Ξ values for indirect referencing

In the previous post I mentioned that indirect referencing was required to compare spectra collected in methanol-d₄ and methanol-d₃. Indirect referencing relies on precisely determined ratios of the ¹H gyromagnetic ratio and the gyromagnetic ratio of the nucleus being referenced. Unfortunately, many different values of this ratio, known as Xi (Ξ), have been reported. Here I test several of these Ξ values to see how closely they match referencing to an internal standard.

Most readers of this blog will be more concerned with referencing ¹³C than any other nucleus, so I examined ¹³C chemical shift referencing. A quick internet search found several different values for the ¹³C/¹H Ξ value. I used each of these values to reference the ¹³C dimension of a HSQC spectrum of cholesteryl acetate in CDCl₃ containing TMS. I then read off the ¹³C chemical shifts of TMS and CDCl₃. The values should be 0.00 ppm for TMS and 77.16 ppm for CDCl₃¹. Results are in the table below.

Sample	13C/1H Ξ	Source	δC TMS	δC CDCl3
10mM DSS in 99.8% D2O, 25oC	0.251449528	2	2.615	80.002
10mM DSS in 99.8% D2O, 25oC	0.251449537	2	2.570	79.972
DSS in 1M NH4NO3 and 1M HNO3, 25oC	0.251449519	2	2.659	80.042
5mM DSS in NH3, 25oC	0.251449531	2	2.609	79.999
10mM DSS in 99.8% D2O, 25oC	0.251449530	2,3,4	2.603	79.999
5mM TSP in D2O, 22oC	0.25144954	5	2.563	79.959
1% TMS in CDCl3, 25oC	0.25145020	3,4	-0.078	77.333
1% TMS in CDCl3, 25oC	0.25145022	6	-0.134	77.255

Clearly, accurate indirect referencing depends on using the correct Ξ value. Using values of Ξ obtained for DSS or TSP gives poor results. The most accurate result is obtained using the TMS derived value, Ξ=0.25145020. This is the value recommended by IUPAC.^3,4

Interestingly, IUPAC recommends two different values of Ξ, depending on the solvent.^3,4 For organic solvents, Ξ=0.25145020 is recommended. For aqueous systems, they recommend using Ξ=0.251449530 and noting that the chemical shifts are referenced to DSS. This is because the methyl groups of DSS in D₂O do not resonate at the same frequency as the methyls of TMS in CDCl₃. In other words, the chemical shift of DSS, which is normally set to 0.00 ppm, is not the same as the chemical shift of TMS, which is also set to 0.00 ppm.

Even comparing the chemical shift of TMS in different solvents is fraught because in solvents other than CDCl₃ the TMS signal does not resonate at 0.00 ppm. Tables of correction factors are available,^4,7,8,9 but are not entirely consistent, and it is not recommended to use them unless one has to compare chemical shifts in different solvents.

My recommendations for referencing spectra are;

• Whenever possible use TMS or DSS as an internal reference.
• Without an internal reference, calibrate ¹H spectra using residual solvent peaks and use indirect referencing with the IUPAC recommended Ξ value to calibrate heteronuclear spectra.
• Use the values in Gottlieb et al¹ to calibrate ¹H spectra. Even though they may not be accurate, they are the most generally accepted values.
• When publishing, describe how you referenced the spectra, including what values you used.
  

References

1. Gottlieb, H. E., Kotlyar, V., and Nudelman, A.
NMR Chemical Shifts of Common Laboratory Solvents as Trace Impurities
J Org Chem. 1997;62(21):7512–7515

2. Wishart, D. S., Bigam, C. G., Yao, J., Abildgaard, F., Dyson, H. J., Oldfield, E., Markley, J. L., and Sykes, B. D.
¹H, ¹³C and ¹⁵N Chemical Shift Referencing in Biomolecular NMR
J Biomol NMR. 1995;6:135-140

3. Harris, Robin K., Becker, Edwin D., Cabral de Menezes, Sonia M., Goodfellow, Robin and Granger, Pierre
NMR nomenclature. Nuclear spin properties and conventions for chemical shifts (IUPAC Recommendations 2001)
Pure Appl Chem. 2001;73(11):1795-1818

4. Harris, Robin K., Becker, Edwin D., Cabral de Menezes, Sonia M., Granger, Pierre, Hoffman, Roy E. and Zilm, Kurt W.
Further conventions for NMR shielding and chemical shifts (IUPAC Recommendations 2008)
Pure Appl Chem. 2008;80(1);59-84

5. Bax, A. and Subramanian, J.
Sensitivity-Enhanced Two-Dimensional Heteronuclear Shift Correlation NMR Spectroscopy
J Magn Reson. 1986;67:565-570 (1986)

6. Indirect Referencing
Iowa State Unversity, Chemical instrumentation Facility

7. Chemical Shift Referencing. Table 2. TMS chemical shifts and solvent susceptibilities in commonly used pure NMR solvents at 25°C
The Hebrew University of Jerusalem, Institute of Chemistry, NMR Lab

8. Hoffman, R.E.
Variations on the chemical shift of TMS
J Magn Reson. 2003;163:325-331

9. Hoffman, R.E.
Standardization of chemical shifts of TMS and solvent signals in NMR solvents
Magn Reson Chem. 2006;44:606-616