Two-dimensional NMR spectroscopy

The example under study is the saccharose (Fig 29).

The aim of this sequence is to correlate signals of identical nuclei with a scalar coupling. For an isolated nucleus, it is made of two impulsions on both side of the evolution period t₁ (Fig. 13).

The preparation begins with a relaxation delay allowing the magnetization to come back to its equilibrium, then the period t₁ occurs with a stepwise increase and finally the t₂ period is the acquisition time^[1].

Fig. 13 : The COSY experiment

Following the double Fourier transform, we get a spectrum in chemical shift on the two axis. Moreover, the cross peaks indicate the nuclei which are coupled within each other and allow then a direct attribution of the neighbouring protons.

We can understand the obtention of the diagonal and crossing signals of the COSY spectrum by the merely means of quantitative consideration^[1].

In fact, if we consider a singlet signal without scalar spin-spin coupling, the preparation allows to set the maximal amount of nuclei at their right position and the first impulsion generates a transverse magnetization M(A) which rotates around the Y axis (Fig. 14).

Fig. 14 : After the first impulsion (Pi/2)x

During the evolution period, the aimantation M(A) precesses with the frequency of the corresponding nucleus resonance in the rotating frame; there is thus a sharing of the spins between the x axis and the y axis (Fig. 15).

Fig. 15 : Evolution of the magnetization during the time t1.

The components Mx and My of the transverse magnetization at the end of the evolution period in the Ox and Oy axis of the rotating frame are then :

Where is the aimantation contribution before the execution of the first impulsion and the apparent transverse relaxation time of the corresponding nucleus.

The second impulsion allows to rotate the y component which stays in the xy plane, in the negative z part direction (-z).

These last one will not be detected (Fig. 16). However, the x part, still in the xy plane will be taken into account.

Fig. 16 : Next to the second impulsion

The magnetization which is going to be detected is of the form : , where as the magnetization along the –z axis followed the formula:  .

The intensity of the signal to be recorded depends thus of the time dependent position of the M(A) vector at the very time of the end of the evolution period. This intensity is determined by the Larmor frequency of the A nucleus. The amplitude is modulated in t₁ versus this frequency and the Fourier transform yields in both dimensions the frequency and then a diagonal signal.In the case of a spin-spin coupling, the second impulsion induce a change in the transverse A magnetization, but also changes of populations for other transitions in the spin system under study.

Therefore, an exchange of magnetization occurs between all the nuclei which are coupled between each other. Their signals, in a set of experiments , are in the same way modulated versus the neighbouring nuclei. This ends up with cross peaks of the 2D spectrum in and and allows us to get a spectrum in which the homonuclear scalar coupling constants are figure out by spots outside of the diagonal.

For example, we might see the coupling between the f3 and f4 protons at the crossing of 4.05 and 4.18 ppm (Spectrum 3).

Spectrum 3 : COSY 90°