307 Chemistry Chapter 10 Nuclear Magnetic Resonance
Nuclear magnetic resonance (NMR) spectroscopy is one of three spectroscopic techniques that are useful tools for determining the structures of organic compounds. [We will learn about infrared (IR) spectroscopy in chapter 11 and about ultraviolet/visible (UVVis) spectroscopy in chapter 14.] Spectroscopic techniques probe the energy differences between two "states" in a molecule by irradiating it with electromagnetic radiation of known frequency. We can observe "transitions", i.e., signals, when the incident radiation has the exact frequency, (that is a Greek nu) so that the energy of the photon, h , matches the energy difference, E, between the two states, E = h (Figure 10.1). Spectroscopic techniques are nondestructive; the excited molecules decay back to the ground state without decomposition. Mass spectrometry (chapter 11) is not a spectroscopic technique; it leads to the destruction of the sample.
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Photons of different energies can probe different types of transitions (Figure 10.2). Different spectroscopic methods use different units to characterize the energies of the photons applied. The units are all related to 1 the general equation, linking energy ( E) to frequency, (unit: s or Hz, named after Hertz). E = h UVVis spectroscopy uses wavelength, (unit: nm), to characterize the energy of the photon. Wavelength is related to frequency by = c . E = hc 1 IR spectroscopy uses wave number, 1/ (unit: cm )
E = hc Nuclear magnetic transitions are probed with radio waves. Compared to other spectroscopic techniques NMR has an additional complication: the
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energy differences between nuclear states and the "resonance frequency" are not constant, but depend on the magnetic field, H0, at which the spectrometer operates i.e., E, H0. At a magnetic field, H0 = 70 kGauss, 1H nuclei resonate at 300 MHz. The energy difference, E, between 1H nuclear levels at 70 kGauss is only ~3x105kcal mol1.
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Therefore, it is not sufficient to give the frequency at which an NMR transition occurs; we have to specify both the photon frequency and the magnetic field strength to describe our results unambiguously. Because of the very small energy difference between the two nuclear spin levels transitions between them are very fast: both levels are in equilibrium (see Chapter 2). G = RTlnK or lnK = G/RT The very low energy difference between our nuclear spin levels ( E ~3 105kcal mol1) means that the population differences between the nuclear spin levels are very small, typically much less than 1%. We will focus our discussion on the magnetic resonance of 1H and 13C nuclei. However many other nuclei also show magnetic resonance effects. The ability to show such effects is determined by the number of protons (Z) and neutrons (N) in the nucleus. Very significantly, nuclei with even Z and even N have no magnetic moment, i.e., they show no magnetic resonance. Unfortunately, this group includes two of the key elements of organic chemistry: 12C (Z = 6, N = 6) and 16O (Z = 8, N = 8). On the other hand nuclei with an odd number of protons or neutrons have magnetic moments and, thus, show magnetic resonance.
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Two features determine how easy it is to record the spectrum of a magnetic nucleus, its natural abundance and its relative sensitivity. For the magnetic nucleus of hydrogen, 1H, the natural abundance is high whereas the magnetic 13C is only a minor component of carbon. The relative sensitivity is related to the energy difference between the nuclear spin levels. It is high for 1H and 19F, but much lower for most other nuclei. Remember that a change in G affects K and the equilibrium populations exponentially. Nucleus 1H 2H 12C 13C 15N 16O 19F 29Si 31P Z N Abundance Relative Sensitivity 1.0
1 0 99.985 1 1 0.015 6 6 99.89 6 7 1.11 0.016 7 8 0.37 0.001 8 8 99.759 0.016 9 10 100.00 0.834 14 15 4.700 0.078 15 16 100.00 0.066 We could record all magnetic nuclei if we had an instrument allowing us to probe the wide range of frequencies required for this purpose.
However, the significant value of NMR lies in the fact that nuclei of the same element, particularly 1H or 13C, resonate at slightly different frequencies, depending on their chemical environment. When we use an 3
NMR spectrometer with a very limited range of frequencies and expand the resulting spectrum, the different responses will give us an insight into different chemical environments. We call this type of spectroscopy highresolution magnetic resonance.
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range 299,997,000 300,000,000 Hz 75,284,940 75,300,000 Hz 10 ppm 0 ppm 200 ppm 0 ppm The value of high resolution 1H NMR lies in three features, each of which provides us important information: 1) The differences in the response frequency of individual nuclei are called chemical shift; they identify the number of different types of nuclei and the chemical environment of a nucleus or group of nuclei; 2) The intensity of the response signal, obtained by integration, provides a measure for the relative number of nuclei giving rise to this signal; 3) Adjacent non-equivalent nuclei cause a splitting (spin spin splitting) of the signal into multiple lines, called multiplets, which identify the number of adjacent nuclei. Typical information gained from examining an NMR spectrum include:
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the number of different chemical shifts identifies the number of different groups present in the molecule; ii) the "position" of signals in the spectrum, the chemical shift, identifies the chemical environment of a group of nuclei; iii) the signal intensity identifies the number of nuclei represented by the signal; iv) the "multiplicity", the number of lines, identifies the number of nearby nuclei interacting with the nucleus/i considered. Instead of denoting the frequency of an NMR transition and the magnetic field strength of the spectrometer, we define chemical shift as the ratio, , of the response frequency relative to that of a standard (TMS) divided by the resonance frequency: = shift from TMS (in Hz) spectrometer frequency (in MHz) Since the resonance frequency is proportional to the magnetic field strength, this is equivalent to denoting the frequency of the signal and the 6 magnetic field strength. This ratio is given in ppm (parts per million, 10 ); it has no dimension. Different nuclei have different ranges of chemical shifts, e.g., Nucleus Range Standard 1 H (10 ppm) Si(CH3)4 (TMS)
13 19 31
i)
C F
(200 ppm) (400 ppm)
Si(CH3)4 CF3COOH
P (700 ppm) 85 % H3PO4 Let us recall that the energy difference between the two nuclear spin levels, (in the direction of the magnetic field, H0) and [oriented antiparallel (opposite) to H0] are very minor. At a field of 70 kGauss 5 kcal mol1 E = h = G = RTln K = 2.303 RT log K [ ] 50.005 [ ] 49.995 n( ) = 1 in 10,000 We now turn to the details of the three key features identified above. 1) Chemical shift Different chemical shifts are caused by different electronic environment of the corresponding 1H nucleus (or group of nuclei). This 5
effect has its root in two physical principles: a) in a magnetic field charged particles (electrons) are moving in circular and fashion; b) a moving charged particle (electron) induces a (small) magnetic field, hlocal (Figure 10.9). The induced field, hlocal, reduces the external magnetic field by a small amount. We call a nucleus experiencing a smaller field, H0 hlocal shielded. Its resonance is shifted to the right (to higher field or upfield). Nuclei experiencing the opposite effect are called deshielded; they experience a larger field, H0 + hlocal. Their resonance is shifted to the left (to lower field or downfield). See Figures 10.8, 10.10, 10.11. Different "functional" groups near a nucleus cause characteristic chemical shifts (Table 10.2). Electronegative atoms have a deshielding effect (Table 10.3), which decreases along an alkane chain, CH3CH2CH2Br 1.03 1.88 3.39 ppm 1H nuclei, which are chemically equivalent, have identical chemical shifts. Chemical equivalence may be due to symmetry or to a molecular motion causing equivalence. See Figure 10.13. Rapid rotation (Figure 10.12) or conformational interconversion (Figure 10.14) will render nuclei equivalent. Be sure to check carefully for equivalence models will help. 2) Integration The intensity of a magnetic resonance signal is proportional to the number of equivalent nuclei represented by that signal. The intensity can be determined by integration, performed by a computer, which determines the volume under the peak. The integrals provide the numerical ratio of the nuclei represented by the signal (Figure 10.15). The three dichloropropanes shown on p. 407 have different chemical shifts and different ratios of 1H nuclei. They also would be good examples to introduce the third important feature of 1H spectroscopy. 3) Spin-spin coupling The few spectra discussed so far showed only single lines (singlets). Such signals are observed for groups of 1H nuclei without any 1H nuclei on an adjacent carbon. For compounds containing a nucleus or group of nuclei on an adjacent carbon the resonances appear as multiplets, groups of lines separated by identical distances. Such multiplets reveal significant information about the connectivity of individual groups in a molecule. The number of lines, representing a nucleus, is determined by the number of nearby nuclei. This effect is caused by the alignment of nuclear magnets parallel or antiparallel to H0. A nucleus aligned parallel to H0
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increases the field and deshields the neighboring nucleus; nuclei aligned antiparallel to H0 shield adjacent nuclei. See Figure 10.17. If the neighboring carbon has n 1H nuclei, the signal is split into m = n + lines (n + rule). The intensities of multiplet lines are determined by the probabilities of having the nuclei "up" ( ) or "down" ( ). The intensities are given by Pascal's Triangle. Note that each new term (number) is the sum of the two terms (numbers) above; that means that you can construct the triangle yourself readily. (Table 10.4). See Figures 10.21, 10.22, Table 10.5 n
singlet 1 doublet 1 1 1 1 1 1 6 5 15 4 10 septet 20 3 quintet 6 sextet 10 15 triplet 2 quartet 3 4 5 6 1 1 1 1 1 1 0 1 2 3 4 5 6
4) Spin-spin coupling complications The simple rules for multiplets given by Pascal's triangle are idealized and do not always apply. We will consider several such cases. i) Coupling to nuclei with very similar chemical shifts. The NMR spectra of compounds having several groups with closelying chemical shifts have distorted spectra; we call these non-first-order spectra. In some spectra no clear multiplet pattern is discernible (Figure 10.23); in others, the multiplet intensities are seriously distorted (Figure 10.24). Recording the spectra at higher magnetic fields will improve the separation of the peaks and change the spectrum in the direction of the idealized pattern. ii) Coupling to non-equivalent nuclei In the majority of compounds hydrogens are coupled to two or three sets of neighboring 1H nuclei. In some compounds these neighbors have 7
identical couplings, giving rise to a "normal" multiplet, cf., the hydrogens at C-2 of 1-bromopropane (Figure 10.27). In other cases, however, nonequivalent nuclei have different coupling constants, resulting in more complicated splitting patterns, cf., 1,1,2-trichloropropane (Figure 10.27). Here, the N + 1 rule has to be applied sequentially for the sets of nonequivalent neighbors. It is convenient to begin with the largest coupling. 5) Enantiotopic and diastereotopic hydrogens (or groups) In some cases the two hydrogens of a CH2 group are non-equivalent. Typically, this is the case for a CH2 group next to a chiral center, e.g., the CH2 of 1,2-dichloropropane. We call such hydrogens diastereotopic, because replacing one (Ha) or the other (Hb) by another function (e.g., Br) would generate diastereomers.
Diastereotopic hydrogens are nonequivalent; they have different chemical shifts and split each other, resulting in more complicated spectra (cf., Chemical Highlight 10.3). [hydrogens whose replacement yields enantiomers are called enantiotopic; they are chemically equivalent]. 6) Fast exchange and consequences The signals of OH functions often show no coupling to the hydrogens at the adjacent carbon. This observation is related to hydrogen bonding (remember?); the coupling is "voided" by a rapid exchange of the proton with other OH groups and with traces of water; any H remains in place for less than 105 s. Therefore, the NMR spectrometer sees only an average peak. The fast exchange can be slowed by cooling, causing the splitting to be observed (cf., Figure 10.29). 7) 13C nuclear magnetic resonance You have learned that NMR spectroscopy is not limited to 1H nuclei. In particular, 13C NMR significantly aids structure elucidation. However, the observation of 13C spectra faces major problems; we have mentioned the low natural abundance of 13C and the significantly lower sensitivity (the resonance frequency of 13C is only 1/4 that of 1H. Furthermore 13C spectra have complex splitting patterns (cf.; Figure 10.30). 8
In order to facility the recording of 13C spectra all 1H splittings are removed by broad-band decoupling. This is achieved by applying a strong radiofrequency signal covering the entire range of 1H frequencies to the sample while the 13C spectrum is recorded. The resulting spectra show single lines for each magnetically distinct type of carbon (Figure 10.31, 32). [The number of 13C chemical shifts expected for a compound is a favorite exam question]. Like 1H spectra 13C spectra also have characteristic chemical shifts reflecting the chemical environment. The range of 13C shifts is much greater (~200 ppm) than that of 1H (10 ppm); 13C chemical shifts show similar trends to those of 1H (cf., Table 10.6) 8) DEPT (distortionless enhanced polarization transfer) Structure elucidation based on 13C spectra is greatly facilitated by modern FT techniques utilizing complex pulse sequences. A DEPT experiment separately identifies CH3, CH2, and CH functions (Fig. 10.33). 9) 2D NMR COSY and HETCOR 2D NMR spectroscopy records a spectrum as a function of two characteristic times. Two Fourier transformations yield a spectrum as a function of two frequencies. We can plot a spectrum correlating two 1H frequencies or 1H with 13C frequencies. These spectra reveal the connectivity of groups (Chemical Highlight 10.4).
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