Absolute Shielding Scale

5 Absolute Shielding Scales. - For lighter elements, the way to the absolute shielding involves a non-relativistically valid relation between the spin-rotation constant, C, and shielding a, applied to at least one primary reference molecule. A review of how spin-rotation constants relate to shielding constants was provided by Bryce and Wasylishen. The C and a tensors for the primary reference are corrected for rovibrational effects and then connected to a commonly used secondary reference (usually a neat liquid substance) via an NMR measurement in the gas phase at the limit of zero density and in the liquid 

CJJ dedicates this report to the memory of the late Joan Mason whose interest in the NMR chemical shift spanned decades, and who introduced her to this Series of volumes as a junior co-author. 

Bakken, T. Enevoldsen, T. Helgaker, H. J. Aa. Jensen, J. Laerdahl, K. Ruud, J. Thyssen, and L. Visscher, DIRAC, A Relativistic Ab initio Electronic Structure Program, Release 3.2. (2000) (http //dirac.chem.sdu.dk). 

Ishikawa, T. Nakajima, M. Hada and H. Nakatsuji, Chem. Phys. Lett., 1998,283, 119. 

There are several methods of establishing an absolute shielding scale. 

Method 1 This involves simultaneous NMR measurements in the free atoms and in a convenient liquid reference or free molecule, as in the experiment described above for protons.  

Methods-. Another method of establishing an absolute shielding scale is by using the relationship [equation (8)] between a and the spin-rotation constant measured in a molecular beam magnetic or electric resonance experiment or by high-resolution microwave spectroscopy. Combined with an accurate calculation of in the molecule, the absolute shielding of a suitable primary reference molecule can be obtained. For C and O the primary reference molecule is CO for P it is PH3. The spin-rotation constant may also be obtained from the ratio of the relaxation times of two nuclei in the same molecule in the gas phase when both are wholly relaxed by the spin-rotation mechanism. In SeF, for example 

Nucleus Primary reference molecule Method Reference Secondary reference liquid Method Reference 

Nucleus molecule Reference neat liquid, sphencal Reference Reference  

CH4) = 30.611 0.024 ppm. They measured the chemical shifts for CO, CO2, OCS and NNO in the gas phase relative to liquid H2O at various densities. After extrapolation to zero-density they used the value CTq( 0, H2O) = 307.9 ppm from the absolute shielding scale of Wasylishen et al. that is based on the absolute ao( 0, CO) = — 42,3 17 ppm to convert the measured chemical shifts at zero density into absolute shieldings ctqC O, CO2) = 225.8 ppm, CTo( 0, NNO) = 184.4 ppm, ao( 0, OCS) = 90.7 ppm, and ao( 0, CO) = —59.5 ppm. These numbers are aU in excellent agreement with the earlier gas phase data of Wasylishen et al Having been extrapolated to zero density the Jackowski data should be more precise. Jackowski also 

5 Absolute Shielding Scales. - Gee and Wasylishen have recommended that the microwave study of AlH be repeated, as the previous one failed to account for the Al nuclear spin-rotation interaction. Their ab initio calculations give a range of values depending on the method used but are all of the order of 300 kHz. The value of the spin-rotation constant for Al in AIF, on the other hand, has been measured, Cj = 8.2 1.3 kHz, which leads to (ct — CTj ) = 320 50 ppm for Al in AIF and 

To have a usable Al absolute shielding scale, what is still needed is the Al chemical shift between a commonly used reference substance such as [A1(H20)6] in infinite dilution and the isolated AIF molecule. 

A microwave study of the spin-rotation tensor of GaF in the gas phase has been reported by Wasylishen et al This provides spin-rotation constants for both the F and the Ga nucleus. A value of (an — aj ) = 945 35 ppm for Ga is derived from the experimental spin-rotation constant. The absolute Ga isotropic shielding obtained from the experimental spin-rotation constant at the ground vibrational state of GaF is 

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The situation with respect to establishing a reliable absolute shielding scale for heavy elements remains somewhat unclear. Two methods that are both in principle exact give significantly different results, whereas more approximate methods give yet another result. As the quantity of interest is difficult to measure experimentally, it wdl be necessary to analyze the causes for the discrepancy in more detail, both theoretically and numerically. Another interesting study could be the analysis of the effects that the differences between the Kutzelnigg and unmodified Dirac response formalisms will have on chemical shifts. In that case, one could use experimental data to decide upon a preferred formahsm. 

There are many unanswered questions about nuclei in the 3rd row and below in the Periodic Table, for transition as well as representative elements. Basis set development for such atoms are required before quantitative results for ct may be expected. The possible importance of relativistic effects, the unknown geometries (especially of complex ions) in solution, and the lack of absolute shielding scales for such nuclei makes any good agreement of small basis set uncorrelated calculations with chemical shifts observed in solution very suspect. 

B From Ref. (56), the 77Se absolute shielding scale, but without the relativistic corrections (300 ppm) in the diamagnetic shielding of the Se free atom used in Ref. (56). 

For the 71Ga nucleus, the availability of an absolute shielding scale also makes possible a comparison of calculated absolute shieldings with experimental values. The standard used experimentally, [Ga(OH2)6]3+ in solution, is unsuitable as a theoretical reference due to the lack of consideration of water molecules beyond the first solvation shell in the calculations. On the other hand, there exists an absolute shielding scale for 71Ga, based on the NMR measurement in an atomic Ga beam at the same time as in the ion at infinite dilution in a D20 solution (57). 

Recent reports of spin-rotation constants for aluminum chloride (35) and aluminum isocyanide (36) have made possible the comparison of experimental and ab initio calculated shielding results. If one were able to measure the27A1 chemical shift of one or both these compounds, it would be possible, in principle, to establish an absolute shielding scale for aluminum however, the high reactivity of these compounds has so farprecludedsuchmeasurements. High-resolution microwave measurements have also been recently carried out on A1H (37) however, analysis of the data did not consider the 27A1 spin-rotation interaction (vide infra). 

We will now give an application of combining experimental SR relaxation and MD simulations to obtain an absolute shielding scale for tin [74]. 

Knowledge of the absolute values of Urej and Uk is a difficult problem. However, if one single value is obtained for nucleus k, the all the other shielding constants can be obtained from the experimental chemical shift and we can establish an absolute shielding scale for the nucleus in question. In this application MD and NMR are used to obtain the absolute shielding scale for tin. Absolute shielding scales have been available for most first and second row elements [75], while it was missing for tin. 

An absolute shielding scale for the Se nucleus has been established on the basis of gas-phase Ti measurements of F and Se in SeFg. Using this scale the Se chemical shift of liquid MC2SC is 3 = 2069. 

Table 2.2 The shielding in ice, ppm the basis for the absolute shielding values is a series of translations from TMS or liquid water back to the absolute shielding scale the experimental monomer shielding using the same absolute scale is ao( H, H2O, gas, 403-463 K) = 30.05 0.0...

Absolute shielding scales based on weighted average of five experimental points. See Apple man and Dailey.20... 

The absolute shielding scales for bromine and iodine are far less precisely determined and are not referenced with respect to the corresponding bare nuclei. For example, using a semi-quantitative theoretical model ° along with experimental data," Ikenberry and Das used Hartree-Fock methods to calculate the shift of the bromide anion with respect to the free anion and obtained -194 ppm." On the basis of experimental solution state measurements, Itoh and Yamagata arrived at -600 ppm for 1 in dilute solution with respect to the free anion. These calculations were expected to be rather crude estimates, even in the opinion of the original... 

It should be clear from the examples provided in this article, that relativistic effects cannot be ignored when one wants to understand NMR chemical shifts throughout the periodic table. While the local heavy-atom effects on the heavy atoms ( HAHA effects) can be very large for absolute shield ings, they tend to cancel to a large extent in relative shifts and are thus probably less important for the interpretation of the observed shifts for different compounds. HAHA effects are nevertheless of interest, not only for the development of reliable relativistic computational methods but also, for example, when deriving absolute shielding scales for heavy nuclei (section 5). 

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