Multidimensional NMR spectroscopy is a powerful technique for studying molecular structure and dynamics at the atomic level. It extends the capabilities of traditional one-dimensional NMR spectroscopy by providing additional information about the correlations between different atomic nuclei in a molecule.

In traditional one-dimensional NMR spectroscopy, a single radiofrequency (RF) pulse is applied to a sample, and the resulting signal is recorded as a function of the frequency of the RF pulse. In contrast, multidimensional NMR spectroscopy involves the application of two or more RF pulses with different frequencies and time delays. The resulting signals are recorded as a function of both frequency and time, generating a multidimensional spectrum.

Two-dimensional (2D) NMR spectroscopy is the most commonly used multidimensional NMR technique. In 2D NMR spectroscopy, two RF pulses are applied to the sample with varying time delays between them. The resulting signals are recorded as a function of both frequency and time, generating a two-dimensional spectrum. The diagonal of the spectrum corresponds to the one-dimensional NMR spectrum, while the off-diagonal peaks provide information about the correlations between different atomic nuclei.

For example, in two-dimensional ^1H-^13C heteronuclear correlation spectroscopy (HSQC), a ^13C-labeled sample is irradiated with a ^1H pulse, and the resulting signal is recorded as a function of both ^1H and ^13C chemical shifts. The diagonal of the spectrum corresponds to the ^13C NMR spectrum, while the off-diagonal peaks provide information about the correlations between ^1H and ^13C atoms in the molecule. By assigning the peaks in the HSQC spectrum to specific atoms in the molecule, it is possible to determine the connectivity between atoms and obtain structural information.

Three-dimensional (3D) and higher-dimensional NMR spectroscopy involve the application of additional RF pulses and time delays. These techniques can provide even more detailed information about molecular structure and dynamics. For example, in three-dimensional ^1H-^15N-^13C triple-resonance spectroscopy, three RF pulses are applied to a sample, and the resulting signals are recorded as a function of ^1H, ^15N, and ^13C chemical shifts. This technique can be used to assign NMR resonances to specific amino acid residues in a protein and to determine the three-dimensional structure of the protein.

Multidimensional NMR spectroscopy is widely used in structural biology, drug discovery, and materials science. It is particularly useful for the study of large and complex molecules such as proteins and nucleic acids, where traditional one-dimensional NMR spectroscopy may not provide sufficient information.