Correlation between 1H and 13C shifts - coincidence or not?

Question

A quick glance at any table of typical chemical shifts will reveal that the chemical shifts of protons $(\delta_\mathrm H)$ tend to correlate pretty well with the chemical shifts of the carbons to which they are attached $(\delta_\mathrm C)$. This correlation is frequently taught in introductory organic chemistry and the rule of thumb

$$\delta_\mathrm C \approx 20 \cdot \delta_\mathrm H,$$

although simplistic, actually holds up fairly well. To illustrate the point further, here is a diagram taken from the textbook by Silverstein et al. on organic spectroscopy:

^{Image taken from: Silverstein, R. M.; Webster, F. X.; Kiemle, D. J. Spectrometric Identification of Organic Compounds, 7th ed.; Wiley: Hoboken, NJ, 2005, p 207.}

To the beginner such a correlation might seem intuitive. However, delving deeper into NMR theory, one learns that the $\ce{^{13}C}$ chemical shifts are generally dictated by paramagnetic shielding, while $\ce{^{1}H}$ chemical shifts are generally dictated by diamagnetic shielding and effects due to neighbouring groups. See, for example, this question: NMR chemical shift range of different elements.

In light of this, how much should we make out of the general correlation seen? i.e., is it best understood to be a pure coincidence, or is there more to it than that?

Answer 1

It is true that a quick glance at any given table of typical chemical shifts will reveal that the chemical shifts of protons $(\delta_\ce H)$ tend to correlate pretty well with the chemical shifts of the carbons to which they are attached $(\delta_\ce C)$. The rule of thumb of this correlation is as shown in the question:

$$\delta_\ce C \approx 20 \cdot \delta_\ce H,$$

This simplistic rule actually holds up fairly well. I wonder is it because of $\ce{^{13}C}$-NMR spectroscopy, characterized by a large range of variation in $\ce{^{13}C}$ nuclear shielding (about thirty times that of protons) and by a simpler analysis of the proton decoupled spectra (Ref.1). My aim at this answer is to provide some contradictory case against it norm.

I think cyclopropane and cyclobutane would provide evidence against the rule of thumb in this case (Ref.2):

$$ \begin{array}{c|lcr} \text{Compound} & \ce{^{1}H}\ (\pu{ppm}) & \ce{^{13}C}\ (\pu{ppm}) & 20 \cdot \delta_\ce H \\ \hline \text{Cyclopropane} & 0.22 & -0.28 & 4.4 \\ \text{Cyclobutane} & 1.94 & 22.4 & 38.8 \\ \text{Cyclopentane} & 1.51 & 25.8 & 30.2\\ \text{Cyclohexane} & 1.44 & 27.0 & 28.8\\ \text{Cycloheptane} & 1.54 & 28.7 & 30.8\\ \hline \end{array} $$

References:

1. O. A. Subbotin, A. S. Kozmin, Yu K. Grishin, N. M. Sergeyev, and I. G. Bolesov, "$\ce{^{13}C}$ NMR spectra of cyclopropane derivatives. Stereoisomeric substituted 2-phenylcyclopropanes," Organic Magnetic Resonance 1972, 4(1), 53-62 (ODI: https://doi.org/10.1002/mrc.1270040106).
2. Horst Friebolin, In Basic One- and Two-dimensional NMR spectroscopy; 3rd Edition, WILEY-VCH: Weinheim, Germany, 1998 (ISBN: 978-3-527-32782-9).

Answer 2

This is not my best answer, but because I'm at work and because I'm the person who asked the question, I'll forgive myself.

Quoting from Hans Reich's website:

All nuclei heavier than $\ce{^1H}$ (with the possible exception of $\ce{^6Li}$ and $\ce{^7Li}$) have $\sigma_\mathrm{p}$ [the paramagnetic shift] as the principal chemical shift effect.

It is fortunate that $\sigma_\mathrm{p}$ often responds in the same way to electron density as does $\sigma_\mathrm{d}$ [the diamagnetic shift], since this results in parallel $\ce{^1H}$ and $\ce{^{13}C}$ chemical shift features. However, a qualitative description of the relationship between $\delta$ and molecular features must consider two factors which affect $\sigma_\mathrm{p}$ and $\sigma_\mathrm{d}$ quite differently and may cause very counterintuitive behavior: the $1/ΔE$ dependence, and orbital symmetry effects.

Reich then goes on to provide specific examples where this dependence falls apart, such as anti-aromatic compounds, the pyridine/pyridinium pair, and phenyllithium. Mathew Mahindaratne's post also provides some counterexamples. (More broadly speaking, this analysis of paramagnetic and diamagnetic shifts also tends to neglect things such as alkynes, where anisotropic effects lead to unusual chemical shifts.)

I'd say that yes, the correlation is coincidental; and Reich's word choice of 'fortunate' supports this.

PS: There are a number of arguments, even in this very post, about how chemical shift is dictated by 'electron density'. These, however, fail to acknowledge the different mechanisms by which electron density affects proton and carbon chemical shifts (which I pointed out in the original question). I think it's very unfortunate that this correlation exists, because it's clearly led to a lot of misconceptions amongst non-NMR specialists.

Answer 3

Maybe it would help to comprehend the coincidental changes in $\ce{^1H}$ and $\ce{^13C}$ chemical shift by understanding the origin of chemical shift. In both cases, very crudely speaking, the influence of ring currents and electronegative elements/groups cause a downfield (away from zero) shift. The factor of 20 quoted is a function of the number of electrons (usually outer ones) involved in forming the bond. So the trend will also be true for other elements e.g. $\ce{^15N}$ where aromatic N compounds i.e. pyridine have a larger downfield shift.