# Referencing x-nucleus spectra using the ^{1}H frequency of TMS

IUPAC recommends that the ^{1}H frequency of TMS be used as the primary chemical shift reference for spectra of all nuclei. The reference can be calculated from the ratio of gyromagnetic ratios of different nuclei. See references.

It is important to understand that precise definitions of “spectrometer frequency” vary with spectrometer manufacturer and have changed over time.

The NUTS SF parameter is the frequency of the transmitter, which is the center of the spectrum (for quadrature data). By convention, the “spectrometer frequency” used to convert from Hz to ppm is the frequency at 0 ppm, usually not the same as the actual transmitter frequency. For low gamma nuclei with large chemical shift ranges, the difference can be significant.

There is a NUTS parameter called **offset** (OF1 for the first dimension) which is defined as the difference, in Hz, between the center of the spectrum and 0 ppm. Thus, the **offset** relates the transmitter frequency to the frequency of 0 ppm.

The 2 macros below perform the necessary calculations for ^{13}Cspectra, using the NUTS Math subroutine. Process and set the chemical shift reference for the ^{1}H spectrum, then run the first macro. Open the ^{13}C spectrum and run the second macro. Alternatively, these 2 steps can be combined into a single macro, see sample.

Note that for 2D data, the macro sets the reference for the dimension that is displayed horizontally. To reference other nuclei, the second macro must be edited to change the gyromagnetic ratio (0.25145020 for ^{13}C) to the value for the chosen nucleus.

NUTSmacro calculate TMS 1H frequency ; uses the NUTS Math subroutine ; various values are stored in memory locations, so the user can check numbers SET MATH DECPLACES 7 ; first, convert the offset from Hz to MHz set math register 0 1000000 do math register 1 of1 do math / do math register 0 memory 2 DO MATH memory 1 SF1 ; calculate the frequency difference between the ; center of the spectrum and 0 ppm do math memory 1 register 1 do math memory 2 register 0 do math - do math register 0 memory 3 ; print the result onto the screen set math comment 1H TMS frequency do math note 50 10 end

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NUTSmacro calculate 13C reference ; the 1H frequency of TMS must first be calculated ; using the macro above SET MATH DECPLACES 7 ; 1H freq for TMS is in memory 3 ; gamma ratio 13C:1H set math register 1 0.25145020 do math memory 3 register 0 do math * do math register 0 memory 4 ; memory #4 contains absolute freq of 0 ppm for 13C ; now calculate the difference between center of spectrum ; and 0 ppm, which is the offset do math memory 4 register 0 DO MATH register 1 SF1 do math - ; convert from MHz to Hz do math register 0 register 1 set math register 0 1000000 do math * ; set offset do math of1 end

*Pure Appl. Chem.*,

Vol. 73, No. 11, pp. 1795–1818, 2001. Available at http://www.iupac.org/publications/pac/2001/pdf/7311×1795.pdf

http://www.chem.wisc.edu/~cic/nmr/Guides/Other/Xi_chem_shift_scale.pdf