Referencing Chemical Shifts¶
Why Shielding Alone Isn't a Chemical Shift¶
Experimental NMR spectra are reported as a chemical shift, δ, in ppm relative to a reference compound — not as an absolute shielding constant. This is partly a matter of convention and partly practical: absolute shielding is difficult to measure directly by experiment, while a difference in resonance frequency relative to a standard is straightforward.
The relationship between a computed isotropic shielding, σ, and the reported shift, δ, is:
Note the sign: a more shielded nucleus (larger σ) has a smaller chemical shift, and vice versa.
Choosing and Computing the Reference¶
The reference compound depends on the nucleus being studied — commonly tetramethylsilane (TMS) for both ¹H and ¹³C. To use this equation, σ(reference) must be computed with exactly the same method, basis set, and NMR keyword (NMR=GIAO) as the sample calculation. Mixing levels of theory between the reference and the sample reintroduces systematic error that the referencing step is specifically meant to cancel out.
Applying It to the Formic Acid Dimer¶
The Output File for this tutorial reports raw isotropic shielding values only — for example, 24.5951 ppm for the carbon atoms. To turn this into a reported ¹³C chemical shift, a separate NMR=GIAO calculation on TMS at the same B3LYP/6-31G level would be needed, and the shift obtained as:
This second calculation isn't included in this tutorial's downloadable files, since it's a separate, standalone job on a different molecule — but the equation above is all that's needed to combine the two once it's run.