Assignment

There are two things we can do with a proton spectrum: try to figure out the structure of an unknown compound or try to assign the peaks to the hydrogen positions of a known compound. The latter process is called assignment: pairing each resonance in a XH spectrum with a hydrogen or a group of equivalent hydrogens in the chemical structure. A "resonance" is a single chemical shift position in the spectrum; it can be a single peak (a singlet) or it may be "split" by J coupling into a complex pattern of peaks—a triplet or a double septet, for example. Sometimes we refer to a "resonance" as a peak, but this can be confusing because it may consist of many peaks of a multiplet pattern. The best way to learn to interpret NMR spectra is to assign the peaks in a spectrum of a known compound. This is much easier than dealing with unknowns and teaches the same principles that will be necessary to analyze unknown spectra. The vast majority of examples in this book will be discussed as assignment problems rather than unknown problems.

We will see that with complex molecules chemical shift is not enough to arrive at a unique assignment; normally, there will be several or many XH resonances with similar chemical shifts, and we can only put these resonances into categories (e.g., XH a to a car-bonyl group or olefinic proton) rather than unique assignments. To uniquely assign we will need to correlate protons to other protons or other spins (e.g., 13C) within the molecule, either by through-bond relationships (i.e., J couplings) or by through-space relationships (i.e., NOEs). Chemical shift correlation is a process of pairing a proton with another spin that is nearby in the bonding network (number of bonds) or by direct distance through space (A), usually by a two-dimensional (2D) experiment. In establishing these relationships, we only "know" a spin by its precise chemical shift. That is why we call the process of correlating two spins chemical shift correlation. So the chemical shift of a proton is

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

not only an imprecise description of its chemical environment but also a precise "address" or "label" by which we can "talk to" that proton and ask questions about its immediate environment in the molecule, in terms of nearby spins. In this sense we can think of each proton as a probe or flashlight, which we can shine on the immediate environment of the molecule to see what is around it. The flashlight is very weak, however, and can only "see" up to about 5 A in space and about three bonds through the bonding network, to identify its neighbors. The neighbors are, of course, only identified by their chemical shifts.

2.2 EFFECT OF BO FIELD STRENGTH ON THE SPECTRUM

A large part of the history of NMR instrument development concerns the effort to attain higher and higher magnetic fields by building stronger and stronger magnets. The first widely available commercial NMR instruments were 60 MHz continuous-wave (CW) instruments (e.g., Varian A-60 and T-60) that only did *H spectra. These magnets were simple electromagnets: copper wire wound on an iron core with a large current passed through the coil. A large amount of heat was generated by the current, so water was passed through the magnet to cool it. Newer instruments came out with 90 MHz (Varian EM-390) and 100 MHz (Varian XL-100) proton frequencies. These were also CW, although by the mid-1970s the strongest electromagnets were being used for the first pulsed Fourier-transform instruments. An early 13 C instrument (FT-80) used an 80-MHz electromagnet with RF pulse electronics and computer built by Nicolet. It operated at 20 MHz for 13C, used 8-mm sample tubes, and had a whopping 8192 bytes of memory!

One hundred megahertz (2.35 T) was the "brick wall" for electromagnets, and it was necessary to develop an entirely new technology to go beyond that limit. Superconductivity is the phenomenon of zero resistance for electrical conductors at low temperature. Special alloys including niobium and titanium can be made into wires that when cooled to 4.2 K (the boiling point of liquid helium) can support large electrical currents without any resistance. This means that if a coil of this wire is immersed in liquid He and a current is passed through the coil, we can connect the end of the coil to the beginning and get the current to flow in a closed loop without any resistance. The large current will produce a very strong magnetic field, and because there is no resistance, there is no loss of energy to heat and the current will be stable. Superconducting magnets can run for decades without any significant loss of magnetic field strength as long as the superconducting coil is kept at liquid He temperature the whole time. The first superconducting NMR instrument I used (in the late 1970s) was a 180 MHz instrument built by Alex Pines at the University of California at Berkeley. The "pulse programmer" was set up using a teletype terminal; the Nicolet computer had to be "bootstrapped" by setting an array of switches (bits) to a specific binary number (address) and hitting the start button, and the audio filters had to be set to the spectral width by twirling dials. Shims were adjusted with a vast array of knobs, and data could be saved on a computer "disk" the size of a large dinner plate. Soon commercial magnets began to climb in field strength: 200, 250, 300, 400, and 500 MHz. Finally, the same technology was extended to 600 MHz, but this was the limit at 4.2 K, the boiling point of He at atmospheric pressure. By reducing the pressure in the helium can, the temperature was lowered and magnets reached 750, 800, and finally 900 MHz. A 900-MHz magnet looks like a space shuttle on its launch pad and requires a whole building devoted to one NMR instrument. Many groups are struggling to come up with the first 1-GHz

(1000 MHz) magnet, but this has become a very difficult goal to achieve. It would seem that the current superconductivity technology has been pushed to a limit, and there is a great need for a fundamental breakthrough. Ceramic superconductors have been developed that can achieve superconductivity at much higher temperatures (77 K and higher), but it has been difficult to form these materials into wires, and the current carrying capacity is very small.

NMR spectrometers cost roughly $1000 per MHz of field strength in the lower range, but above 600 MHz the cost rises exponentially to more than $5 million for a 900-MHz system. Why do people pay so much money to get higher magnetic fields? There is an obvious advantage in sensitivity because increasing the Bo field increases the population difference between the a and j states proportionately. This increases the net magnetization of the sample at equilibrium and thus increases the FID signal received after the pulse. Another factor enters in during the recording of the FID: The Larmor frequency, vo, is proportional to Bo, so we have the nuclear magnets precessing at a higher speed when we increase the magnetic field. Just as turning the crank on a generator faster produces a higher voltage in the output, spinning the net magnetization faster generates a bigger FID. So we expect the sensitivity to be proportional to Bo2, but in reality you cannot increase Bo while keeping everything else constant, so it works out in a practical sense to about BoL5. That means that a 13 C acquisition on a 200-MHz instrument would require 27 times as long as the same experiment on a 600-MHz instrument to achieve the same signal-to-noise ratio (600/200 to the 1.5 power, then squared because signal-to-noise ratio varies with the square root of the number of scans).

But it turns out that there is a much more important advantage to stronger magnets: resolution. What do we mean by resolution? In a technical sense, resolution is the width of an NMR line measured in hertz at one half the height of the peak. The peak width depends on the rate of decay of the FID, which is determined by the homogeneity of the magnetic field (shimming) and the inherent rate of decay of the net magnetization in the x-y plane (determined by a relaxation parameter of that proton called T2). In this sense, resolution is the same at 1.41 T (60 MHz) as it is at 21.1 T (900 MHz): about 1 Hz for a "small" molecule in organic solvent. But there is a broader and more important meaning of "resolution" that has to do with the ability to separate one proton resonance (chemical shift with splitting pattern) from another without overlap. We say that two proton signals ("signal" is another word for resonance) are "resolved" if there is no overlap between the group of peaks associated with one chemical shift and the group of peaks associated with another. As molecules become larger, the corresponding *H spectra become more complex because a larger number of resonances (chemical shift positions) is spread out over the same range of chemical shifts: roughly 0-10 ppm. As this happens there is more and more chance for overlap because many chemical shifts fall very close to each other. The spread or footprint of a XH resonance is determined by the J couplings, which are measured in units of hertz (the total width of the multiplet pattern is roughly equal to the sum of all J couplings to that proton). The larger this footprint, the fewer the unique XH signals that can be squeezed into the fixed 0-10 ppm territory without overlap. This is where a fundamental difference between the J coupling and chemical shift becomes crucial to this discussion: J couplings represent interactions between a pair of nuclei and as such their strength is always measured in hertz and is independent of magnetic field. Chemical shifts (expressed as frequency in hertz) are proportional to magnetic field, which is why we normally use units of parts per million (millionths of the Larmor frequency), so we have the same ppm value regardless of hertz value. Normally, we look at a proton spectrum with a horizontal

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