# 2D NMR Basics

The 2D NMR experiment belongs as well to the Fourier transform spectroscopy than to the impulsion one and relies on a sequence of three time intervals: preparation, evolution and detection (3). In some experiment another time interval is added before the detection: the mixing time (Fig. 8).

**Fig. 8**: Scheme for time pulse in a 2 D NMR experiment (3)

#### The preparation time

Upon the preparation time the spin system under study is firstly prepared, for example it is submitted either to a decoupling experiment or just to a transverse magnetization by the means of a 90° impulsion. It allows the excited nuclei to get back their equilibrium state between two successively executed pulse sequence (5)

#### The evolution time t_{1}

During the evolution time \(t_1\), the spin system is evolving under the effect of different factors, each coherence evolves at its own characteristic frequency as a function of the chemical shift and of the scalar coupling of the corresponding nucleus.

#### The Mixing time

It is made of a pulse sequence which achieves coherence transfers in such a way that different frequencies can be correlated.

#### The detection time

The acquisition of the modulated signal takes place during the detection period. The sequence we just described does not constitute by itself a 2D NMR experiment.

### JEENER

The idea of Jeener consists in the stepwise increasing of the evolution time t_{l}. This will allow to get an NMR signal under the aspect of a sampling of free precession signals of the s(t_{2}) type. These FID will differ from each other only by the t_{l} period duration written under a matricial form s(t_{l} ,t_{2}) (5). The t_{l} delay is the time between the first and the second pulse (Fig.9).

**FIG 9**: Sampling of signals of free precession of the type s(t2)

The first Fourier transform as a function of t_{l} gives us an interferogram of the form (Fig. 10).

**Fig. 10: **Interferogram of the form 4

A second Fourier transform, versus the second variable t_{2}, gives an NMR spectrum with two frequencies dimensions F_{1} and F_{2} (Fig. 11). The result of this two fold Fourier transform does not get two spectra and but only one spectrum as a function of two independent frequencies, exhibiting a peak with the coordinates . Thus, an aimantation evolving with the frequency in the time course t_{1} has been converted in another coherence evolving with the frequency during the period t_{2}.

**Fig. 11:** NMR spectrum in two dimensions following the second Fourier transform(4).

This double Fourier transform in both dimension yields thus a matrix . (spectrum 3).