Two-dimensional nuclear magnetic resonance spectroscopy

Two-Dimensional Nuclear Magnetic Resonance is an advanced spectroscopic technique that builds upon the capabilities of one-dimensional NMR by incorporating an additional frequency dimension. This extension allows for a more comprehensive analysis of molecular structures. In 2D NMR, signals are distributed across two frequency axes, providing improved resolution and separation of overlapping peaks, particularly beneficial for studying complex molecules. This technique identifies correlations between different nuclei within a molecule, facilitating the determination of connectivity, spatial proximity, and dynamic interactions.
2D NMR encompasses a variety of experiments, including COSY, TOCSY, NOESY, and HSQC. These techniques are indispensable in fields such as structural biology, where they are pivotal in determining protein and nucleic acid structures; organic chemistry, where they aid in elucidating complex organic molecules; and materials science, where they offer insights into molecular interactions in polymers and metal-organic frameworks. By resolving signals that would typically overlap in the 1D NMR spectra of complex molecules, 2D NMR enhances the clarity of structural information. 2D NMR can provide detailed information about the chemical structure and the three-dimensional arrangement of molecules.
The first two-dimensional experiment, COSY, was proposed by Jean Jeener, a professor at the Université Libre de Bruxelles, in 1971. This experiment was later implemented by Walter P. Aue, Enrico Bartholdi and Richard R. Ernst, who published their work in 1976.

Fundamental concepts

Each experiment consists of a sequence of radio frequency pulses with delay periods in between them. The timing, frequencies, and intensities of these pulses distinguish different NMR experiments from one another. Almost all two-dimensional experiments have four stages: the preparation period, where a magnetization coherence is created through a set of RF pulses; the evolution period, a determined length of time during which no pulses are delivered and the nuclear spins are allowed to freely precess ; the mixing period, where the coherence is manipulated by another series of pulses into a state which will give an observable signal; and the detection period, in which the free induction decay signal from the sample is observed as a function of time, in a manner identical to one-dimensional FT-NMR.
The two dimensions of a two-dimensional NMR experiment are two frequency axes representing a chemical shift. Each frequency axis is associated with one of the two time variables, which are the length of the evolution period and the time elapsed during the detection period. They are each converted from a time series to a frequency series through a two-dimensional Fourier transform. A single two-dimensional experiment is generated as a series of one-dimensional experiments, with a different specific evolution time in successive experiments, with the entire duration of the detection period recorded in each experiment.
The end result is a plot showing an intensity value for each pair of frequency variables. The intensities of the peaks in the spectrum can be represented using a third dimension. More commonly, intensity is indicated using contour lines or different colors.

Homonuclear through-bond correlation methods

In these methods, magnetization transfer occurs between nuclei of the same type, through J-coupling of nuclei connected by up to a few bonds.

Correlation spectroscopy (COSY)

The first and most popular two-dimension NMR experiment is the homonuclear correlation spectroscopy sequence, which is used to identify spins which are coupled to each other. It consists of a single RF pulse followed by the specific evolution time followed by a second pulse followed by a measurement period.
The Correlation Spectroscopy experiment operates by correlating nuclei coupled to each other through scalar coupling, also known as J-coupling. This coupling is the interaction between nuclear spins connected by bonds, typically observed between nuclei that are 2-3 bonds apart. By detecting these interactions, COSY provides vital information about the connectivity between atoms within a molecule, making it a crucial tool for structural elucidation in organic chemistry.
The COSY experiment generates a two-dimensional spectrum with chemical shifts along the x-axis and y-axis and involves several key steps. First, the sample is excited using a series of radiofrequency pulses, bringing the nuclear spins into a higher energy state. After the first RF pulse, the system evolves freely for a period called t₁, during which the spins precess at frequencies corresponding to their chemical shifts. The correlation between nuclei is achieved by incrementally varying the evolution time to capture indirect interactions. This series of experiments, each with a different value of t₁, allows for the detection of chemical shifts from nuclei that may not be observed directly in a one-dimensional spectrum. As t₁ is incremented, cross-peaks are produced in the resulting 2D spectrum, representing interactions like coupling or spatial proximity between nuclei. This approach helps map out atomic connections, providing deeper insight into molecular structure and aiding in the interpretation of complex systems.
Cross peaks result from a phenomenon called magnetization transfer, and their presence indicates that two nuclei are coupled which have the two different chemical shifts that make up the cross peak's coordinates. Each coupling gives two symmetrical cross peaks above and below the diagonal. That is, a cross-peak occurs when there is a correlation between the signals of the spectrum along each of the two axes at these values.
An easy visual way to determine which couplings a cross peak represents is to find the diagonal peak which is directly above or below the cross peak, and the other diagonal peak which is directly to the left or right of the cross peak. The nuclei represented by those two diagonal peaks are coupled.
Next, a second RF pulse is applied to allow magnetization to transfer between coupled nuclei. The resulting signal is recorded continuously during a detection period after the second RF pulse. The data are then processed through Fourier transformation along both the t₁ and t₂ axes, creating a 2D spectrum with peaks plotted along the diagonal and off-diagonal.
When interpreting the COSY spectrum, diagonal peaks correspond to the 1D chemical shifts of individual nuclei, similar to the standard peaks in a 1D NMR spectrum. The key feature of a COSY spectrum is the presence of cross-peaks as shown in Figure 1, indicating coupling between pairs of nuclei. These cross-peaks provide crucial information about the connectivity within a molecule, showing that the two nuclei are connected by a small number of bonds, usually two or three bonds.
COSY is especially useful when dealing with complex molecules such as natural products, peptides, and proteins, where understanding the connectivity of different nuclei through bonds is crucial. While 1D NMR is more straightforward and ideal for identifying basic structural features, COSY enhances the capabilities of NMR by providing deeper insights into molecular connectivity.
The two-dimensional spectrum that results from the COSY experiment shows the frequencies for a single isotope, most commonly hydrogen along both axes. Diagonal peaks correspond to the peaks in a 1D-NMR experiment, while the cross peaks indicate couplings between pairs of nuclei.
COSY-90 is the most common COSY experiment. In COSY-90, the p1 pulse tilts the nuclear spin by 90°. Another member of the COSY family is COSY-45. In COSY-45 a 45° pulse is used instead of a 90° pulse for the second pulse, p2. The advantage of a COSY-45 is that the diagonal-peaks are less pronounced, making it simpler to match cross-peaks near the diagonal in a large molecule. Additionally, the relative signs of the coupling constants can be elucidated from a COSY-45 spectrum. This is not possible using COSY-90. Overall, the COSY-45 offers a cleaner spectrum while the COSY-90 is more sensitive.
Another related COSY technique is double quantum filtered COSY. DQF COSY uses a coherence selection method such as phase cycling or pulsed field gradients, which cause only signals from double-quantum coherences to give an observable signal. This has the effect of decreasing the intensity of the diagonal peaks and changing their lineshape from a broad "dispersion" lineshape to a sharper "absorption" lineshape. It also eliminates diagonal peaks from uncoupled nuclei. These all have the advantage that they give a cleaner spectrum in which the diagonal peaks are prevented from obscuring the cross peaks, which are weaker in a regular COSY spectrum.

Exclusive correlation spectroscopy (ECOSY)

Total correlation spectroscopy (TOCSY)

The TOCSY experiment is similar to the COSY experiment, in that cross peaks of coupled protons are observed. However, cross peaks are observed not only for nuclei which are directly coupled, but also between nuclei which are connected by a chain of couplings. This makes it useful for identifying the larger interconnected networks of spin couplings. This ability is achieved by inserting a repetitive series of pulses which cause isotropic mixing during the mixing period. Longer isotropic mixing times cause the polarization to spread out through an increasing number of bonds.
In the case of oligosaccharides, each sugar residue is an isolated spin system, so it is possible to differentiate all the protons of a specific sugar residue. A 1D version of TOCSY is also available, and by irradiating a single proton the rest of the spin system can be revealed. Recent advances in this technique include the 1D-CSSF TOCSY experiment, which produces higher quality spectra and allows coupling constants to be reliably extracted and used to help determine stereochemistry.
TOCSY is sometimes called "homonuclear Hartmann-Hahn spectroscopy".