Shift average

The presence of isotopic impurities causes clear effects in the vibrational spectra. Almost all modes studied so far show frequency shifts on S/ S substitution [81, 107]. The average shift of the internal modes is ca. 0.6 cm , and of the external modes it is 0.1-0.3 cm (Tables 3, 4 and 5). Furthermore, the isotopomers which are statistically distributed in crystals of natural composition can act as additional scattering centers for the phonon propagation. Therefore, in such crystals the lifetime of the phonons is shortened in comparison with isotopically pure crystals and, as a conse-... 

Table 9-4. Average shifts in atomization energies upon basis set enlargement [kcal/mol]. Based on data taken from Martell, Goddard, and Eriksson, 1997. 

The H NMR spectrum showed the paratropic shift expected of protons in an antiaromatic system. Because it is difficult to evaluate the magnitude of paratropic shift in a charged species, the average shift of protons in 3 were com-... 

Figure 4. Plot of the shift of various pairs of ferrous and ferric compounds vs. the average shift of that pair. The num-...

If vi and 1 3 modes can be identified, their frequencies are assumed to decrease by 0.943 and 0.977, respectively, upon substitution of for If and cannot be separately identified and enumerated, an average shift of 0.96 is adopted. 

The average shift of the a protons in the % spectra remains fairly constant, except for al 1 11 ithium. No reason can be given for the drift in the values for the individual protons. 

We can connect this energy shift per perturbing atom to an absolute average shift by multiplying by the rare gas number density N and integrating over the volume. If we also replace U(ft,ft,r,R) using Eq. (11.19), Eq. (12.16) becomes... 

According to table 9 an average shift of the f-d configuration can be determined to be around -130 cm-1/GPa. This is approximately five times larger than the average shift of the f-f transitions which is on the order of —25 cm-1/GPa. The f-d configuration of U4+ shifts faster compared to the 4f elements, a result which is not unexpected if the already larger shift of the f-f transitions (see sect. 4.2) is taken into account. 

Fig. 3. Range of chemical shifts for aH in amino acids. The bars are centered at the average shift value for the respective amino acid (BioMagResBank [http //www. bmrb.wisc.edu/] (54)). The dark grey bars represent the 68% and the light grey bars the 95% confidence interval. The values for diamagnetic proteins were taken from the BioMagResBank in mid-February 2007. The vertical black lines highlight the random coil shift. The x marks the random coil shift for oxidized cysteine.

FIGURE 2. Chemical shifts of 6,6,6-trifluoro-l-hexanol in mixtures of water and dioxane. The circles are experimental values, and the solid curve represents the calculated density-corrected average shifts. The dashed line corresponds to a linear interpolation. Reproduced by permission of Academic Press, Inc., from Reference 29... 

Spin-averaged shifts and widths Is ground-state... 

Information on differences in basicity of 4-azaazulenones was obtained from NMR spectra in CDC13 and trifluoroacetic acid (TFA). An alteration of the average shift of ring protons on going to the acetic solvent (see Table III) was thought to reflect differences in basicity. Thus, the order 5 > 7 8 > 6 has been established (86MI1). 

The problem is that we cannot easily compute the ionization energy and the electron affinity. In a recent work we therefore suggested to use a simple parametrized version of the shift where IP —EAp is replaced with an average shift parameter e [46] ... 

The sample is homogeneous with respect to the RF field and the temperature. 5) All spins are subjected to the same RF field. 6) Chemical shift differences are small relative to the average shift frequency. 

Since the two ions are essentially the same chemically but merely differ slightly in how they pack into the crystal, it is not surprising the average shifts do not differ significantly. For comparison, the chemical shift of a 1 M solution of calcium formate is 8 172 ppm. Again, we expect similarity, but not identity, with respect to the isotropic solid-state shift. In the solution case the ion is surrounded by a solvation sphere, whereas in the crystal, the solvent is other ions. It is not unreasonable to expect a moderate shift due to that effect. It is also very often the case that principal values are individually more sensitive to intra-and intermolecular effects than are isotropic shifts. ... 

When an axial Gin ligand is present (either natural as in stellacyanin or introduced by site-directed mutagenesis), the same orientation of the magnetic anisotropy tensor is maintained, and comparison of the average shift of the two P-CH2 Cys protons in different proteins may prove helpful (Diederix et aL, 2000 Fernandez et at., 1997 Salgado et al., 1996 Vila and Fernandez, 1996). 

C24a + C24b). For those attached to CHs-groups the average shift will be ... 

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