The chemical shift of an atom in a molecule, is the relative nuclear magnetic energy level it has due to the presence of the environment around it. It is unique and specific for the atom within the molecular environment and its location depends on the relative field strength of the magnetic field in the NMR spectrometer. To understand how chemical shifts work lets first take a look at operating frequency.
Operating Frequency or Larmour Frequency or Precession Frequency
The larmour frequency or the operating frequency or the precession frequency is the frequency at which a particular nuclei will resonate to give the signal. The operating or larmour frequency (ω0) is calculated using the larmour equation:
ω0 = γ . H0
where, γ is the gyromagnetic ratio of the nuclei and H0 is the actual strength of the applied magnetic field. The gyromagnetic ratio of the nucleus under test is dependant in turn upon the magnetic moment μ and the spin number I and the planck’s constant. The gyromagnetic ratio is a constant for a particular nucleus in a given environment. Thus the larmour frequency, or the frequency at which the signal is obtained, is dependant on the strength of the applied magnetic field H0.
let us say that the proton of tetramethylsilane (which is considered to be an NMR standard – the reason for which will be explained below) is 42.576 MHz/T. Then if this proton is kept in a strong magnetic field H0 of strength 9.395 T, the larmour frequency ω0 at which this proton would resonate would be
ω0 = 42.576 x 9.395
= 400 MHz (approximately)
Since no two magnets are identical, scientists have declared that the nuclei of the tetramethylsilane (TMS) is the standard, with respect to which the NMR instrumentation can be calibrated. Thus instead of being approximately 400 MHz, the instrumentation is calibrated to be exactly 400 MHz.
The same nucleus if placed in a stronger magnetic field with the field strength of 18.79T, would provide a larmour frequency of approximately 800 MHz and would resonate to give a signal at this frequency. Since TMS is the standard, here, the instrument would be calibrated to say that the signal of TMS would come at exactly 800 MHz.
NMR instruments are known by the frequency at which the protons of TMS would be observed. Thus when one says that the NMR instrument is of 400 MHz it means that the peak for the TMS protons would appear at a frequency of 400 MHz.
Why is tetramethylsilane (TMS) considered a reference standard?
Unlike other spectroscopic methods, where the signals are fixed at particular frequencies or wavelengths, in NMR, the signal is dependent on the field strength as well as the gyromagnetic ratio of the nuclei. Since no two magnets have the same field strength H0, the frequency at which signals are obtained would vary correspondingly. Therefore, there was a need to characterize and specify the location of the signals. This problem becomes evident when we take a look at the diagram showing 11 compounds, that have signals which are distinct and well separated, however an unambiguous numerical locator cannot be directly assigned to each.
Another problem which existed is that not all scientists would have access to the same instrument. Hence there would be a difference in the values one would obtain from instrument to instrument.
In order to avoid these situations, the scientific community decided to eliminate the problems by keeping a standard reference with respect to which a numerical value can be assigned. Such a reference standard would have to have the following characteristics:
- should be chemically inert and non-reactive
- easily removed from the sample after measurement
- should have a single sharp resonance peak
- the peak it displays should be far away from most peaks normally observed and should not interfere with the resonances normally observed for organic molecules.
δ Chemical Shift Scale or Chemical Shift Referencing
The changes observed in larmour frequency for nuclei are very small. For example, the peak for protons in benzene would be observed at say 400.001234 MHz. Stating such values and remembering them would be difficult. Also they would be dependant on the NMR instrument used. Thus it is therefore important to change the scale to a uniform scale which would take into account the reference standard of TMS.
The scientific community therefore came up with the δ-chemical shift scale (or the delta chemical shift scale) in order to bring into play the chemical shift referencing. What this scale does is basically quotes the chemical shift relative to an agreed reference compound (mostly TMS).
For example, in the case of proton NMR, the reference compound which we would take is TMS. The frequency at which TMS is observed is say at νTMS (measured in Hz). Now, supposing we are observing our sample and the frequency of one of the protons in molecule is at ν (measured in Hz), then, the chemical shift of the proton of the sample molecule would be calculated by the formula:
Typically the chemical shift is very small, and so the number obtained is multiplied by 106 and its value is quoted as parts per million or ppm. Thus the formula for obtaining values in δ ppm (or delta ppm) is
The following chart gives an idea where to expect protons from different functional groups with respect to this scale in proton NMR when the solvent is CDCl3. Note- if the solvent is different some regions may change but not very dramatically. We will see the effects of solvents later.