Susceptibility corrections

Glaser RW, Ulrich AS (2003) Susceptibility corrections in solid-state NMR experiments with oriented membrane samples. Part I applications. J Magn Reson 164 104—114... 

It might appear that a magnetic susceptibility correction would be needed if the susceptibilities of sample and reference differ, but this is not the case. With the field/frequency lock established via the deuterated solvent, the applied magnetic field (H0) simply shifts slightly to maintain the magnetic induction (B0) inside the sample tube constant so as to keep the 2H on resonance. If different deuterated solvents are used for sample and reference, a simple correction must be made for the difference in their 2H chemical shifts. 

In the experimental spectra and tables shown in this chapter, the chemical shifts given are those measured from the particular reference, without susceptibility corrections. 

Chemical shifts ( 0.1 ppm) relative to the signal for Mg(C104)2. extrapolated to infinite dilution. More positive values refer to lower shielding. Bulk susceptibility corrections have been made. 

Ref. 94, l5N spectra of labelled compounds, originally referred to liquid NH +381-93 ppm from neat CH3N02, Table VII no bulk susceptibility correction. 

In 1960 Bothner-By observed that for several simple organic compounds, a change from the gaseous to the liquid state was accompanied by a shift to low field of the protons in excess of that calculated using the classical bulk susceptibility correction. It was found possible to calculate the observed shift jS/ of a solute proton i in a solvent j by use of the empirical relationship—... 

There came back an enthusiastic report of a substantial chemical shift difference between the adsorbate and the material in the liquid phase, to be followed shortly by another communication which stated that the difference disappeared when a magnetic susceptibility correction was applied to the results. This illustrates a problem which arises whenever one attempts to measure a chemical shift value in a heterogeneous system, the problem of a suitable reference and of eliminating magnetic susceptibility effects which are particularly troublesome in such systems of dubious geometry. Differences between chemical shifts in the same molecule, if they can be resolved, are... 

The theory of the susceptibility corrections in solid state NMR experiments with oriented membrane samples has been described. To determine the necessary corrections, a general analysis is presented for the demagnetizing field of a layered sample of rectangular block geometry, with the normal of the layers parallel to the main field or tilted about an axis of the block. The correction to the line position of the block sample was found to be approximately equal to that of the spheroid which can be inscribed into the block, and for which the correction is well known. It was shown that sample and support materials contribute to that average according to their volume filling factors. 

For convenience, internal standards are most frequently used. Tetramethylsilane (TMS) is almost universally adopted for resonances, and is usually sufficiently soluble in non-aqueous solvents. The standard texts also describe the use of external standards and the application of bulk susceptibility corrections. Some factors influencing the susceptibilities of mixed solvents and the calculation of bulk susceptibility effects are discussed in sect. 4.24.1. 

Bulk susceptibility corrections ( b) are required when using an external... 

The effect of van der Waals forces ((5 ) is difficult to assess. Experimentally has been obtained by comparing vapour and solution shifts of non-polar solutes, and making susceptibility corrections. Buckingham et suggest the existence of two components, one due to distortion of the electronic environment of the solute nucleus by the solvent in its equilibrium configuration, the other due to a time-dependent distortion of solute electronic structure as solvent molecules move. 

The same contributions appear in the expression of the bulk susceptibility (corrected for diamagnetism)... 

It is often found that the Curie law Eq. (21) is followed by many magnetically dilute substances other than free atoms or ions. There is, in addition, a second-order contribution to the paramagnetic susceptibility, the so-called temperature-independent paramagnetism Not. (also abbreviated TIP, cf. section 1,1.3.6) which arises from states separated from the ground state by an energy k T It follows that the molar susceptibility corrected for diamagnetism may be frequently represented by the Langevin-Debye expression... 

Note that this equation refers to the whole molecule. To find out the number of unpaired electrons on the transition metal atom in a complex an allowance must be made for all of the paired electrons present in the molecule. These effects are approximately additive and are listed for some of the more common species found in complexes in Table A9.1. A more complete list is given in a reference at the end of this appendix. To make the correction one sums the appropriate values. So, for [Ni(H20)6] S04"-H20, the corrections are Ni 12 SOj 40 7H2O 7(2 x 3 + 5) = 77—a total of 129 ( X 10 Vs atom). The correction calculated in this way, D, say, is added to Xm and the sum is x m the susceptibility corrected for diamagnetism. That is,... 

Magnetic properties have an importance in the NMR of liquid crystals [18,19], but the moments of the nuclear spins responsible for the NMR signal are far too small to make any contribution to magnetic susceptibilities. However, bulk susceptibility corrections to the NMR chemical shift of a standard immersed in the sample can be used to determine diamagnetic susceptibilities. The chemical shift of the standard is shifted to lower fields in a cylindrical sample due to the bulk magnetization, according to ... 

This frequency in practice is not as absolute as we should like. TMS shifts are temperature dependent, and temperatures are not always accurately reproduced. Further, a bulk susceptibility correction which depends on the shape of the container and its orientation relative to the magnetic field must be made (Section 8.1). 

Medium effects include that of bulk susceptibility, which depends on the geometry of the sample and the composition of the solution. For a perfectly spherical sample, the nuclear magnetic shielding contribution a of the bulk susceptibility is zero. For other shapes a susceptibility correction is needed because of polarization of the sample near the liquid surface. For an infinitely long cylinder, oriented with the cylindrical axis perpendicular to the direction of the magnetic field as in an electromagnet, the frequency shift due to bulk susceptibility of a pure solvent (as for a molecule observed in infinite dilution) is related to the molecular magnetic susceptibility x, or the volume susceptibility Xv of the solvent by... 

When an external homonuclear reference is used the reference resonance frequency depends on the geometrical arrangement, so that if the reference material is contained in a capillary tube this should be coaxial with the NMR tube. The reference resonance frequency also depends on the temperature, so that any variable temperature studies on the sample necessitate corrections due to the temperature dependence of the reference itself. The latter can only be obtained from observations relative to a truly temperature-independent standard such as an isolated xenon atom. When an internal homonuclear reference is used, the same temperature dependence corrections have to be made, and in addition the reference frequency will be concentration dependent owing to the van der Waals and other interactions with the components of the sample. Of course, in this case there will be no bulk susceptibility corrections to the chemical shift, since all observed molecules, including the reference, are subject to the same a. ... 

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