# Nuclear Magnetic Resonance

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1 Nuclear Magnetic Resonance NMR is probably the most useful and powerful technique for identifying and characterizing organic compounds. Felix Bloch and Edward Mills Purcell were awarded the 1952 Nobel Prize for their work in the area, although the technique did not become practical for organic compound structure determination until the 1960s. Analysis of the nuclear Schrödinger equation indicates that nuclei have spin quantum numbers. The nuclear spin quantum number, I (where I is integer or halfinteger), has values that are related to the nuclear shape and to the number of the different types of nuclear particles. Nuclei with even mass numbers and even numbers of protons have I = 0 (e.g., 12, 16 ). These nuclei cannot be used for NMR. Nuclei with odd mass numbers (due to odd numbers of either protons or neutrons) have I = n / 2 (e.g., 1 H, 13, 19 F, 31 P, which are all I = 1 / 2 ). Nuclei with even mass numbers as a result of odd numbers of both protons and neutrons have I = n, where n is an integer. If I is non-zero, the nucleus is spinning and must have one of several possible spin states. All of the spin states are degenerate in the absence of an applied external magnetic field, but in an applied field, the spin states have different energies, because the spin can align with or against the applied magnetic field. The difference in energy between the spin states is small, even in a large magnetic field, and corresponds to the energy in the radiofrequency part of the electromagnetic spectrum. The difference in energy between the spin states is: "E = #hb 0 where γ is the 2\$ magnetogyric ratio of the nucleus (the ratio of the magnetic moment to the angular momentum, sometimes called the gyromagnetic ratio), h is Planck s constant, and B 0 is the applied magnetic field. Because E = hν, the frequency of the radiation that! corresponds to the energy difference is " = #B 0 2\$ The higher field NMR at Rose-Hulman has a field strength B 0 of 7 Tesla (corresponding to 300 MHz for proton NMR), generated by a superconducting electromagnet. The magnet itself! is about 4 inches tall and 5 inches across, with hole about 1.5 inches across into which the sample is inserted. To maintain its superconducting properties, the magnet needs to be cooled to liquid helium temperature (~4 K). If the helium level drops too much, the top of the magnet will become exposed, and the resulting heat will boil off the helium, possibly suffocating anyone in the room. The magnetic field is strong enough to erase credit cards and damage watches within 1 meter of the instrument. (For comparison, the earth s magnetic field strength is ~5 x 10-5 Tesla.) Note that, because the magnetogyric ratio differs for each type of nucleus (see Table 4), the frequency range that corresponds to the difference in energy is also different. Thus, at a given field 29

2 strength, different nuclei will absorb at different frequencies, and so only one type of nucleus at a time will be observable. Increasing B 0 results in higher resolution (and requires more expensive instruments) because the energy difference between the spin up and spin down states increases, which makes the transitions easier to distinguish. In addition, the coupling constants between nuclei, which determine the splitting patterns, are due to the nuclear magnetic fields of nearby nuclei. Because these small magnetic fields are constant regardless of the imposed field, overlap of splitting from different resonances is less likely because the signals are effectively further apart. Table 4. Properties of Selected Nuclei Magnetogyric Isotope Spin Abundance ratio (γ/10 7 ) omments (rad/sec Tesla) 1 H I = 1 / % Nearly all organic compounds contain hydrogen 2 H I = % Quadripolar nucleus 3 H I = 1 / Li I = 3 / % Useful for organometallics 12 I = % Useless for NMR 13 I = 1 / % N I = % Quadripolar nucleus 15 N I = 1 / % F I = 1 / 2 100% P I = 1 / 2 100% Nucleic acids, some organic reagents The NMR signal for a nucleus depends on the local environment within the molecule. hemical shift is a small effect that results from the magnetic field of the electron cloud near the nucleus. Because electron clouds are asymmetric within molecules, the electron clouds interact with different nuclei differently. The electron clouds reorganize in the imposed magnetic field; the structure-dependent asymmetries in the clouds result in slight perturbations (a few parts per million for proton NMR) of the magnetic field experienced by the nuclei. These perturbations decrease the magnetic field perceived by the nucleus: B loc = B 0 (1-σ). Because the apparent field strength at the nucleus is different, the radiofrequency that is required for absorption will also be different. If a relatively dense electron cloud surrounds the nucleus, the opposing field induced in the electron cloud will have a relatively strong effect. This effect is called shielding, and results in 30

3 smaller chemical shifts. For a given chemical group (e.g., a methyl group), the induced field is proportional to the strength of the external field. hemical shift, δ, is the difference in hertz from the reference compound divided by the instrument frequency. hemical shifts are given in ppm (parts per million) of the base radiofrequency used. This means that all instruments, regardless of field strength will have the same chemical shift. Even with current instruments, the magnetic field drifts somewhat; an internal standard is necessary to calibrate the signals. TMS (tetramethylsilane, below) is in wide use as a standard, because it is the most strongly shielded compound commonly used. TMS has a δ of 0 (by definition). TMS has 12 hydrogens, all in the same environment, so it yields a strong signal. Si Tetramethylsilane (TMS) The likely range of chemical shift for 1 H is ~15 ppm, which corresponds to a range of 4500 Hz for a 300 MHz instrument. A number of different terms are used to describe relative chemical shift (Figure 15). The terms upfield and downfield are from instruments that use variations in applied magnetic field to observe nuclei at different chemical shift; most modern instruments employ a constant magnetic field, and vary the frequency of electromagnetic radiation used to excite the nuclei. Figure 15. Definition of some of the terms used to compare chemical shifts. Because 12 has I = 0, it cannot be used for NMR. However, protons are found in essentially all organic molecules, and 1 H NMR is highly useful for organic structure determination. As mentioned, the field experienced by a nucleus depends on several factors: B 0 ± E 0 ± P, where B 0 is the applied field, E 0 is the effect due to electron cloud of the attached carbon as modified by nearby functional groups, and P is the 31

4 coupling effect from protons on adjacent carbons. A single proton splits adjacent protons because it may exist with its spin axis up or down, resulting in two possible states and therefore in a doublet of peaks. A pair of protons splits adjacent protons into three peaks: both protons may be spin up, both may be spin down, or (with twice the probability) one may be spin up while the other is spin down. In this case, the paired spin up/down state does not alter the δ; the other conditions result in a slight change upfield or downfield of the expected resonance. hemically equivalent protons do not split each other. Ethane has a single peak at δ = 0.9 ppm. Benzene has a single peak at δ = 6.9 ppm. The coupling constant, J, determines the degree of splitting. Typical values of J for proton NMR are between 1 and 15 Hz, with J = ~7 Hz for alkanes. At least in simple cases, the coupling effect generally occurs over 3 bonds (e.g., for the system below, the two H b will split H a, and H a will split the two H b ). Ha H b H b A 1 H NMR spectrum thus contains three types of information that are useful in helping to determine the structure of the compound: 1. The chemical shift, which is the result of the function groups in close proximity to the proton. 2. The splitting pattern, which is the result of other hydrogens within three bonds of the hydrogen of interest. 3. The peak area for a particular resonance, which is proportional to the number of protons present in that environment. A full description of the use of NMR to determine molecular structure is beyond the scope of this manual. However, a correlation table that summarizes the chemical shifts observed by different protons in different environments may be found on the next page (Table 5). 32

5 Table 5. Predicting hemical Shifts for 1 H-NMR Spectra (adapted from Table 12.4, J.M. Hornback rganic hemistry, 1998) Type of Hydrogen hemical Shift (δ) Type of Hydrogen hemical Shift (δ) 0.9 Br l 3.0 N H N H Variable (1-4) 3.7 H Variable (2-5) 2 N F H 2.2 H 7-8 N I 2.2 Variable (6-8) N H H H Procedure: Find the functional group near the proton of interest. Take the chemical shift listed and: Add 0.3 if H 2 instead of, or add 0.7 if H instead of. Add 0.3 for electronegative group or atom attached to the adjacent carbon. When two electronegative groups are attached to the same carbon, both groups affect the hydrogens: add the indicated values from the table together, add the correction for the methylenyl or methinyl hydrogen, and subtract 0.9 from the total. The value obtained by these calculations is a prediction, and may deviate from observed values by 1 ppm or more. 33

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