physical chemistry - NMR chemical shift range of different elements

A typical $\ce{^1H}$ NMR runs from approximately 0 to 10 ppm, give or take a bit. $\ce{^13C}$ NMR runs from 0 to 200. And $\ce{^59Co}$ NMR runs from -5000 to 15000 ppm!

There seems to be some correlation with atomic number, although three points hardly make a trend. Is there an explanation for this? I'm not interested in the exact numbers, but rather the relative orders of magnitude.

Answer

The are a number of important factors that contribute to the shielding of a nucleus. Chemical shifts arise due to differences in the local magnetic field in the different environments within a molecule, driven by overall electron density about that nucleus. That is to say, the effective magnetic field experienced by a nucleus is a function of the shielding constant, σ. There are a number of components of σ.

$$B_\mathrm{eff} = B_\mathrm{o}(1- \sigma)$$

• σ_dia is the local diamagnetic contribution


• σ_para is the local paramagnetic contribution


• σ_m is the neighbour anisotropy effect


• σ_rc is the ring current contribution


• σ_ef is the electric field effect



• σ_ef is the solvent effect

The two most important factors for the chemical shift range are the diamagnetic and paramagnetic contribution. All other contributions are quite small and operate within the effects of these fist two.

The diamagnetic contribution comes predominantly from electrons in the s-orbital; for most nuclei this is almost constant for all arrangements. Its effect diminishes with increasing distance from the nucleus, which is why s-orbitals play a more important role than p-orbitals. Only for those nuclei that have their outer orbitals as s-orbitals ($\ce{^1H, ^2H, ^7Li, ^{23}Na}$ for example) will the diamagnetic contribution be the dominant contributing factor, and this effect is generally small, providing only modest chemical shift ranges of up to tens of ppm.

The paramagnetic contribution is the dominating factor for all nuclei that have electrons in outer shell p, d and f orbitals. Paramagnetic shielding comes from the imbalance of electron density of the valence electrons in the outer orbitals. The way I get my brain around this is by thinking that the larger the non-spherical orbitals, the harder it is to get uniform distribution. The effect of paramagnetic contribution is large; up to many thousands of ppm.

To address your question, there is a general relationship that describes the expected chemical shift range being proportional to the inverse cube of the valence shell radius and also to the populations of the p and d orbitals. So, you are correct in your observation of chemical shift range being basically proportional to atomic number.

A useful reference for you is:
W. von Philipsborn, Chem. Soc. Rev. 1999, 28, 95. DOI: 10.1039/A706424A