for analysis. (Larger field machines are also favoured on account of having intrinsically higher signal arising from the Boltzmann distribution of magnetic spin states.) Chemical shift referencing Chemical shift is usually expressed in parts per million (ppm) by frequency, because it is calculated from: where is the absolute resonance frequency of the sample and is the absolute resonance frequency of a standard reference compound, measured in the same applied magnetic field . Since the numerator is usually expressed in hertz, and the denominator in megahertz, is expressed in ppm. The detected frequencies (in Hz) for 1H, 13C, and 29Si nuclei are usually referenced against TMS (tetramethylsilane), TSP (Trimethylsilylpropanoic acid), or DSS, which by the definition above have a chemical shift of zero if chosen as the reference. Other standard materials are used for setting the chemical shift for other nuclei. Thus, an NMR signal observed at a frequency 300 Hz higher than the signal from TMS, where the TMS resonance frequency is 300 MHz, has a chemical shift of: Although the absolute resonance frequency depends on the applied magnetic field, the chemical shift is independent of external magnetic field strength. On the other hand, the resolution of NMR will increase with applied magnetic field. Referencing methods Practically speaking, diverse methods may be used to reference chemical shifts in an NMR experiment, which can be subdivided into indirect and direct referencing methods. Indirect referencing uses a channel other than the one of interest to adjust chemical shift scale correctly, i.e. the solvent signal in the deuterium (lock) channel can be used to reference the a 1H NMR spectrum. Both indirect and direct referencing can be done as three different procedures: "Internal referencing, where the reference compound is added directly to the system under study." In this common practice, users adjust residual solvent signals of 1H or 13C NMR spectra with calibrated spectral tables. If substances other than the solvent itself are used for internal referencing, the sample has to be combined with the reference compound, which may affect the chemical shifts. "External referencing, involving sample and reference contained separately in coaxial cylindrical tubes." With this procedure, the reference signal is still visible in the spectrum of interest, although the reference and the sample are physically separated by a glass wall. Magnetic susceptibility differences between the sample and the reference phase need to be corrected theoretically, which lowers the practicality of this