Introduction To Twodimensional

We are now ready to discuss the most exciting and most powerful technique in NMR, a simple idea that led to an explosion of NMR applications, extending the power of NMR beyond organic chemistry to become a powerful tool in structural biology. Until now, we have looked at an NMR spectrum as a simple graph of intensity (vertical scale) versus frequency (horizontal chemical-shift scale). In a simple one-dimensional (1D) NMR spectrum, we get structural information from the chemical shift and peak area, and in 1H spectra we can learn about near neighbors in the bonding network by examining the coupling patterns of resolved multiplets. We can gain more specific information about interactions between protons (NOE and J coupling) by using low-power irradiation or shaped-pulse selective excitation of specific resonances in the 1D spectrum. But we are severely limited by the chemical shift "space" available for resolution of many resonances in a single frequency scale and by the need to examine relationships one at a time in separate selective experiments. In 2D NMR we have two frequency scales: the familiar direct measurement of frequency by Fourier transformation of the FID on the horizontal scale and an indirect second frequency scale on the vertical scale. This second dimension is created by recording a series of hundreds of 1D spectra, each time lengthening a delay in the pulse sequence, just as we sample the FID at discreet intervals in real time using the analog-to-digital converter. This incremented delay becomes a second (indirect) time domain, and Fourier transformation of this time domain yields the second frequency scale. Intensity is a third axis coming out of the paper, usually represented by color coding (intensity plot) or a contour (topographic) map. Depending on the way we do the experiment, we can map out specific kinds of interactions between spins. For example, if we are looking at NOE interactions, we will see a "spot" of intensity at the frequency of Ha on the horizontal chemical-shift scale and the frequency of Hb on the

NMR Spectroscopy Explained: Simplified Theory, Applications and Examples for Organic Chemistry and Structural Biology, by Neil E Jacobsen Copyright © 2007 John Wiley & Sons, Inc.

vertical chemical-shift scale, if Ha and Hb are less than 5 A apart. All of the information for all possible NOE interactions is contained in this single "map" produced by a single NMR experiment! 2D NMR essentially allows us to selectively excite each of the chemical shifts in one experiment and gives us a matrix or two-dimensional map of all of the nuclei affected by each perturbation.

Let's look at the overall strategy for a 2D pulse sequence. There are four steps to any 2D experiment:

1. Preparation: Excite nucleus A, creating magnetization in the x-y plane.

2. Evolution: Indirectly measure the chemical shift of nucleus A.

3. Mixing: Transfer magnetization from nucleus A to nucleus B (via J or NOE).

4. Detection: Measure the chemical shift of nucleus B.

Of course, all possible pairs of nuclei in the sample go through this process at the same time. Preparation is usually just a 90° pulse that excites all of the sample nuclei of a given type (e.g., 1H, 13C, etc.) simultaneously. Detection is simply recording an FID and finding the frequency of nucleus B by Fourier transformation. A simple 1D spectrum is just steps 1 and 4. To get a second dimension, we have to measure the chemical shift of nucleus A before it passes its magnetization to nucleus B. This is accomplished by simply waiting for a period of time (called ti, the evolution period) and letting the nucleus A coherence rotate in the x-y plane. The experiment is repeated many times (e.g., 512 times), recording the FID each time with the delay t1 incremented each time by a fixed amount. The time course of motion of the nucleus A magnetization as a function of t1 (determined by its effect on the final FID) is unraveled by a second Fourier transform, defining how fast it rotates during the t1 delay and giving us its chemical shift. Mixing is a combination of RF pulses and/or delay periods that induce the magnetization to jump from A to B as a result of either a J coupling or an NOE interaction (close proximity in space). Different 2D experiments (e.g., NOESY, COSY, HETCOR, etc.) differ primarily in the mixing sequence because in each one we are trying to define the relationship between A and B within the molecule in a different way. We now have quite an array of tools for transfer of magnetization: transient NOE (z-magnetization transfer via NOE), INEPT transfer (antiphase to antiphase coherence transfer via J-coupling), TOCSY transfer (multiple in-phase to in-phase coherence transfers via J coupling), and ROESY transfer (NOE transfer in the x'-y' plane in a spin lock). Each of these can be applied to create a specific 2D experiment (COSY, HETCOR, HSQC, HMBC, NOESY, ROESY, TOCSY, etc.).


Let's pick a concrete example we are familiar with: the INEPT transfer from 1H to 13C. The simplest INEPT sequence is just 90° (1H) - r - 90°(1H)/90°(13C), where the r delay is for J-coupling evolution of the 1H doublet into antiphase and the simultaneous 90° pulses give coherence transfer from 1H to 13C. Normally, we would set this delay to 1/(2 J) to get complete conversion from in-phase to antiphase 1H coherence (Ix ^ 2Iy Sz), and we would put simultaneous 180° pulses on 1H and 13 C in the center of the delay to refocus 1H chemical-shift evolution. But for a 2D experiment we want 1H chemical-shift evolution, so we make

Figure 9.1

the delay t into the simple evolution delay t1. During the t1 delay, the required antiphase component 2Iy Sz is oscillating due to chemical-shift evolution of the Iy part (Fig. 9.1). The frequency of this oscillation is just the offset of this proton (Ha) in the 1H spectrum: Qa. At some point in this oscillation, we execute the simultaneous 90o pulses and transfer this magnetization to antiphase 13C coherence (2Sy Iz), which oscillates at the frequency in the 13 C spectrum of the 13 C (Cb) that is bonded to Ha: Qb. This oscillation is recorded in the 13C FID, and Fourier transformation gives a 13C spectrum with a peak at frequency Qb. At this particular value of t1, the 1H coherence is at a positive maximum, and coherence transfer starts the 13 C FID at a positive maximum, leading to a positive peak of maximum intensity in the 13C spectrum (Fig. 9.1, top). Now we repeat the experiment with a slightly longer value of t1, so that the moment of coherence transfer happens when the 1H coherence is zero. No 13C coherence is produced, and the FID is just noise. Fourier transform gives no 13C peak in the 13C spectrum (Fig. 9.1, middle). A third experiment is done with the t1 value incremented a bit further, and this time the 1H coherence is at a negative maximum. Coherence transfer gives a negative maximum of13 C coherence at the start of the 13 C FID, and Fourier transformation gives an upside-down 13C peak in the 13C spectrum (Fig. 9.1, bottom). In this way, the peak intensity in the 13C spectrum oscillates in a way that exactly follows the oscillation of 1H coherence during the evolution (t1) delay. The intensity of the

Figure 9.2

13C peak can be plotted as a !H FID with t\ as the timescale (the "indirect time domain"). Understanding this is the core of understanding the genius of the 2D idea—creating a "fake" time domain with a delay that allows us to generate a second "indirect" frequency scale. Fourier transformation of this 1H FID (Fig. 9.2, put together from peak heights of a large number of 13 C spectra) gives a 1H spectrum with a peak at the frequency of the original 1H (fta). The second Fourier transform traces backward from the intensity variation of the 13C peak to the history of the 1H as it undergoes chemical-shift evolution during t1. We can say that during t1 we "encoded" the chemical shift of Ha, and this encoded information turns up in the peak height dependence of the Cb peak on the value of the incremented delay t1. The second Fourier transform "decodes" this information and gives us the chemical shift of Ha. The experiment provides a correlation between the chemical shift of Ha (Qa) and the chemical shift of Cb (^b), proving that they are directly bonded to each other (J coupled). In 2D NMR, we do not correlate spins or positions within a molecule; we can only make connections between chemical shifts (frequencies). It is our job in interpreting the 2D spectrum to try to convert this information into structural conclusions.

In Figure 9.1 we show only one component of the proton magnetization (2Iy Sz) undergoing chemical-shift evolution during the t1 delay, and it is the magnitude of this component at the moment of magnetization transfer that determines the magnitude of the 13 C FID obtained at the end. This is true because magnetization transfer always selects only one component of magnetization. For INEPT transfer we can ignore in-phase 1H coherence (Ix, Iy) because it cannot undergo coherence transfer, so let's look only at the chemical-shift evolution of 2Iy Sz:

The simultaneous 90o pulses on 1H and 13C give INEPT transfer only for the first term:

2IySzcos(Qat1) - 2IxSzsin(fiat1)

2SxIzcos(ftat!) - 2IxSxsin^O

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