The methods we have described to this point are examples of one-dimensional experiments. In a one-dimensional experiment, the signal is presented as a function of a single parameter, usually the chemical shift. In a two-dimgnsional experiment, there are two coordinate axes. Generally these axes also represent ranges of chemical shifts. The signal is presented as a function of each of these chemical shift ranges. The data are plotted as a grid; one axis represents one chemical shift range, the second axis represents the second chemical shift range, and the third dimension constitutes the magnitude (intensity) of the observed signal. The result is a form of contour plot where contour lines correspond to signal intensity.
In a normal pulsed NMR experiment, the 90o excitation pulse is followed immediately by a data acquisition phase in which the FID is recorded and the data are stored in the computer. In experiments that use complex pulse sequences, such as DEPT, a preparation phase is included before data acquisition. During the preparation phase, the nuclear magnetization vectors are allowed to precess, and information may be exchanged between magnetic nuclei. In other words, a given nucleus may become encoded with information about the spin state of another nucleus which may be nearby.
Of the many types of two-dimensional experiments, two find the most frequent application. One of these is H-H Correlation Spectroscopy, better known by its acronym, COSY. In a COSY experiment, the chemical shift range of the proton spectrum is plotted on both axes. The second important technique is Heteronuclear Correlation Spectroscopy, better known as the HETCOR technique. In a HETCOR experiment, the chemical shift range of the proton spectrum is plotted on one axis, while the chemical shift range of the 13C spectrum for the same sample is plotted on the second axis.
When we obtain the splitting patterns for a particular proton and interpret it in terms of the numbers of protons located on adjacent carbons, we are using only one of the ways in which NMR spectroscopy can be applied to a structure proof problem. We may also know that a certain proton has two equivalent protons nearby that are coupled with a J value of 4 Hz, another nearby proton coupled with a J value of 10 Hz, and three others nearby that are coupled by 2 Hz. This gives a very rich pattern for the proton we are observing, but we can interpret it, with a little effort, by using a tree diagram. Selective spin decoupling may be used to collapse or sharpen portions of the spectrum in order to obtain more direct information about the nature of coupling patterns. However, each of these methods can become tedious and very difficult with complex spectra. What is needed is a simple, unbiased, and convenient method for relating coupled nuclei.
The pulse sequence for a COSY experiment contains a variable delay time as weIl s an acquisition time. The experiment is repeated with different delay times, and the data collected during the acquisition are stored in the computer. The value of the delay time is increased by regular, small intervals for each experiment, so that the data that are collected consist of a series of FID patterns collected during acquisition, each with a different value of delay time.
To identify which protons couple to each other, the coupling interaction is allowed to take place during delay. During the same period, the individual nuclear magnetization vectors spread as a result of spin-coupling interactions. These interactions modify the signal that is observed during acquisition. Unfortunately, the mechanism of the interaction of spins in a COSY experiment is too complex to be described completely in a simple manner.
An initial relaxation delay and a pulse prepare the spin system by rotating the bulk magnetization vectors of the nuclei by 90o. At this point, the system can be described mathematically as a sum of terms, each containing the spin of only one of the two protons. The spins then evolve during the variable delay period (called t0. In other words, they precess under the influences of both chemical shift and mutual spin-spin coupling. This precession modifies the signal that we finally observe during the acquisition time (t2). In addition, mutual coupling of the spins has the mathematical effect of converting some of the single-spin terms to products, which contain the magnetization components of both nuclei. The product terms are the ones we will find most useful in analyzing the COSY spectrum.
Following the evolution period, a second 90o pulse is introduced; this constitutes the next essential part of the sequence, the mixing period (which we have not discussed previously). The mixing pulse has the effect of distributing the magnetization among the various spin states of the coupled nuclei. Magnetization that has been encoded by chemical shift during ti can be detected at another chemical shift during t2. The mathematical description of the system is too complex to be treated here. Rather, we can say that two important types of terms arise in the treatment. The first type of term, which does not contain much information that is useful to us, results in the appearance of diagonal peaks in the two-dimensional plot. The more interesting result of the pulse sequences comes from the terms that contain the precessional frequencies of both coupled nuclei. The magnetization represented by these terms has been modulated (or "labeled") by the chemical shift of one nucleus during tx and, after the mixing pulse, by the precession of the other nucleus during t2. The resulting off-diagonal peaks (cross peaks) show the correlations of pairs of nuclei by means of their spin-spin c oupling. When the data are subjected to a Fourier transform, the resulting spectrum plot shows the chemical shift of the first proton plotted along one axis (fl) and the chemical shift of the second proton plotted along the other axis (f2). The existence of the off-diagonal peak that corresponds to the chemical shifts of both protons is proof of spin coupling between the two protons. If there had been no coupling, their magnetizations would not have given rise to off-diagonal peaks.
In the COSY spectrum of a complete molecule, the pulses are transmitted with short duration and high power so that all possible off-diagonal peaks are generated. The result is a complete description of the coupling partners in a molecule. Since each axis spans the entire chemical shift range, something on the order of a thousand individual FID patterns, each incremented in ti, must be recorded. With instruments operating at a high spectrometer frequency (high-field instruments), even more FID patterns must be collected. As a result, a typical COSY experiment may require about a half hour to be completed. Furthermore, since each FID pattern must be stored in a separate memory block in the computer, this type of experiment requires a computer with a large available memory. Nevertheless, most modem instruments are capable of performing COSY experiments routinely.
In gigure 39, the COSY spectrum for isopentyl acetate is given. The proton spectrum of isopentyl acetate is plotted along each axis. The COSY spectrum shows a distinct set of spots on a diagonal, with each spot corresponding to the same peak on each coordinate axis. Lines have been drawn to help you identify the correlations. In the COSY spectrum of isopentyl acetate, we see that the protons of the two equivalent methyl groups (1) correlate with the methine proton (2). We can also see correlation between the two methylene groups (3 and 4) and between the methine proton (2) and the neighboring methylene (3). The methyl group of the acetate moiety (6) does not show off-diagonal peaks, because the acetyl methyl protons are not coupled to other protons in the molecule.
Figure 39. COSY spectrum for isopentyl acetate.
You may have noticed that the COSY spectra shown contain additional spots besides the ones examined in our discussion. Often these "extra" spots have much lower intensifies than the principal spots on the plot. The COSY method can sometimes detect interactions between nuclei over ranges that extend beyond three bonds. Besides this long-range coupling, nuclei that are several atoms apart but that are close together spatially also may produce off-diagonal peaks. We learn to ignore these minor peaks in our interpretation of COSY spectra. In some variations of the method, however, spectroscopists make use of such long-range interactions to produce twodimensional NMR spectra that specifically record this type of information.
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