Two-dimensional NMR

The development of two dimensional NMR in the 1970s was probably the greatest advance in the history of the technique. The addition of another dimension to NMR spectra expanded the types of information obtainable and made possible the vast array of tailored multi-dimensional experiments available today. The development of two dimensional experiments relied upon the introduction of pulsed NMR and the use of the fourier transform to process the data. To generate two dimensional data a variable delay between two pulses must be used. Incrementing the variable delay allows chemical shift information to be regularly sampled and later processed with the fourier transform to give a second dimension. Read on for more details.

On a modern, pulsed spectrometer a 1D NMR spectrum is acquired by applying a 90^o pulse and recording the intensity of the magnetisation precessing in the xy-plane. As the magnetisation sweeps towards a detector the measured intensity increases then decreases as the magnetisation moves on, creating a sinusoidal signal. As the magnetisation relaxes back to equilibrium along the z-axis the overall intensity decreases, creating a decaying sinusoidal signal known as the Free Induction Decay (FID). The frequency that the magnetisation rotates in the xy-plane corresponds to the chemical shift. Fourier transformation converts the time-domain FID to a frequency-domain spectrum, as explained in more detail here.

Note that all the data is digitized. The FID is a list of intensity - time pairs that records the signal intensity at regular time intervals, and the spectrum is a list of intensity - frequency pairs.

Two dimensional NMR requires at least two pulses separated by a delay, labelled Δ in the figure below. As the delay is increased different FIDs, and thus spectra, are obtained. Typically the delay is incremented hundreds of times and hundreds of FIDs are recorded. Fourier transformation of all the FIDs produces a collection of 1D spectra where the signals are modulated by the length of the incremented delay.

Every one of the 1D spectra obtained after the first fourier transform consists of  points with three values - intensity, frequency (chemical shift from the first FT), and time (the delay used). Extracting the intensity from the first point in each of the 1D spectra and plotting it against the delay value produces an FID-like signal, known as an interferogram. Repeating this process for the second point, and the third, and so on, produces a collection of interferograms, as shown in the figure below. Fourier transformation of the interferograms converts from the time domain to the frequency domain producing a collection of points that describe intensity at two frequency co-ordinates. In the figure below stack plot representations are used, but more often two-dimensional NMR data is shown as a contour plot.

The key concept here is that the chemical shift signal in the second dimension is recorded one point at a time. Matrix manipulation of the data during processing allows interferograms to be constructed that can be fourier transformed to obtain data points with two frequency co-ordinates.