e 2m p c I, (22.1) = g N β p I(I +1), (22.2) = erg/gauss. (22.3)

Transcription

1 Chemistry 26 Molecular Spectra & Molecular Structure Week # 7 Nuclear Magnetic Resonance Spectroscopy Along with infrared spectroscopy, nuclear magnetic resonance (NMR) is the most important method available for the determination of molecular structure particularly for large organic molecules and biopolymers. While infrared spectroscopy provides information about the functional groups that are present in a molecule, NMR yields the number of (and in certain cases the separations between) certain atoms in the sample. What is the basis of NMR spectroscopy? As we have seen in earlier lectures, electrons and many nuclei have magnetic dipole moments that lead to non-zero values of the spin nuclear angular momentum. By applying a magnetic field, it is possible to separate single axis components of this nuclear spin angular momentum and to induce transitions between them. Specifically, if a nucleus has an intrinsic spin angular momentum I with magnitude I(I +) h, the nuclear magnetic dipole moment µn is equal to µ N = g N e 2m p c I, (22.) where g N is the nuclear g-factor and m p is the proton mass. Because nuclear structure is complex, the values of g N are non-integer and are most easily determined experimentally. The absolute magnitude of the nuclear magnetic moment is e µ N = g N 2m p c [I(I +)]/2 h = g N β p I(I +), (22.2) where the nuclear magneton β p (commonly denoted β N ) is defined as β p e h 2m p c = erg/gauss. (22.3) Due to the increased proton mass, the nuclear magneton is (/836) th of the Bohr magneton (to which we ll return in our discussion of ESR). The projected components of the nuclear angular momentum, denoted by M I h, obviously run from I to +I in integral steps, and the z-component of the nuclear spin eigenfunctions follow Î z M I > = M I h M I >. Only nuclei with either odd mass or odd atomic number, or both, have non-zero values of I. Thus, common nuclei such as 2 C and 6 O cannot be used in NMR spectroscopy, but H (I=/2), 2 D (I=), 3 C (I=/2), 4 N (I=), 5 N (I=/2), 7 O (I=3/2), 9 F (I=/2) and 3 P (I=/2) can. Magnetic Resonance and Selection Rules As we know from an analysis of the Zeeman effect, in the absence of an external magnetic field the different values of M I are degenerate, and no spectroscopy is possible. 57

2 Classically, the interaction between a nuclear magnetic moment and an external magnetic field B is µ N B = g N β p h I B = g N β p h BI z, (22.4) where we have chosen the z-axis to coincide with the direction of the applied magnetic field. Quantum mechanically we have Ĥ = g N β p h BÎz = γ n BÎz, (22.5) where γ N g N β p / h is the magnetogyric ratio. Thus, Ĥ M I > = g N β p BM I M I >, M I = I,I,..., I (22.6) The application of the static magnetic field results in evenly spaced energy levels that diverge as the magnetic field is increased, as shown in Figure 22. for the simple I = /2 case. Energy M = -/2 I I = /2 B (rf field) B 0 M = +/2 I Figure 22. NMR field splittings for a spin /2 nucleus, with the magnetic field along the z-axis. In principle, the application of electromagnetic radiation to the collection of nuclear spins can result in the absorption or emission of radiation by the system. To determine what frequencies are involved we must, as always, determine the selection rules. Since the selection rules will clearly be of the magnetic dipole type, we must consider the interaction of a time dependent magnetic field B and the perturbing Hamiltonian Ĥ (t) = B ˆµ N = h β p g N (B x Î x + B y Î y + B z Î z ). (22.7) 58

3 Let us suppose the static B 0 field is applied in the z-direction. For the z-component of the B perturbing field, matrix elements are of the form < ψ m Îz ψ n > = < M I Îz M I > = M I hδ M I,M I, (22.8) and since the nuclear spin eigenfunctions are orthonormal the z-component of the time varying field cannot induce NMR transitions. For the x and y B components, it is best to use the so-called ladder operators (that are analogous to the creation and annihilation operators we talked about in harmonic oscillator approaches to vibrational spectroscopy) α = Îx ± iîy. These operators create the M I ± > states from the M I > state, and so the Îx and Îy matrix elements lead to terms such as 2 < M I Îx M I > = < M I Î+ + Î M I > = cδ M I,M I + + dδ M I,M I. (22.9) The y-axis matrix elements are similar, and so the B x and B y components lead to the NMR selection rules M I = ±. Since the energy levels are equally spaced the transition frequency is ν NMR = γ N B/2π, which is called the Larmor frequency. Thus, although there are 2I+ nuclear spin energy levels, in this simplest analysis of NMR spectroscopy there is only a single NMR frequency for a given nucleus, whose magnitude depends on the nuclear g-factors and the static magnetic field. Higher magnetic fields lead to larger splittings and, as we will see, higher sensitivities and spectroscopic resolution. At fields of 0 kilogauss (kg), the NMR frequencies (in MHz) of common nuclei are: H 2 H B 3 C 4 N 9 F 3 P NMR spectrometers are typically classified by the resonance frequencies they operate at, and since the maximum attainable fields are of order several Tesla H (proton) machines typically work at frequencies of several hundred MHz, or in the radio part of the electromagnetic spectrum. In the absence of a static field all of the M I > components are equally populated, and the energy difference between the components is small compared to kt even for the largest achievable fields. Thus, the population differences are extremely small and unless the magnetic moments are coupled to other degrees of freedom the sensitivity of NMR is such that largish samples are required. If the magnetization of the sample is denoted by M, only the M z component has a non-vanishing value (denoted M 0 here), the M x,y components vanish when time averaged. Qualitatively, the x,y-components of the 59

4 magnetization precess about the z-axis at the Larmor frequency. Interestingly, the M z and M x,y can evolve over two different time scales denoted T and T 2 defined by d dt M z = T (M z M 0 ), d dt M x,y = T 2 M x,y. T is typically called the longitudinal or populational relaxation time, T 2 the transverse relaxation or dephasing time since only the T decay actually results in changes of the populations of states that possess different energies when the static magnetic field is applied. We will return to these processes in Lecture 23. NMR Chemical Shifts IfalltheNMRfrequenciesofprotonsinasampletrulyabsorbedatthesamefrequency, NMR spectroscopy would not be the tremendously important tool that it is. Fortunately, life is more complicated and more interesting! In liquid ethanol, for example, the low resolution NMR spectrum consists of three lines whose separation increases with increasing static magnetic field. The three lines arise from the three chemically distinct protons in the molecule. Why? The above derivation is only valid for an isolated nucleus. Within molecules, the magnetic field at each nucleus arises both from the applied external field and also from the magnetic fields of nearby electrons and other nuclei. If we term this molecular magnetic field B I, then mathematically it can be proven that B I = -σ IB 0, where σ I is a symmetric second-rank tensor (or matrix) with six independent components of the total nine components in the tensor. σ I is analogous to the polarizability tensor we discussed in the lecture on Raman spectroscopy, and is referred to as the shielding tensor at nucleus i. As before, there is a principal axis system that diagonalizes the shielding tensor and that rotates with the molecular framework. Since the rotation time scale is fast compared to the NMR time scale, < B i >= < σ I > B 0. As it so happens, the shielding tensor averaging runs over the principal values and < σ I > = Tr σ I σ i, and the true field at nucleus i is given by B I = B 0 ( σ i ), (22.0) where σ i is a scalar quantity called the shielding or screening constant. The shielding constant can be evaluated theoretically, and is found to possess both a diamagnetic term (or positive term since the applied field is decreased) and a paramagnetic term (here the field is increased). These evaluations are complex, and to make a long story short the diamagnetic term is larger than the paramagnetic term for protons, and σ H is positive. Asinglenucleusiwithshieldingconstantσ i haseigenvalues g I β p B 0 ( σ i )M I,i for a static field B 0 applied along the z-axis. When several nuclei are involved, only one nuclear magnetic moment may change its orientation according to the selection rules, and the frequencies that appear in an NMR spectrum are simply ν i = h β p B 0 g i ( σ i ), i =,2,... (22.) 60

5 where the index i runs over the non-zero spin nuclei of interest. Thus, identical nuclei in chemically equivalent environments have the same values of g i and σ i, and as a result their NMR transitions occur at the same frequency. Clearly, the higher the value of the static magnetic field the wider the separation of the different transition frequencies. Higher fields therefore lead to a much better ability to distinguish the inequivalent nuclei in complex species and to better sensitivity (by increasing the population difference between the different nuclear spin states), and so are highly desirable. An example is shown in the benzyl acetate spectrum presented in Figure Here, the so-called chemical shift scale is used, which is the change in NMR transition frequency for a fixed B 0. Since the shielding constant is and since it depends on both the spectrometer frequency and B 0, chemical shifts are always reported with respect to a standard. The chemical shift is labeled δ i, and is typically of order a few p.p.m., so δ i (ν ref ν i ) ν ref 0 6 (p.p.m.) (22.2) For organic work, the standard reference is tetramethylsilane (TMS), for which all the protons are equivalent and which thus yields a single NMR line. The TMS shielding constant is quite large, and so most organic compounds appear to positive values on the chemical shift scale. Figure 22.2 The NMR spectrum of benzyl acetate. An important aspect of NMR spectroscopy is its linearity in terms of number of spins. That is, the integrated areas under the peaks in a given NMR spectrum are proportional to the number of nuclei in chemically equivalent environments. It is necessary to use the integrated areas since, as we shall see next, the NMR linewidths are highly dependent on 6

6 both the molecular environment and the state of the sample (temperature, liquid, solid, etc.). Thus, the number of proton peaks, their relative intensities, and their chemical shifts are of great utility in determining molecular structure. This latter property of chemical shifts is true because certain functional groups tend to have rather similar shielding constants in a range of different molecular topologies. Figure 22.3 presents an overview of the chemical shifts of important organic functional groups containing hydrogen that have been complied from thousands of NMR spectra. Figure 22.3-A simplified correlation chart for proton chemical shifts. NMR Spin-Spin Splittings Under very high spectral resolution, the NMR transitions from chemically equivalent nuclei are found to split into a suite of closely spaced lines. These splittings are found to be independent of the applied static field B 0, and are due to neighboring nuclei of the same spin in the same molecule (that is, they are intramolecular in nature and not due to interactions between molecules in a sample). Just as for spin-spin interactions in molecular spectra, two nuclear spins I and I 2 couple as follows: (h/ h 2 )J 2 Î Î2, where J 2 is called the nuclear spin-spin coupling constant. The Planck s constants at the beginning of the equation are inserted to give the overall J 2 the units of Hertz, that is frequency. For two spins, the overall Hamiltonian becomes Ĥ = g Nβ p B 0 h ( σ )Îz g Nβ p B 0 ( σ 2 )Îz2 + hj 2 h h 2 Î Î2. (23.3) 62

7 Due to the spin-spin term, the Hamiltonian is not separable and perturbation theory must be used. The exact details of the splittings are complex and depend on a number of factors. Fortunately, for proton NMR a qualitative approach can be used to understand the nature of the splittings induced, which are quite valuable in determining molecular structures. For these spin /2 nuclei there are two M I levels, ±/2, typically labeled as α and β. Consider a case where there are A m X n protons in a molecule. To calculate the splittings induced by one group in the molecule upon the other, the number of different combinations of the α and β functions must be determined. The case of a single proton is quite straightforward, the adjacent spin can either be up or down. The two orientations lead to slightly different magnetic fields at nearby nuclei, and as a result their NMR transitions are split into doublets. More generally, if one wants to find the number of ways that k objects can be selected from a total group of n number objects, the result is nc k = n! k!(n k)!. With protons, it turns out that binomial coefficients are needed to calculate the number of splittings induced by the n protons on group X, which can be determined graphically by use of Pascal s triangle: n where each entry is the sum of the two numbers to its right and left in the line above it. Thus, nearby methylene groups split spectra into triplets with a :2: ratio(αα:αβ, βα:ββ), nearby methyl groups into quartets with ratios of :3:3:, etc. (that is, n adjacent protons split the NMR signal into n+ components with intensity ratios given by Pascal s triangle). Figure 22.4 presents two simple examples of these effects in the NMR spectra of acetaldehyde and methanol. When there are several nearby functional groups, a number of splitting patterns can be induced, whose relative size depends on the value of the spinspin coupling constant J 2. As we will see next time, these values depend not only on the types of groups and nuclei involved, but on the geometry of the molecule (that is the distances and angular orientations of the spins in the groups). The resulting line widths therefore vary greatly, and can render quite messy the NMR spectra of large molecules. Fortunately, there are a number of very powerful NMR tools in which the RF fields are 63...

8 applied in sophisticated pulse sequences and that enable the determinations of molecular structures for species as large as biopolymers. These form the subject of our next lecture. Figure High resolution NMR spectra of liquid acetaldehyde (CH 3 CHO) and ethanol (CH 3 CH 2 OH). In the acetaldehyde spectrum, the area of the doublet is three times that of the quartet. For the methylene group in ethanol, it is clear that the spin-spin coupling constant for the methyl group is larger than that for the hydroxyl proton. 64

9 Chemistry 26 Molecular Spectra & Molecular Structure Week # 7 Fourier Transform & Multi-Dimensional NMR For the simple NMR spectra discussed in Section 22, one means of recording the chemical shift spectrum is to sweep the static magnetic field strength B 0 across each of the peaks. Another is to sweep the RF frequency associated with B. Signal averaging can then be used to improve the overall signal-to-noise ratio (SNR). The disadvantage of these techniques is that the swept field scanning times are long, and so the inherent sensitivity is low. Much better sensitivity can be obtained when operating NMR spectrometers in a pulsed mode. To see how this works, let s consider again the nature of the magnetization of an NMR sample under the application of a static magnetic field for a spin /2 system (so for protons, 3 C, 5 N, etc.). AsFigure23.remindsus, intheabsenceofamagneticfieldthereareequalnumbersof up and down spins (α and β), and the net magnetization M 0 is zero. Upon the application of B 0 along the laboratory z-axis, a net magnetization along the z-axis is established, and the spins precess about the field at the Larmor frequency. Figure 23. Magnetization for a spin /2 sample. (a) In the absence of the static magnetic field, the population of α and β spin states are equal, while (b) in the presence of the field M 0 is non-zero and the precession of the spins occurs at the Larmor frequency ν = γ N B/2π. Fourier Transform NMR (FT-NMR) Now, let us suppose that the sample is exposed to an intense RF pulse with RF magnetic field strength B and with a frequency equal to the Larmor frequency. If the pulse is applied orthogonal to the static B 0 field and is strong enough, the magnetization 65

10 will precess into the xy plane. Since the magnetization is rotated by 90 degrees, such a pulse is called a π/2 pulse, and is illustrated graphically in Figure Because the spins are now precessing at the Larmor frequency in the xy plane, the signal induced by these precessing spins can be detected by a fixed coil in the laboratory. Figure 23.2 Illustration of a π/2 pulse. (a) If an intense RF pulse is applied for the correct length of time, the net magnetization vector is rotated into the xy plane. (b) For an observer fixed in the laboratory reference frame, the magnetization vector precesses in the xy plane at the Larmor frequency, and thus induces a current in the fixed coils that can be amplified and detected with standard RF circuitry. Remember that NMR transitions are magnetic dipole allowed, and that the frequency is very low, in the few hundred MHz range for even the strongest fields presently achievable. Thus, the Einstein A-coefficients are very small and the transitions are very easy to saturate. Once the pulse is turned off, protons with the same chemical shift will be precessing at the same frequency and with the same phase. Let s imagine for the sake of simplicity that there are only two chemically distinct protons to worry about. After the pulse, each ensemble of protons precesses at it s own Larmor frequency (but starts with the same phase). Cycling currents are induced in the detector coils, which leads to a variation of the signal at frequencies near the Larmor frequency as well as the beat frequency between the chemically distinct protons. As we noted in Lecture 25, the magnetization also decays by two mechanisms whose time scales are labeled T and T 2 (the populational and dephasing times). For a single suite of protons whose magnetization decay is dominated by dephasing, the magnetization follows the form M y = M 0 cos ωt e t/t 2, (23.) 66

11 where ω is the Larmor frequency. For the two proton case outlined above, the time domain signal therefore contains an overall envelope that is modulated at the beat frequency, with a decreasing amplitude whose decay is set by T 2. This time domain signal is known as the free induction decay, or FID. The FID for the two proton case is shown in Figure 23.3(a). Figure 23.3 A graphical outline of the basics of FT-NMR spectroscopy. (a) After the application of an intense RF pulse, the precessing magnetization associated with chemically distinct nuclei induces a time domain signal, or free induction decay, in the detection circuitry. The oscillations and beats are caused by the different Larmor frequencies of precession, while the overall decay is caused by either populational relaxation or dephasing (or both). (b) Through the process of Fourier inversion, the time domain FID is converted into a frequency spectrum. In this case, the two chemically distint nuclei present lead to a doublet in the frequency domain. (c) Reality is, of course, more complex. Here is the FID of the proton NMR spectrum from ethanol. How is the frequency, or chemical shift, domain spectrum we presented in Lecture 25 recovered from the FID? Put briefly, the solution is to use the technique of Fourier transforms. The quantitative formulation for the time domain FID is given by S(t) = I(ν)e 2πiνt dν, (23.2) where the S(t) function is the time domain FID, I(ν) is the related signal or intensity function in the frequency domain, and e 2πiνt is a weighting function that oscillates at frequency ν (the integral then sums over all possible frequencies). Numerically, I(ν) is 67

12 evaluated as follows. If the cosine form of the magnetization given in (23.) is re-written as the sum of complex exponentials, eq. (23.2) may be inverted to yield I(ν) re M 0 { e (2πiν + iω /T2)t dt e (2πiν iω /T 2)t dt} re M 0 { (2πiν + ω)i /T 2 ) + (2πiν ω)i /T 2 ) }. (23.3) At typical NMR operating frequencies, both ν and ω/2π are of order 00 MHz, so the first term is very small (something like 0 8 s). The difference in the denominator of the second term is close to zero near resonance, however, and so this overall expression is of order T 2, which for liquids is something like s. The second term clearly dominates, and thus the overall intensity expression is I(ν) = M 0 T 2 + (2πν ω) 2 T 2 2. (23.4) Clearly, this is a Lorentzian function, and is the typical shape of an NMR transition. The full width half maximum of the lines is ν = /(πt 2 ) (or T if the populational relaxation is faster), and so is inversely proportional to the timescale over which the spin coherence decays. As noted previously, T 2 times in liquids are of order second, and the chemical shiftsof ppmleadtodifferencesofseveralhzfor400mhzprotonnmrs. Thefrequency covered by an FT-NMR spectrum depends on the frequency content of the initial pulse, while the instrumental resolution depends on how long the FID is acquired. The integrals above run up to, but in practice they are cut off after a certain time window where the FID has decayed to negligible values. Clearly, this time window must be long compared to T or T 2 if the spectrum is to have several points across the individual NMR transitions. In the above derivation, we have assumed the instrument is perfect and that differences in the Larmor frequencies arise only from the sample under study. In reality, field gradients will always exist and so the magnetic field in one region of the sample will be different from that in another region. This leads to inhomogeneous broadening of the NMR transitions, and so the observed line widths are often inverted to yield a so-called effective transverse (or dephasing) time T 2. T /T 2 Measurements and Spin Echoes While in principle the relaxation times can be directly determined by an examination of the FID, there are much more sensitive and elegant methods based on the use of multiple pulse sequences in NMR. These multiple pulse sequences are the basis of a suite of very powerful multi-dimensional NMR techniques, and so we ll look at two of their simplest implementations here. To measure the longitudinal relaxation time T, the inversion recovery technique is used. Here, the first step is to apply not a π/2 pulse but a 80 degree or π pulse to the system (by leaving on the RF pulse for twice as long as in a 90 degree pulse, for example). In this case, the net magnetization becomes directed along the z axis in the laboratory reference frame. No signal can be detected at this stage because 68

13 the detection coils in the xy plane are not sensitive to magnetizations along the z-axis. After the intense pulse, the α and β spin populations are equal. Once the pulse is finished, the spin populations begin to relax back toward their Boltzmann distributions. After a suitable interval τ, a π/2 pulse is applied to the system, which rotates the magnetization into the xy plane where it can be detected via the FID. The frequency domain spectrum is then recovered by Fourier transform, and the signal intensities for various chemical shifts measured in the normal fashion (see Figure 23.4). Figure 23.4 An illustration of the π pulse technique for the determination of the longitudinal relaxation time T. The top part of the figure illustrates the pulse and temporal evolution sequence, the bottom the result of measurements over a wide range of temporal delay values whose exponential decay depends directly on T. Clearly, the magnitude of the signal after the application of the π/2 pulse depends on the relative sizes of τ and T. For τ delays short compared to T, the spin populations have not relaxed back to their thermal distributions and the maximum magnetization is obtained. For temporal delays long compared to the longitudinal relaxation, the signal is gone before the 90 degree pulse is delivered and no FID is detected. The length of the magnetization vector, and hence the strength of the NMR signal, decays exponentially as τ increases. T can therefore be measured by fitting an exponential to the strengths observed over a series of spectra acquired with widely varying τ. What about T 2? Here, we must be able to eliminate the effects of inhomogeneous broadening to reveal the true dephasing time. The means by which this is done is the key to most of the modern advances in NMR spectroscopy of complex systems. This simplest example is called an NMR spin echo in which a pulse of magnetization is formed, allowed to partially dephase, and then reflected in a fashion that reforms the original pulse some time 69

14 later. The sequence of events is illustrated in Figure Unlike the T measurements, a π/2 pulse is first applied to the system to rotate the net magnetization into the xy plane. Figure 23.5 (top) The pulse sequence used to generate NMR spin echoes. (bottom) The exponential decay that results from the spin echo experiment that can be used to measure the dephasing time T 2. The spins rotate at their Larmor frequencies, and are initially in phase. Because the Larmor frequencies are all slightly different, the packet of spins that were initially coherent begins to fan out, the spreading being related to the differences in the chemical shifts. After some time τ, a π (80 degree) pulse is applied to the system. The magnetization vectors remain in the xy plane, but the direction of their precession is inverted. Hence, the magnetization of the faster precessing spins are directed back toward the slower precessing spins, and vice versa. Clearly, after another interval τ we are back to where we started from (by time reversal symmetry) and the spins are lined up! This is called refocusing, after which the spins begin to spread again. Who cares? One of the important features of the refocusing technique is that the size of the echo is independent of any local fields provided they remain constant during the 2τ duration of the experiment. Hence, the size of the echo is independent of the inhomogeneities in the B 0 field. The intrinsic dephasing time arises from fields that do fluctuate on molecular time scales, and so there is no guarantee they will be refocused by the π pulse. Thus, the echo observed decays as T 2, as illustrated in Figure So, interestingly enough, we use a combination of both π/2 and π pulses for the measurement of T and T 2, but in different orders. 70

15 Two Dimensional NMR For large molecules with sizable numbers of protons, the NMR spectrum obtained with straightforward FT-NMR techniques can become hopelessly congested. The large number of spin-spin interactions present, etc., makes things quite difficult for such abundant spin systems. One way to simplify things is to examine other nuclei in the sample, such as 3 C or 5 N. These are called dilute spin spin species because it is unlikely that there is more than one or a few such nuclei in any given molecule. Thus, spin-spin couplings between like nuclei can typically be ignored. It is not possible to ignore dilute spin-abundant spin couplings, however. For example, when observing a 3 C spectrum, the spectral complexity would be induced by the coupling of the 3 C nucleus in the molecule with nearby protons. For example, the CH 3 group in ethanol would have its 3 C peak split into a :3:3: quartet by the methyl protons. If, however, the protons are irradiated by a second, intense RF field (that is very different in frequency than that for 3 C, see Lecture 25) their spin orientations undergo rapid precession. The 3 C nucleus therefore senses an average orientation for the proton spins, and only a single transition results. This important technique is called spin decoupling. Spin decoupling also improves the sensitivity of NMR by collapsing the transitions into a single feature for chemically equivalent nuclei. The price paid in this case is that the integrated intensities are no longer proportional to the number of nuclei. Figure 23.6 A 2D NMR spectrum of 3 C, in which the horizontal (or f ) axis represents the 3 C H coupling constants and the vertical (or f 2 ) axis the chemical shifts. By combining spin decoupling techniques with spin-echo experiments such as those outlined above, it is possible to reduce the complexity of NMR spectra by plotting the resulting information along two axes (hence the name 2D NMR). For example, we can use spin decoupling to remove the effects of spin-spin coupling. If we also utilize spin echo 7

16 techniques, we can refocus spins with different chemical shifts to yield single transitions. In practice, by chosing a clever sequence of pulses and Fourier transforms, it is possible to display spin coupling in one dimension and chemical shifts in another, and thereby greatly simplifying the appearance of NMR spectra (or at least reduces the spectral congestion so more complex species can be studied). An example of this is presented in Figure 23.6 which presents a 2D 3 C spectrum of a moderate-sized organic molecule. Alternatively, 2D NMR spectra can plot the chemical shifts of abundant versus dilute spins or even abundant versus abundant spins. Figure 23.7, for example, presents the proton- 5 N 2D NMR spectrum of the BLA protein obtained during a stopped flow folding experiment. By plotting the proton chemical shifts along the horizontal axis and the 5 N chemical shifts along the vertical axis, the different spin coupling interactions are spread out such that individual coupling terms can be measured. By combining information in spectra such as this with similar results from proton-proton or proton- 3 C 2D NMR spectra, the complete coupling map of the biopolymer can be obtained. This data set along with the primary sequence of the protein (the sequence in which the amino acids are linked) is often sufficient to determine the three dimensional structure of the protein to.5-2 Angstrom resolution! In this case, unlike X-ray crystallography, the proteins are in aqueous media and crystals are not required. Substantial amounts of material are needed, however, and the structural assignment is not yet possible for the large proteins that can be studied with X-rays. Progress in this field is rapid, however, any many exciting new results can be expected! Figure 23.7 The proton- 5 N spectrum of BLA during protein folding. Refolding was initiated by inducing a ph jump. (A) The 2D NMR spectrum in the denatured state, where (C) presents the well resolved 2D NMR spectrum of the native state at ph 7.0. (B) Depicts the kinetic NMR spectrum acquired during the folding reaction, and such spectra can be used to trace the folding pathways in proteins. 72