrum and Tj = 200 ps. xc is the correlation time of motion. R is the reduction factor, giving the total normalized intensity of the spectra for x, = 200 ps. (For x, = 0 all the spectra have total intensity 1)...

In the low-field condition, the quantization axis is defined by the EFG main component In this situation, and rj can both be determined from powder spectra when recorded in an externally applied field. Figure 4.14 shows simulated spectra as is often encountered in practice such as in applied-field measurements of diamagnetic compounds or fast-relaxing paramagnetic compounds at high temperatures. The simulated traces differ in detail from a single-crystal spectrum as shown in Fig. 4.13, but their features still correlate in a unique manner with rj and the sign of... 

Powder spectra of paramagnetic compounds measured with applied fields are generally more complicated than those shown in Fig. 4.14. Large internal fields at the Mossbauer nucleus that are temperature- and field-dependent give rise to this complication. If, however, the measurement is performed at sufficiently high temperature, which is above ca. 150 K, the internal magnetic fields usually collapse due to fast relaxation of the electronic spin system (vide infra, Chap. 6). Under... 

In the case of paramagnetic complexes their experimental magnetic parameters are determined by computer simulation of the powder spectra [59], Together with the corresponding calculated values, obtained using a relativistic spin-unrestricted ZORA approach, they all are collected in Table 2.8. 

CW ENDOR spectrum measurements carried out at 120 K (the optimum temperature for measuring resolved CW ENDOR powder spectra of carotenoid radicals) shows resolved lines from the P-methyl hfc (Piekara-Sady et al. 1991,1995, Wu et al. 1991, Jeevarajan et al. 1993b) (see Figure 9.5). The lines above 19 MHz are due to neutral radicals according to DFT calculations (Gao et al. 2006). 

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)]. 

Two corollaries stem from this generalization. Since a spin-1/2 nucleus gives only two hyperfine lines, there can be no variation in spacings. Thus powder spectra cannot be analyzed to extract the orientations of hyperfine matrix axes for such important nuclei as 3H, 13C, 19F, 31P, 57Fe, and 103Rh. Secondly, since the observable effects in powder spectra depend on the magnitude of the matrix... 

The 1 -> 4 transition is only weakly allowed compared with the 1 - 2, 2 - 3, and 3 -> 4 transitions however, it is often observed, particularly in powder spectra since it tends to be considerably sharper than the other transitions. Notice that the 1 - 3 and 2 -> 4 transitions are still forbidden. Since the wave functions are field-dependent, the Sz matrix elements also depend on the field. Thus the observed 1 -> 2, 2 -> 3, and 3 -> 4 transitions would be different than predicted from the Sz2 matrix at 1000 G. 

Fig. 16. Typical powder spectra for radicals with one spin — nucleus (7).

Hyperfine interactions likewise produce characteristic inflections in the derivative curve. Anisotropic hyperfine coupling is usually accompanied by anisotropic g values and as a result, the powder spectra are often quite complex. Typical powder spectra for paramagnetic species having one nucleus with / = are shown in Fig. 16. An unambiguous analysis of the more complex experimental spectra often requires the use of two microwave frequencies and a variation in the nuclear isotopes. The latter technique is illustrated by a comparison of the spectra for 14N02 and 15N02 on MgO as shown in Fig. 17. 

For a balanced historical record I should add that the late W. E. Blumberg has been cited to state (W. R. Dunham, personal communication) that One does not need the Aasa factor if one does not make the Aasa mistake, by which Bill meant to say that if one simulates powder spectra with proper energy matrix diagonalization (as he apparently did in the late 1960s in the Bell Telephone Laboratories in Murray Hill, New Jersey), instead of with an analytical expression from perturbation theory, then the correction factor does not apply. What this all means I hope to make clear later in the course of this book. 

Isotropic and Second-Order Anisotropic Powder Spectra Correlations. 151... 

The first term in (24) was already calculated in (9). The second term can be neglected, as the CSA is usually too weak to require the second-order treatment. The last term is the second-order cross-term between the two interactions. A complete review of the second-order cross-terms and their effect on high-resolution solid-state NMR powder spectra of quadrupolar nuclei was recently published by Ashbrook et al. [31]. 

H NMR spectra are profoundly influenced by motions.1 7 It is possible to calculate the powder spectra in the presence of any type of motion by taking into account the geometry, and amplitudes and rates of motions involved.80,81 Consider a C-2H bond which can jump between three equivalent sites,... 

A remarkable example of polymorphism has been found recently for Pigment Red 53 2 (Ca-salt). In addition to the a-, y- and 8-crystal modifications [35, 36] twelve more crystal phases were found and characterized by their X-ray powder spectra. The phase transformation could be achieved by heating P.R.53 2 in different organic solvents at 60-200°C [37],... 

Samoson, A. and Lippmaa, E. (1983) Excitation phenomena and line intensities in high-resolution NMR powder spectra of half-integer quadrupolar nuclei. Phys. Rev. E, 28, 6567-6570. 

The EPR powder spectra of the low-spin complexes [0s(NH3)5L][CF3S03]3 (L = H20 or (5)) have been analyzed the negative sign obtained for the axial splitting when L = (5) has been rationalized in terms of Os L backbonding. Crystal field parameters have also been derived. The spectral and electrochemical properties of [Ru(NH3)5L]" (Ru or Ru L =RC02 R = 4-py-A-Me+ or L = RCONH R = Ph, 4-py-A-Me", 4-py-A-H+) have been studied in detail as a function of pH the carboxamido Ru complexes are weak bases and are deprotonated only in strongly acidic solution. ... 

For (35 R = R = COjMe) the ESR powder spectra turned out to be very sensitive to the dihedral angle of the carbonyl oxygen with respect to the ring plane (cf. quantum chemical calculations Section 4.12.2). A very small discrepancy between the angles for both C=0 groups caused spin densities on both S atoms to diverge strongly and hence S lines in the spectrum to be considerably... 

It is important to note that even without hyperfine data, the powder spectra give valuable information about the carrier of the ESR spectrum. Both the molecular symmetry of the molecule and the effective distance between the unpaired electrons usually can be deduced from the spectra. 

---