Indirect referencing

Most chemists use the residual protonated solvent peak to reference their spectra, but in two dimensional heteronuclear spectra, like HMBCs, the residual solvent peak is often distorted or not present at all. The ¹H dimension of such experiments can usually be referenced by aligning it to a 1D ¹H spectrum. The heteronuclear dimension, however, is more difficult to reference correctly. The best way to reference such spectra is to use indirect referencing to calculate the chemical shifts based on the frequency ratio of the nuclei involved.

If you have a spectrum that you can accurately reference, for example a 1D ¹H spectrum, then you can transfer the referencing to other spectra and other nuclei. The first step is to obtain the frequency of the 0 ppm position in the referenced spectrum. This can be calculated using

ν₀ = ν_c - ν_s.δ_c.10^-6

where ν is frequency in MHz of the zero position of the spectrum (ν₀), the center of the spectrum (ν_c), and of the spectrometer (ν_s), and δ_c is the chemical shift of the center of the spectrum. In TopSpin this value is stored in the processing parameter SF and can be simply read out.

Secondly, the frequency of the zero position can be converted to the zero position of other nuclei by multiplying by the ratio of the two nuclei's gyromagnetic ratios. Originally these ratios were calculated but more recently they have actually been measured. The table below lists ratios for some of the more frequently studied nuclei.

Nuclei	γ Ratio
1H - 1H	1.000000000
2H - 1H	0.153506088
13C - 1H	0.251449530
14N - 1H	0.07226317
15N - 1H	0.101329118
19F - 1H	0.94094011
23Na - 1H	0.264519
29Si - 1H	0.19867187
31P - 1H	0.404808636

Finally, the frequency of the zero position of the second nucleus can be used to calculate the chemical shift of the center of the spectrum using the equation above. Alternatively, in TopSpin the frequency of the zero position can be entered as the value for SF in the dimension to be referenced.

If you are processing your data with nmrPipe, referencing requires calculating the chemical shift of the center of each non-¹H dimension. To make life easier I have written a web based calculator that is available here.