Chemistry 307 Chapter 10 Nuclear Magnetic Resonance

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1 Chemistry 307 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, ν (that is a Greek nu) for which the energy of the photon, hν, matches the energy difference, ΔE, between the two states, ΔE = hν (Figure 10.1). Spectroscopic techniques are nondestructive; the excited molecules decay back to the ground state without decomposition. Mass spectrometry (chapter 11, which we will not discuss) is not a spectroscopic technique; it leads to the destruction of the sample. 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

2 the general equation, linking energy (Δ E) to frequency, ν (unit: s 1 or z, named after the German physicist ertz). Δ E = h ν UVVis spectroscopy uses wavelength, λ (unit: nm), to characterize the energy of the photon. Wavelength is related to frequency by ν = c / λ. Δ E = h c / λ IR spectroscopy uses wave number, 1/λ (unit: cm 1 ) Δ E = h c ~ ν Nuclear magnetic transitions are probed with radio waves. Compared to other spectroscopic techniques NMR has an additional complication: the energy differences between nuclear states and the resonance frequency are not constant, but depend on the magnetic field, 0, at which the spectrometer operates i.e., Δ E, ν α 0. At a magnetic field, 0 = 70 kgauss (7 Tesla), 1 nuclei resonate at 300 Mz, at 0 = 117 kgauss (11.7 Tesla), 1 nuclei resonate at 500 Mz. ΔE Magnetic Field Strength, [kgauss] 2

3 Therefore, it is not sufficient to give the frequency at which an NMR transition occurs; in addition to the photon frequency we have to specify the magnetic field strength to describe our results unambiguously. Instead of denoting these two parameters for each NMR transition, we define chemical shift as the ratio, δ, of the response frequency relative to that of a standard (TMS) divided by the resonance frequency: δ = shift from TMS (in z) spectrometer frequency (in Mz) Since the resonance frequency is proportional to the magnetic field strength, this is equivalent to denoting the frequency of the signal and the magnetic field strength. This ratio is given in ppm (parts per million, 10 6 ); it has no dimension. The energy difference between the two nuclear spin levels, α (in the direction of the magnetic field, 0, up ) and β [oriented antiparallel (opposite) to 0, down ] are very minor; at 70 kgauss it is only ~3x10 5 kcal mol 1. Transitions between them are very fast; they are in equilibrium. The equilibrium populations of the nuclear spin levels are almost identical; they differ by much less than 1%. ΔE = hν = kcal mol 1 ΔG = RTlnK = RT log K lnk = ΔG /RT [α] [β] Δn(α β) = 1 in 10,000 3

4 We will focus our discussion on the magnetic resonance of 1 and 13C nuclei. owever 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. Two features determine how easy it is to record the spectrum of a magnetic nucleus, its natural abundance and its relative sensitivity. The magnetic nucleus of hydrogen, 1, has a high natural abundance while 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 1 and 19F, but much lower for most other nuclei. Remember that a change in ΔG affects K and the equilibrium populations exponentially. Nucleus Z N Abundance Relative Sensitivity C C N

5 16O F Si P In principle, we could record a spectrum of all magnetic nuclei on an instrument probing the wide range of frequencies required for this purpose, shown here for the range from 15N (25.4Mz) to 1 (300Mz) at 70kG. = 70 kg 15 N 13 C 1 19 F Resonance Frequency, ν [Mz] 300 In such an instrument chlorofluoromethane would show six signals. 5

6 owever, the significant value of NMR lies in the fact that nuclei of the same element, particularly 1 or 13C, may resonate at slightly different frequencies, depending on their chemical environment. When we use an NMR spectrometer focused on the limited range of frequencies of a single type of nucleus and expand the resulting spectrum, the different responses will give us insight into different chemical environments. We call this type of spectroscopy high-resolution magnetic resonance. 6

7 10 ppm 0 ppm 200 ppm 0 ppm Different nuclei can have substantially different ranges of chemical shifts; the wider the range the more detailed the structural information. Nucleus Range Standard 1 (10 ppm) Si(C3 ) 4 (TMS) 13 C (200 ppm) Si(C3 ) 4 19 F (400 ppm) CF3 COO 31 P (700 ppm) 85 % 3 PO 4 igh Resolution Magnetic resonance 7

8 The value of high resolution 1 NMR lies in three features, of which each provides us important information: 1) The different response frequencies of individual nuclei are called their 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, J coupling) of the signal into multiple lines, called multiplets, which identify the number of adjacent nuclei. Typical information gained from examining an NMR spectrum include: 1i The number of different chemical shifts identifies the number of different types of groups present in the molecule; it does NOT necessarily reveal the actual number of groups present in the molecule 1ii The position of signals in the spectrum, the chemical shift, identifies the chemical environment of a group of nuclei; 2 The signal intensity identifies the relative number of nuclei represented by the signal; 3 The multiplicity (the number of lines in a signal) identifies the number of nearby nuclei interacting with the nucleus/i considered. We now turn to the details of the three key features identified above. 1) Chemical shift 8

9 Different chemical shifts are caused by different electronic environment of the corresponding 1 nucleus (or group of nuclei). This effect has its root in two physical principles: a) a magnetic field causes charged particles (electrons, such as the lone pairs at electronegative atoms) to move in circular fashion; and b) a moving charged particle (electron) induces a (small) magnetic field, hlocal. The induced field, hlocal, reduces or enhances the external magnetic field 0 by a small amount. We call a nucleus experiencing a smaller field, 0 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 higher field, 0 + hlocal. Their resonance is shifted to the left (to lower field or downfield). See Figures 10.8, 10.10, The hydrogen nuclei of alkanes occur at high field (~1 ppm): they are shielded by their own electrons. A hydrogen nucleus without electrons (+) is strongly deshielded. Different functional groups near 1 nuclei cause 9

10 characteristic chemical shifts (Table 10.2). Electronegative atoms have a deshielding effect; the magnitude of the effect correlates with the electronegativity of the heteroatom (Table 10.3). These effects decrease along an alkane chain, Br C 2 C 2 C ppm If a 1 nucleus has more than one neighboring electronegative atoms, the effect is cumulative, C 3 C 2 2 C ppm 10

11 You would describe (report) the chemical shifts of 2,2- dimethylpropanone as δ = 0.89 (0.9), 1.80 (1.8), 3.26 (3.3) ppm. Equivalent Nuclei The question whether a group of nuclei are magnetically equivalent or nonequivalent is of great significance for the interpretation of NMR spectra. 1 nuclei, which are equivalent, have identical chemical shifts and couple to other nuclei in identical fashion. Equivalence may be due to symmetry or caused by a molecular motion exchanging positions (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 this is another area where models will help you. 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 11

12 area under the peak. The integrals provide the numerical ratio of the nuclei represented by the signal (Figure 10.15). To describe chemical shift and signal intensities of (C 3 ) 3 CC 2 O, you would say δ (ppm) = 0.89 (9 ), 1.80 (1), 3.26 (2). The three dichloropropanes shown on p. 407 have different chemical shifts and different ratios of 1 nuclei. C 3 three 1 signals 1 : 2 : 3 5.9, 2.35, 1.0 ppm C 3 four 1 signals 1 : 1 : 1 : , 3.55, 4.15, 1.6 ppm two 1 signals 4 : 2 3.7, 2.25 ppm [You may have trouble understanding why 1,2-dichloropropane has 4 chemical shifts; please, be patient, we ll soon get to that.] 12

13 3) Spin-spin coupling The few spectra discussed so far showed only single lines (singlets). Such signals are observed for groups of 1 nuclei without any 1 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 (in z). Such multiplets reveal significant information about the connectivity of individual groups in a molecule. The number of lines representing a nucleus (or group of equivalent nuclei) is determined by the number of nearby nuclei. This effect is caused by the alignment of nuclear magnets parallel or antiparallel to 0. A nucleus aligned parallel to 0 increases the field and deshields the neighboring nucleus; nuclei aligned antiparallel to 0 shield adjacent nuclei. See Figure Empirically signals with n neighboring nuclei are split into an n + 1 multiplet; if a is coupled to (b)n, its signal has (n + 1) lines. This relationship is called the n + 1 rule. Example: 3 C O C C 2 C ppm 1.0 ppm 3 C3 interacting with C2: (n + 1) triplet 2.2 ppm 3 C3 not coupled: (n + 1) singlet 2.4 ppm 2 C2 interacting with C3: (n + 1) quartet 13

14 3 C C C ppm 1.6 ppm 6 (C3)2 interacting with C: (n + 1) doublet 3.7 ppm 1 C interacting with (C3)2: (n + 1) septet Note that J coupling is a mutual interaction. The strength of the interaction (the magnitude of J) is a function of a) the distance between the nuclei and b) the magnetic moments of these nuclei. For any two nuclei, these parameters must be identical, e.g., J a -C C- b = J b -C C- a ow do these interactions arise? When placed in a magnetic field magnetic nuclei align themselves either parallel ( up, α) or antiparallel to the field ( down, β). As a result nuclei in their vicinity experience either a slightly larger or a slightly smaller magnetic field than the nominal field, 0. We can explain the number of lines in a multiplet and their intensities by simple statistic considerations. The intensities of multiplet lines are determined by the probabilities of having the nuclei up or down. For example, a nucleus, B, can have two orientations, up or down. The signal of the neighboring nucleus, A, is split into two lines; because of the miniscule energy difference between α and β spins, the levels of B are populated essentially equally: therefore the two lines of A have identical intensities (1 : 1). Two equivalent nuclei, B, have four probabilities: αα, αβ, βα, and ββ. Because αβ and βα are equivalent, there are three signals in the ratio of 1 : 2 : 1. Three equivalent nuclei, B, have eight probabilities: 14

15 ααα, ααβ, αβα, and βαα, αββ, βαβ, and ββα, and βββ. Because the permutations with 2 αs are equivalent, and so are those with 2 βs, A has four signals in the ratio of 1 : 3 : 3 : 1. The multiplet intensities are given by Pascal's Triangle. Note that each new term (number) is the sum of the two terms (numbers) above; this means that you can construct the triangle yourself readily. (Table 10.4). Pascals Triangle n singlet 1 0 doublet triplet quartet quintet sextet septet Please, consult Figures 10.21, 10.22, Table ) 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. 15

16 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 more than one set of neighboring 1 nuclei. In some compounds non-equivalent neighbors have identical couplings, giving rise to a normal multiplet, for example, the hydrogens at C-2 of 1-bromopropane (Figure 10.27). Br C 2 C 2 C 3 2 neighb sex 2 neighb t 2+3 neighb t In contrast, the non-equivalent nuclei (C and C 3 ) of 1,1,2- trichloropropane interact with the central C with different coupling constants, resulting in a more complicated multiplet (Figure 10.27). 2 C C C 3 1 neighb q(d) 1 neighb d 1+4 neighb d 16

17 17

18 2 C C C 3 In cases where you are dealing with two different coupling constants, the n + 1 rule has to be applied sequentially for the sets of nonequivalent neighbors. It is best to mention the larger coupling first. The pattern of Figure (left) the quartet splitting is larger than the doublet splitting; the multiplet is a quartet of doublets (q(d)) and NOT a doublet of quartets (d(q)). 5) Enantiotopic and diastereotopic hydrogens (or groups) In some cases the two hydrogens of a C 2 group are non-equivalent. Typically, this is the case for a C 2 group next to a chiral center, e.g., the C 2 of 1,2-dichloropropane. We call such a pair of hydrogens diastereotopic, because replacing one ( a ) or the other ( b ) by another atom or group (e.g., Br) would generate diastereomers. C 3 C 3 C 3 a C-1 b a Br Br b Diastereomers 18

19 Diastereotopic hydrogens are nonequivalent; they have different chemical shifts and split each other, resulting in more complicated spectra (cf., Chemical ighlight 10.3). [hydrogens whose replacement yields enantiomers are called enantiotopic; they are chemically equivalent]. Now you understand why 1,2-dichloropropane has 4 chemical shifts: the two s at C-1 are next to a chiral carbon and, therefore, nonequivalent. C 3 four 1 signals 1 : 1 : 1 : , 3.55, 4.15, 1.6 ppm 6) Fast exchange and consequences The signals of O functions often show no coupling to the hydrogens at the adjacent carbon. This observation is related to hydrogen bonding (which is coming up in Chapter 8); the coupling is voided by a rapid exchange of the proton with other O groups and with traces of water; any remains in place for less than 10 5 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 1 nuclei. In particular, 13C NMR significantly aids structure elucidation because of a wide range of chemical shifts. owever, the observation of 13C spectra faces major problems; we have mentioned the low natural abundance of 13C (strike 1) and the significantly lower sensitivity (the resonance frequency of 19

20 13C is only 1/4 that of 1; strike 2). Furthermore 13C spectra have complex splitting patterns (cf.; Figure 10.30; strike 3?). In order to facility the recording of 13C spectra (and avoiding strike 3) all 1 splittings are removed by broad-band decoupling. This is achieved experimentally by applying a strong radiofrequency signal, covering the entire range of 1 frequencies, to the sample while the 13C spectrum is recorded. The resulting spectra show single lines for each magnetically distinct carbon (Figure 10.31, 32). 13C spectra, like 1 spectra, also have characteristic chemical shifts reflecting the chemical environment. Although 13C chemical shifts show similar trends to those of 1 (cf., Table 10.6), their range of chemical shifts is much greater (~200 ppm) than that of 1 (10 ppm); therefore, the number of 13C chemical shifts is indicative of the actual number of magnetically distinct carbons. [The number of 13C chemical shifts expected for a compound is a favorite exam question ]. We close our first foray into NMR with two special topics. 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 C 3, C 2, and C functions (Fig ). The top trace has all 13C signals, the second, third and fourth trace have the 20

21 C 3, C 2, and C groups, respectively. The two signals that do not appear in the 2 nd, 3 rd, and 4 th trace are quaternary carbons. 21

22 9) 2D NMR COSY and ETCOR 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 1 frequencies (COSY) or 1 with 13C frequencies (ETCOR). These spectra reveal the connectivity of groups (Chemical ighlight 10.4). The diagonal line contains the resonances of BrC 2 (bottom left), C 2 (center) and C 3 (top right). The off-diagonal responses occur symmetrically between peaks representing 1 nuclei that interact with each other. These responses indicate that the C 2 group interacts with both the BrC 2 and the C 3 groups. 22

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