Two-Dimensional NMR Spectrometry Thomas C. Farrar Department of Chemistry University of Wisconsin Madison, Wis. 53706
This article is the second in a two-part series. In part one (ANALYTICAL CHEMISTRY, May 15) we discussed one-dimensional nuclear magnetic resonance (NMR) spectra and some relatively advanced nuclear spin gym nastics experiments t h a t provide a capability for selective sensitivity en hancements. In this article we present an overview and some applications of two-dimensional NMR experiments. These powerful experiments are im portant complements to the one-di mensional experiments. As in the more sophisticated one-dimensional experi ments, the two-dimensional experi ments involve three distinct time periods: a preparation period, t0; an evolution period, ίχ; and a detection pe riod, ti.
For example, in an ERNST experi ment (enhancement via refocused nu clear spin-polarization transfer, dis cussed in Reference 1) the preparation period involves a proton relaxation pe riod and a π/2 pulse on the proton spins. Sometimes the preparation peri od also contains a number of 13C pulses that are used to ensure that the carbon magnetization, M 0 ( 13 C), is zero at the
obtain the frequency domain signal. The ERNST experiment and all of the others discussed in Reference 1 are one-dimensional experiments, because only a single time response is recorded and only a single Fourier transform is required to obtain the desired frequen cy domain data. The FID signal, as we have seen, is the result of phase modu lation arising from precessing nuclear
INSTRUMENTATION end of the preparation period. The evo lution period may contain 13C and pro ton pulses. The evolution times are of ten multiples of 1/(4J), where J is the JCH spin-coupling constant. During the detection period for the ERNST ex periment the decoupler is turned on and the carbon free induction decay (FID) signal is detected (recorded). Af ter the experiment is completed, the FID signal is Fourier-transformed to
magnetizations with different chemical shifts and spin-coupling constants and, consequently, different resonance frequencies. In all of the experiments discussed so far, the phase modulation effects of chemical shifts and spin cou plings are usually present during either the i] or the t% periods, or both. By carefully controlling the time periods during which the chemical shift phase modulation and t h e spin-coupling
Figure 1. A carbon (π/2)χ pulse rotates the magnetization into the xy plane where it begins to dephase because of chemical shift and spin-coupling interactions. After an evolution time τ = (t,)/2 = 1/(4J), the carbon a and β magnetizations are 90° out of phase with one another. A carbon x y pulse initiates the refocusing of both the chemical shift and the spin-coupling dephasing. After a further evolution time τ = 1/(4J), the magnetizations are completely refocused. The upper row shows a three-dimensional perspective of the magnetization vectors in the rotating frame. The bottom row shows the magnetizations as seen looking down the ζ axis onto the xy plane.
0003-2700/87/0359-749A/$01.50/0 © 1987 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 59, NO. 11, JUNE 1, 1987 · 749 A
phase modulation are expressed, we open up an entire new area of NMR experiments: two-dimensional Fourier transform NMR (2D FT-NMR). In one-dimensional NMR experi ments we normally represent the signal analytically as a function of t% S(i2). If we record a large number of one-di mensional signals as a function of the evolution time t\, we can represent these different one-dimensional signals by the functions Si(t 2 ), S 2^2), S 3 ( i 2 ) , . . . . S„(i 2 ) or, more succinctly, as a two-dimensional array S(ii,f 2 ). In 2D F T - N M R spectroscopy, we collect such an array of one-dimensional sig
nals, and this array is Fourier-trans formed twice to obtain a two-dimen sional frequency spectrum, F(a>i, ω2). Thus, SÎÎLÎJ)-—
2 X FFT —-*— F(wv u2), where FFT refers to the fast Fourier transform algorithm. In 2D F T - N M R experiments the structure of the array, S(ti, Î2), depends primarily on the following parameters: the chemical shifts and coupling constants present and the periods during which they are expressed, the
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evolution periods (tj) used, the pulses that are applied, and the times during which the decoupler is operating. In most of the experiments that follow we will arrange the experimental conditions such that only one parameter (e.g., spin coupling) is expressed during the evolution time, and a second parameter (e.g., chemical shift) is expressed during the detection period. This allows one to have a final twodimensional frequency spectrum in which one parameter (e.g., chemical shift) is expressed along one of the frequency dimensions, and the second parameter (e.g., spin coupling) is expressed along the second frequency dimension. Refocusing pulses are used to eliminate the expression of chemical shifts (or, in some cases, spin-coupling constants), and the decoupler can be used to suppress the expression of spin coupling during various time periods. Two-dimensional experiments To make these concepts clearer, let us consider the 13C and proton spectra of 13 CHC13. (Although we will use proton and carbon spins, we could equally well use two general spins, A and X, respectively, both with spin 1/2, for the following discussion.) The first experiment we consider is shown in Figure 1. The spectrometer reference frequency, ωη, is slightly less than the reso nance frequency for the carbon nuclear spin that is coupled to the proton in the α-spin state. In a time τ = ίχ/2 = 1/(4J), there will be a dephasing of the carbon magnetization because of chemical shift effects and spin-coupling interac tions. In the present case, in a time τ, the α-carbons will become 90° out of phase with the β-carbons (Figure lb). A carbon wy pulse initiates the refocusing of both the chemical shift (or preces sion) and the spin-coupling dephasing (Figure lb'). At the end of the t\ evolu tion period, both the chemical shift and the spin-coupling dephasing are refocused (Figure lc). Consider next an experiment in which we refocus the chemical shift dephasing but not the spin-coupling dephasing during the evolution time. The pulse sequence used here is shown in Figure 2. The dephasing and refocusing is shown in Figure 3. Here the πχ pulse on the proton spins interchanges their spin states. Conse quently, the spin-coupling effects cause the carbon magnetizations to continue to dephase at point b' rather than refocus. The chemical shift dephasing, however, is refocused. The above two experiments are familiar be cause they are very similar to the first part of an INEPT (insensitive nuclei enhanced by polarization transfer) or ERNST experiment. The following ex periment is quite different because we add the possibility of switching on the
Figure 2. In this pulse sequence the carbon π pulse at the midpoint of the evolution period initiates the refocusing of the carbon chemical shift and spin-coupling dephasing, but the proton π pulse suppresses the refocusing of the spin coupling by in terchanging the proton spin states. The carbon magnetization continues dephasing.
proton decoupler during part of the evolution time and during the acquisi tion. The effect of turning on the de coupler is to suppress the dephasing attributable to spin coupling. The pulse sequence for executing this ex periment is shown in Figure 4, and the magnetization vector diagram for the carbon spins is shown in Figure 5. Because the proton decoupler is on during the first half of the ί ι evaluation period, only chemical shift dephasing occurs. During the second half of ii (again, τ = ty/2 = l/[4/]), the chemical shift dephasing is refocused (via the carbon wy pulse), but as the decoupler is now off, spin-coupling dephasing oc curs. In Figure 5c the carbon chemical shift is completely refocused, but be cause of spin coupling the carbon-α and carbon-/? magnetizations are out of
Figure 3. The carbon π/2 pulse rotates the magnetization into the xy plane. The magnetizations dephase because of the chemical shift and spin-coupling interactions. At point b, after an evolution period of τ = 1/(4J), the carbon a and β magnetizations are 90° out of phase. The carbon jr pulse initiates the refocusing of both the chemical shift and spin-coupling dephasing, but the proton π pulse suppresses the refocusing of the spin coupling by interchanging the proton spin states. After a further evolution period, τ = 1/(4J) (point c), the chemical shift dephasing has been refocused, but the spin-coupling dephasing has continued and the carbon a and β magnetizations are now 180° out of phase.
Figure 4. A pulsed NMR experiment in which spin-coupling effects are suppressed during the first part of the evolution period and during the acquisition period.
phase. Because τ = 1/(4J), the a and β magnetizations are 90° out of phase in this example. In general, however, τ is varied over a relatively large range of values, which causes the phase differ ence in the a and β magnetizations to vary. If at this point we again turn on the decoupler, the carbon magnetiza tions continue to precess 90° out of phase with one another at a rate deter mined only by the carbon chemical shift offset. The signal detected is the vector sum of the two magnetizations and has in this case an amplitude that is only 70% that of the original carbon magnetization. If we change the evolu tion time such that τ = 1/(2J), then the final proton-decoupled carbon magne tizations will be 180° out of phase, and the resulting carbon signal will be zero. This is summarized graphically for a
ANALYTICAL CHEMISTRY, VOL. 59, NO. 11, JUNE 1, 1987 · 753 A
Figure 5. During the first part of the evolution period only chemical shift dephasing is expressed (during the time between a' and b). From b' to c, the chemical shift dephasing is refocused and spin-coupling dephasing takes place. During the detection period, further dephasing attributable to spin coupling is suppressed.
series of τ values in Figure 6. Figure 6 is a two-dimensional plot of the results of the above experiment in which the transformed frequency spec tra are given along the F2 axis and the evolution time is plotted along the ίχ axis. We see that the signal amplitude varies sinusoidally as a function of the evolution time, t\. If we Fourier trans form this ti waveform, we obtain a fre quency equal to J/2. This gives peaks at ± J/2; the two-dimensional frequen cy plot is given in Figure 7. Because the source of the amplitude modulation along ii is the expression of the spin coupling, the F ι frequency gives the spin-coupling constant, and the F2 fre quency gives the chemical shift value. These kinds of experiments are use ful for understanding the basic con-
cepts of 2D NMR but are not very use ful for most NMR experiments. One of the simplest 2D NMR experiments, and one that is also useful, is the Jresolved 2D F T - N M R experiment in which the chemical shift is plotted along one axis and the spin-coupling constant along the second axis. The pulse sequence used for the heteronuclear version of this experiment is shown in Figure 8. We see in this relatively simple ex periment, first done by Ernst and oth ers (2-5), that only spin-coupling phase modulation is expressed during the evolution period t\ (the chemical shift phase modulation is refocused). During the detection period, t2, spin-coupling phase modulation is suppressed by turning on the decoupler. Consequent ly, during this period only chemical shift phase modulation is expressed. This summarizes the basic concept of 2D F T - N M R spectroscopy: Whenever we have a systematic variation of a sig
nal (i.e., a phase modulation) due to a single property of a spin system (e.g., chemical shift or spin coupling) during a given evolution time, we can separate the effects of that property. Up to this point we have considered only two spins, X (carbon) and A (hy drogen). The concepts and ideas devel oped for two spins can readily be gener alized to more complex spin systems. For the three-spin system, A?X, the X spectrum is a triplet. The outer lines of the triplet are phase-modulated in the same way as an AX doublet, but at a frequency of + J and —J with respect to the central peak. The central peak is not phase-modulated at all because of spin-coupling effects. In other words, the outer pair of lines for the triplet behaves like an AX doublet, but with twice the phase modulation frequency (recall that the AX doublet is modulat ed at a rate ± J/2). A3X exhibits a quartet spectrum, and it is also similar to an AX doublet, but in a different
Figure 6. A two-dimensional plot with frequency plotted along the F2 axis and the evolution time, tu along the second axis.
Figure 7. A two-dimensional transform of the experiment shown in Figure 6.
The amplitude of the signal is a function of the spin-coupling dephasing that took place during the second part of the evolution period.
Chemical shift dephasing is refocused in the evolution period f1f and spin-coupling dephasing is sup pressed during the detection period f2. t^ contains spin-coupling information only, and f2 contains chemi cal shift information only; c is the 13C chemical shift.
754 A · ANALYTICAL CHEMISTRY, VOL. 59, NO. 11, JUNE 1, 1987
From A Through H, lust Some of the Compounds rou Can Measure At Low Picogram Levels
Figure 8. The pulse sequence used for a heteronuclear 2D J-resolved NMR spectrum. This sequence is the one commonly used. This example is, again, for a two-spin AX system in which each spin has a spin of 1/2.
HETCOR experiment for CH3C1 is giv en in Figure 9. The overall result of the HETCOR experiment is that proton chemical shift (&H) dephasing is expressed dur ing the evolution period t\, and only carbon chemical shift (5c) dephasing is expressed during the detection period. A 2D FT of S(h,t2) yields a 2D F T NMR frequency spectrum _F(o>i,u>2) with the proton chemical shifts along the F\ axis and the carbon chemical shifts along the F% axis. In contrast to the SPI (selective pop ulation inversion) experiment in which carbon-proton correlations are worked out on a selective one-carbon-at-a-time basis, the HETCOR experiment shows simultaneously all of the carbon-pro ton correlations. A less trivial example, that for methyl vinyl ketone (H 3 CC(0)-CH=CH 2 ), is shown in Figure 10. The methyl carbon, C a , at about 20 ppm, is correlated with the methyl protons at about 2.5 ppm. The Cc at
way. The modulation frequency for the inner pair of lines in the ΑΛΧ quartet is ± J/2, exactly the same as for the AX doublet. The modulation frequency for the outer pair of lines is ± 3 J/2. By making use of the ability to ex press the phase modulation of the chemical shift, the spin coupling, or both at various times during a pulse sequence, a number of very useful twodimensional experiments can be per formed. In Table I we summarize some 2D NMR experiments and indicate the information that may be obtained from them. COSY and CHESY Two of the more useful and common 2D NMR experiments are the homonuclear chemical shift correlated experi ment, COSY, and the heteronuclear shift correlated experiment, HETCOR or CHESY. In these experiments the chemical shift is expressed along both the Fi and F 2 axes. An example of the
Table 1. Information available from selected 2D FT-NMR experiments" Experiment
F2
Information Heteronuclear coupling constants Homonuclear J& δ Correlation of bx and δΑ Identification of all scalar cou pling interactions Spatial proximity and three-dimensional molecular structure Heteronuclear connectivities
Heteronuclear J-resolved
JAX
δχ
Homonuclear 2D J CHESY or HETCOR
JAA
δΑ
h
δχ
COSY
δΑ
δΑ
2D NOESY
δπ,
δ*
JHH
JHH
δΑ + δ χ
δχ
2D INADEQUATE a
F1
J, spin-coupling constant. 5, chemical shift
ALelaldehyde Acetaminophen Acetylc holme 4-Acelyl Erythromycin A Ν Acetyl Serotonin Adenine Adenosine 5-Adenosyl Methionine Adrenaline L-Alanine- L Tryptophan L-Alanine L Tyrosine Albuterol 4 Aminoazobenzene 4 - A m i nobiphe η y lami η e thrtrtyrhfghfdghhfdghgfhfghgh Amoiapine Anhydro Erythromycin A Aniline Anthraqumone gfhgfhfhfghfghfghfgh Arterenol Ascorbic Acid (Vitamin C) Benzidine BHA (Butyl Hydroxy Amsole) BHT (Butyl Hydroxy Toluene) Biogenic Amine Metabolite. e-Bioplerm gfhfghgfh Butyl Hydroxy Anisole (BHA) Butyl Hydjony Toluene (BHT) Bulolenine Calieic Acid (3.4 D.hydroiycinnamic Acid) Calte.ne Capsaicin Carbidopa Catechol Catecholamines Catechol Estrogens Chlorophenols Chlorophenols Choline Cisplalin Codeine Coumanc Acid Cysteine Cystine Cylosme Dopamine (3HT) Desmethyldoxepine Desipramine DE5-N-Meihylerythromycin DHBA (Dihydroxybenzylamine) Dichbrobcnzidme 2,3 Dihydiobemoic Ac.d 2,5-Dihydrobenio.c Acid (Gent.sic Acid) DihydiociHeic Acid Dihydroxybemyldmine (rwja 3.4-DiWroirafr)
Dilaudid (Hydromorphone) W.N Dimethyll.yptamme Diphenyllriaime DOPA DOPAC Dopamine (3 HT)(DA| Dopamine Glucuromde DOPEG Do.epin Enkephalins Enkephalins Epinine Equllla Equllladfsfd Erythromycin, A, B, D Erythromycin Estolaie Eryihiomycin Ethylsuccinale Estradiol Estiiol Estiioldsf Estrone Elhylparaben Fenoierol Fe.ulic Acd Fluphenazine Folic Acid N-Formyl L-Kynu.emne Gallic Acid (2.4,3 Tnhydroiybenzoic And) Gentisic Acid (2,5 D. hydroxybenzoic Acid) Glutathione Glycyl-L-Tryplophan Glycol I rytonn· Guanine Guanine Guanine GuaninefdHistamine Homogentmc Acid Homogentmc Acid Ii,:m^v e :„ll, t Acid(HVA) Hcmcvan.liw Acid Sulfate H.::... .·. . ... . Alcohol Ho-demne Hydromorphone (D.laud.d) Chlorophenols S-HTOHydronytyramine) 3 Hydioxyanlhianillic Acid 4-Hydroxy ben zoic Acid 5-Hydioxykynuienine MHyd.oiymandehcAcid Ρ Hydroxymandelic Acd 6 Hydroxymelstomn 4.Hydroxy 3 -Methoxyphe.iylaoelic Acid 4 Hydroxy 3 M-" Enkephalins Enkephali
unie Acid i) :id c Acid
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Figure 9. The two-dimensional CHESY spectrum for a sample of 13CHCI3. The F| dimension shows the chemical shift of the proton, and the F2 dimension shows the chemical shift of the carbon.
140 ppm is correlated with the proton at about 6.4 ppm. Because the two pro tons bonded to the Cd carbon are not chemically equivalent, we see two con tours at a carbon chemical shift of about 130 ppm, one for each of the two protons (at about 5.8 and 6.3 ppm). The ketone carbon, C b , has no directly bonded proton and does not show up on the heteronuclear correlated 2D FT-NMR spectrum. This magnificent experiment pro vides in one fell swoop the following: carbon sensitivity enhancement, elimi nation of the problem of spectral line overlap, and simultaneous correlation of all carbon and proton resonances in an unambiguous fashion. In addition, it does all of these things much faster than any other method. This experi
ment is especially useful for complex molecules and/or for situations in which there are several scalar coupling constants between the protons and car bons (or other proton-coupled X nu clei). For more examples and details see References 6-8. As a final example, we show the pro ton 2D FT-COSY spectrum for methyl vinyl ketone. This spectrum (Figure 11) shows all of the proton resonances correlated with themselves along the diagonal. The off-diagonal peaks show which protons are spin-coupled to one another. In the present case we see that there is no coupling between the methyl protons and the olefinic pro tons, but the olefinic protons are all strongly coupled to one another. The two-dimensional double quantum ex periment (the INADEQUATE [incred ible natural abundance double quan tum transfer] experiment) allows one to obtain similar spectra for carboncarbon couplings. The proton 2D NOESY (Nuclear Overhauser en hancement spectroscopy) experiment provides information about the through-space connectivity between the various groups of coupled protons. Application to large molecules Using a combination of most of these techniques, Bax and co-workers have shown how the complete structure of very complex molecules can be deter mined. NMR measurements of a dilute solution of a molecule can now estab lish the complete carbon-carbon con nectivity and many, if not most, of the spatial arrangements between the pro tons. A recent elegant example by Bax and co-workers (9) is the structure of
From I Through Z, Just Some of the Compounds You Can Measure At Low Picogram Levels S~L«-,*
Indole 3 Aceialdehydo Indoleacetic Acid Indole pyruvic Acid dsffdffdff sfdfdsfdsfdsf Iso Homovan.llic And dsfdsfdsfdfdsf I VMA Isoitupnne Kyouiemc A. .d L Dopa Uu< enkephalin dfsdfdsfdsfdsfdsf Menadione S Marcaplovaline (Penicillamine) Meienephnni Melaptolarenol Met «·•·..·:..,ι π Meth.on.ne 3 Melhoxy.a Hydrnxyphenylglycol 3 Melhoxy,4-Hydr
