13C-Decoupled J-Coupling Spectroscopy Using Two-Dimensional

Letter pubs.acs.org/JPCL

C‑Decoupled J‑Coupling Spectroscopy Using Two-Dimensional Nuclear Magnetic Resonance at Zero-Field 13

Tobias F. Sjolander,*,† Michael C. D. Tayler,‡,¶ Arne Kentner,†,§ Dmitry Budker,‡,∥,⊥ and Alexander Pines*,†,⊥ †

Department of Chemistry, University of California at Berkeley, Berkeley, California 94720-3220, United States Department of Physics, University of California at Berkeley, Berkeley, California 94720-7300, United States ¶ Magnetic Resonance Research Centre, Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, U.K. § Institute for Technical and Macromolecular Chemistry, RWTH Aachen University, 52062 Aachen, Germany ∥ Helmholtz Institute Mainz, Johannes Gutenberg University, 55099 Mainz, Germany ⊥ Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720-3220, United States ‡

S Supporting Information *

ABSTRACT: We present a two-dimensional method for obtaining 13C-decoupled, 1 H-coupled nuclear magnetic resonance (NMR) spectra in zero magnetic field using coherent spin-decoupling. The result is a spectrum determined only by the proton− proton J-coupling network. Detection of NMR signals in zero magnetic field requires at least two different nuclear spin species, but the proton J-spectrum is independent of isotopomer, thus potentially simplifying spectra and thereby improving the analytical capabilities of zero-field NMR. The protocol does not rely on a difference in Larmor frequency between the coupled nuclei, allowing for the direct determination of J-coupling constants between chemically equivalent spins. We obtain the 13C-decoupled zero-field spectrum of [1−13C]-propionic acid and identify conserved quantum numbers governing the appearance of cross peaks in the twodimensional spectrum.

N

containing only a single type of NMR-active nucleus are eliminated, minimizing solvent background. The zero-field NMR spectrum of a liquid-state sample is determined by the isotropic J-coupling Hamiltonian.1 One of the key requirements for obtaining “J-spectra” is the existence of couplings between more than one spin species in the molecule of interest, for example 13C and 1H. If a coupled spin system comprises only one type of nucleus (e.g., all 1H spins), the Hamiltonian commutes with the operator for the total magnetization of the system, which therefore must be timeindependent.1 Consequently, homonuclear J-spectra at zerofield have until now been unavailable. In this Letter, we introduce an indirect two-dimensional approach for obtaining 13C-decoupled 1H-coupled J-spectra in ZULF NMR. The presence of a secondary spin species in the molecule, e.g. 13C, is still required, but it is made “invisible” by averaging out its couplings to the other nuclei while the pure proton J-spectrum is encoded. This is termed homonuclear Jspectroscopy. Such spectra are of interest in ZULF NMR, because the J-spectrum corresponding to isotopomers of the

uclear magnetic resonance (NMR) performed in zero and ultralow field (ZULF)1−4 where spin−spin couplings dominate over the Zeeman interaction with external magnetic fields, and detected with alkali vapor-cell magnetometers,5−8 allows accurate chemical fingerprinting in spite of the absence of chemical shifts. Moreover the instrumentation is miniaturizable9,10 and requires no cryogens. The technique is therefore a candidate for a chip-scale point-of care device. The ZULF regime has further advantages, potentially enabling other specialized applications. These include (i) ultrahigh resolution, with demonstrated line widths down to 20 mHz, allowing the determination of coupling constants with unparalleled accuracy;11,12 (ii) the ability to observe nuclear spin interactions that are otherwise masked or truncated by a large magnetic field;13,14 (iii) the study of low-field relaxation phenomena;15,16 (iv) elimination of artifacts or distortions due to magnetic susceptibility effects; and (v) improved skin-depth penetration for imaging and spectroscopy through metal containers.17,18 Below 100−200 pT, magnetic fields no longer have any observable effect on the spectra (assuming coherence time limited line widths of 20 mHz). We term this zero-field. NMR spectra at these fields have fewer lines than in the nearzero field regime,19,20 and in the case of anisotropic materials, the transition frequencies are independent of sample orientation.21 In addition, signals from liquid-state molecules © XXXX American Chemical Society

Received: February 13, 2017 Accepted: March 14, 2017 Published: March 14, 2017 1512

DOI: 10.1021/acs.jpclett.7b00349 J. Phys. Chem. Lett. 2017, 8, 1512−1516

Letter

The Journal of Physical Chemistry Letters same molecule are entirely different.12 While a 13C, or some other heteronucleus, is necessary in order to detect J-spectra, the proton J-spectrum is independent of the location of the label. Homonuclear J-spectroscopy therefore offers significant practical advantages for the study of molecules that are not isotopically enriched and thus are made up of mixtures of isotopomers. Decoupling of heteronuclear interactions also simplifies crowded ZULF-NMR spectra and allows accurate determination of homonuclear J-couplings in the presence of heteronuclear couplings even if they are of similar magnitude. With 2D detection we retain information on the location of the 13 C label. We also note that in zero-field all spins have zero Larmor frequency; thus, our method allows direct determination of J-coupling constants between chemically equivalent protons, which is a problem that has attracted interest over the past years.22,23 Indeed our protocol should work for strongly coupled systems in high-field as well, though without the advantage in resolution offered by ZULF. The fastest way to manipulate spins at zero field is strong DC pulses, though other methods exist.24−26 During such a pulse, the spin system is primarily governed by the Hamiltonian

Hp =

∑ γi B·Ii

free evolution during which time the signal is detected (t2). Data are collected as a function of t1 and t2 and subjected to a 2D fast Fourier transform. Current ZULF hardware necessitates the use of 2D-detection because of the large (∼30 ms) dead time after each pulse (see the Supporting Information). The protocol is summarized in Figure 1.

Figure 1. Schematic representation of the acquisition protocol presented in the text with the Hamiltonian governing the spin-system evolution at each stage identified.

We will now outline the spin dynamics during each stage of the pulse sequence in turn, from the point of view of a general carbon/proton spin system. The liquid-state zero-field spin Hamiltonian may be written in terms of heteronuclear and homonuclear parts as

(1)

i

HJ = 2π ∑ Jin Ii ·Sn + 2π ∑ Jij Ii ·Ij + 2π

where B is the pulse field and γi is the gyromagnetic ratio of spin i; the sum runs over all the spins in the sample. The Jcoupling terms have been ignored; as for the pulse fields used in this work, we have |γiB| ≫ |J|. A DC pulse rotates all spins in the sample proportionally to their gyromagnetic ratios. For a 1 H/13C system, limited isotope selectivity can be achieved by exploiting the particular gyromagnetic ratios involved, γH/γC ≈ 3.98, meaning a π pulse on 13C is close to an identity operation on 1H. Selective inversion of 13C spins is a common method for preparing evolving spin states in ZULF NMR.1 In this work we also use sequences built from such quasi-selective 13C π rotations to perform coherent spin-decoupling. The pulse sequence (τ/2 − x − τ − y − τ − x − τ − y − τ/ 2)n ≡ XY4, where x and y denote π pulses along the corresponding axes and τ is the pulse spacing, averages to zero terms in the Hamiltonian linear in the spin-operator for spins properly rotated by the pulses.27 The J-coupling Hamiltonian, HIS = 2π JI·S, where I and S are angular momentum operators, is linear in each coupled spin. Thus, to first order in average Hamiltonian theory,28 application of XY4 averages 1H/13C Jcouplings to zero, giving H̅ 1IS = 0.29−31 This assumes the pulse angles are chosen to be π pulses on 13C. However, the fact that the gyromagnetic ratios of 1H and 13C are not integer multiples of one another introduces a systematic flip angle error to each pulse. To deal with this, as well as other issues of experimental implementation, we use a modified version of XY4, to be presented in a forthcoming publication (xyxy̅ ̅

xy̅ ̅ xy

xyxy ̅ ̅

xy ̅ xy̅ )n

i,n

i>j

∑ JnmSn ·Sm n>m

= HIS + HII + HSS (3)

where Ii and Sn are angular momentum operators for the proton and carbon spins, respectively. The Jin are heteronuclear coupling constants, while the Jij and Jnm describe the homonuclear couplings. The goal of homonuclear J-spectroscopy is to observe the spectrum corresponding only to the average Hamiltonian H̅ J1 = HII + H SS, which can be implemented by means of 2. For the important case of a hydrocarbon with a single 13C label, HSS is zero and the homonuclear part is reflective only of the proton−proton Jcoupling network, HII. The goal of the preparatory steps in the sequence in Figure 1 is to generate a density operator which is nonstationary not just with respect to HJ but also the spindecoupled Hamiltonian H̅ 1J . The experiment must start with a spin-polarized state. In general, there may be two kinds of spin order present at the start of a liquid-state ZULF experiment, scalar order and vector order.32,33 Magnetic field pulses along the detector axis converts scalar order into observable coherences; pulses transverse to the detector axis convert vector order into coherences.32 We consider the vector order along the z-axis originating in a prepolarizing permanent magnet and initiate zero-field evolution by inverting the carbon spin polarization via a transverse DC magnetic-field pulse, calibrated to effect a π rotation on 13C and a ∼4π rotation on 1H. After the pulse, the part of the density operator containing observable coherences is

(2)

The overbar indicates reversal of the direction of the pulse, and all pulses have the same duration and spacing. The four-pulse subcycles in 2 are separated for clarity. Our pulse sequence for detection of homonuclear J-spectra in zero-field consists of two preparatory steps: a single DC pulse to initialize zero-field evolution and a mixing period during which the system is allowed to evolve freely in order to build up the desired coherences. The preparation steps are followed by a period of spin-decoupling for a variable time (t1) and finally

ρ′(0) ∝ (∑ Ii , z − i

∑ Sn,z) n

(4)

We note that vector spin order may not be converted into a spin state that evolves under H̅ 1J by means of a magnetic field pulse because the negligibly small chemical shifts make the protons equivalent during the application of the pulse [e−iHpt ρ′(0)e iHpt , H̅ J1] = 0 1513

(5) DOI: 10.1021/acs.jpclett.7b00349 J. Phys. Chem. Lett. 2017, 8, 1512−1516

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The Journal of Physical Chemistry Letters

Figure 2. (a) Energy level diagram for propionic acid. (b) Effective energy level diagram during the decoupling. In both cases the states have been labeled with the quantum number for total angular momentum of the spin system, F. Allowed transitions have ΔF = ± 1, 0 and are marked with arrows. In addition the angular momentum of groups of equivalent spins is conserved, so the transitions are also grouped according to their K and L values. The color coding is used in later figures. Additional degeneracies have been suppressed for clarity.

However, if the protons are magnetically inequivalent, meaning their couplings to the 13C nucleus are different, then evolution under HIS generates the desired coherences. In effect the 13C nucleus is used to perform a selective pulse,34 affecting the two groups of protons differently. ρ″(0) = e−iHJtmρ′(0)e iHJtm

(6)

[ρ″(0), H̅ J1] ≠ 0

(7)

Following the mixing period, tm, spin decoupling is turned on and the system is allowed to build up phase for a time t1 while evolving purely under H̅ 1J 1

1

ρ″(t1) = e−iH̅ J t1ρ″(0)e iH̅ J t1

(8)

Figure 3. Zero-field NMR J-spectrum for [1−13C]-propionic acid. The superposed stick spectrum corresponds to diagonalization of HJ, using numerically optimized values for the coupling constants. Each transition has been assigned K and L quantum numbers and color coded according to the scheme in the energy level diagram in Figure 2. The spectrum is the sum of 2500 transients, and the magnitude of each transient was ∼30 fT.

The signal is acquired by measuring the total z-magnetization, Mz, as a function of free evolution time, t2 S(t1 , t 2) = Tr{Mz†e−iHJt2ρ″(t1)e iHJt2}

(9)

and the 2D Fourier transform of the data gives the spectrum corresponding to H̅ 1J , termed the homonuclear J-spectrum, along the indirect dimension F1. To demonstrate the technique, we used a home-built ZULF NMR spectrometer based on a 87Rb vapor-cell magnetometer (see the Supporting Information) and a sample of [1−13C]propionic acid. Ignoring the hydroxyl proton, which exchanges rapidly on the J-coupling time scale, the atoms in this molecule comprise a spin system of two magnetically inequivalent groups of protons coupled to a single carbon-13 (see Figure 2). The Jcoupling Hamiltonian may be written as HJ /2π = 2JCH K· S + 3JCH L·S + 3JHH K·L

energy level diagram shown in Figure 2a. The transitions predicted by exact diagonalization of HJ were fit in the leastsquares sense to the measured spectrum, giving the following 99.9% confidence levels for the J-coupling constants: 2JCH = −7.084 ± 0.002 Hz, 3JCH = 5.497 ± 0.003 Hz, and 3JHH = 7.563 ± 0.006 Hz (see the Supporting Information). We recorded the 13C-decoupled, 1H-coupled J-spectrum of propionic acid following the protocol outlined in Figure 1. The numerically optimized mixing time was 350 ms. After the preparation steps the carbon spin was decoupled from the rest of spin system using 2 for a time t1 ranging from 0 to 1.8 s, in steps of 17.6 ms. Each pulse had a duration of 200 μs, and the delay between pulses was 2.0 ms. After the decoupling period, the signal was detected under free evolution for 10 s. The Fourier-transformed 2D data set is shown in Figure 4 with the spectrum corresponding to the proton−proton Jcouplings along the carbon-decoupled dimension, F1, and the full J-spectrum along F2. A one-dimensional (1D) 13Cdecoupled spectrum was reconstructed by projecting all data points in the shaded red region onto F1. The result is plotted in black in Figure 4. Following the work in ref 12, the characteristic frequencies of H̅ 1J = 2π 3JHHK·L can be readily evaluated. We have K={0,1} (two protons) and L={1/2 ,3/2} (three protons), and the spectrum should consist of one peak at 3/2 3JHH and one peak at 5/2 3JHH. Fitting the transitions

(10)

where K and L are the total angular momentum operators for the two proton groups and S corresponds to the carbon spin. The sequence 2 generates the average Hamiltonian H̅ 1J = 2π 3 JHHK·L (see the Supporting Information). The data are conveniently analyzed in terms of the quantum numbers K and L, corresponding to the eigenvalues of the operators K2 and L2, respectively. These quantum numbers are conserved throughout the entire acquisition protocol, because both operators commute with all of HJ, Hp, and H̅ 1J . This follows from K and L both being the angular momenta of magnetically equivalent groups of protons. The nondecoupled zero-field J-spectrum of [1−13C]propionic acid is presented in Figure 3 with the corresponding 1514

DOI: 10.1021/acs.jpclett.7b00349 J. Phys. Chem. Lett. 2017, 8, 1512−1516

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Figure 4. Experimental 2D detected zero-field NMR spectrum of [1−13C]-propionic acid, recorded using the pulse sequence in Figure 1. F2 corresponds to the full zero-field J-spectrum and F1 to the 1H-only J-spectrum. In F1 there are two peaks at 3/2 3JHH = 11.4 ± 0.7 Hz and 5/2 3JHH = 19.0 ± 0.6 Hz. The stick spectra are the results of numerical diagonalization of HJ (F2) and H̅ 1J (F1).

predicted by H̅ j1 to the reconstructed 1D 13C-decoupled spectrum gives 3JHH = 7.61 ± 0.07 Hz, consistent with the value obtained from the full 1D J-spectrum at this level of confidence. Small shifts may result from incomplete decoupling. The individual peak positions were determined to be 11.4 ± 0.7 and 19.0 ± 0.6 Hz (see the Supporting Information). The 13Cdecoupled spectrum consists of two distinct lines, described by a single parameter, as opposed to 14+ lines described by three parameters for the 13C-coupled spectrum in Figure 3. The decoupling thus significantly simplifies fitting and interpretation. In the context of chemical analysis, assuming spins other than 13C and 1H can be ruled out, the 13C-decoupled spectrum unambiguously corresponds to an ethyl group. In addition, the exact value of the coupling constant is a sensitive reporter on both the intra- and inter- molecular chemical environment.35,36 The location of the cross peaks may be explained by comparing the quantum numbers for each transition during the decoupling with those in a free molecule. Inspecting the energy level diagrams in Figure 2, we see that only eigenstates with K = 1 may give cross peaks in the 2D spectrum as there are no transitions with K = 0 in the energy level diagram for H̅ 1J . We also note that peaks with L = 1/2 may give cross peaks at only 3/2 3JHH, while peaks with L = 3/2 may give cross peaks at both 3/2 3JHH and 5/2 3JHH. There are strong peaks at 5.47 and 10.94 Hz in the 1D propionic-acid spectrum assigned to K = 0. Consistent with the argument made above, these peaks give no discernible cross peaks in the 2D spectrum. The rest of the spectrum also conforms to the expected behavior. For example the peak at 5.76 Hz is assigned to K = 1, L = 3/2 and may therefore give cross peaks at both 3/2 3JHH and 5/2 3JHH in the decoupled dimension. These peaks are partially overlapping in the 1D spectrum, but the 5.76 Hz peak gives strong cross peaks, thereby simplifying assignment. Similarly, the two peaks at

13.05 and 13.75 Hz are partially overlapping in the 1D spectrum but are clearly distinct in the correlation spectrum, as the cross peaks occur on different sides of 0 in F1. We also note the presence of vertical streaks, also known as F1 noise, in the data at 8.65 and 10.9 Hz. The appearance of these features means their phase is uncorrelated with the evolution period t1, implying they do not correspond to spin dynamics. We note that a climate control fan causes lowamplitude building vibrations at 10.9 Hz, which are picked up by our detector. This feature becomes negligible when enough scans are taken, as in Figure 3, but this is not feasible in a 2Ddetected experiment. We do not know the cause of the feature at 8.65 Hz. In conclusion, we performed the first demonstration of heteronuclear spin-decoupling in ZULF NMR and introduced the concept of homonuclear J-spectroscopy in zero-field. The two-dimensional scheme used for detection helps with spectral assignment and circumvents the dead time imposed by current ZULF detection hardware. The homonuclear J-spectrum of [1−13C]-propionic acid is significantly simpler to interpret than the full J-spectrum, while still providing the same chemical information. This demonstrates the promise of our approach for the analysis of more complicated molecules. Moving forward, we expect 13Cdecoupling to become an important part of ZULF NMR, as it provides chemically distinct spectra no matter which part of the molecule is 13C labeled. This opens the door for unambiguous ZULF NMR of molecules at natural isotopic abundance, provided the requisite sensitivity could be attained.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.7b00349. 1515

DOI: 10.1021/acs.jpclett.7b00349 J. Phys. Chem. Lett. 2017, 8, 1512−1516

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Details regarding the experimental setup and the spectral fitting process; explicit calculation of H̅ 1J (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Tobias F. Sjolander: 0000-0002-0564-4804 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Science Foundation under award CHE-1308381 and in part by the European Commission under the Marie Curie International Outgoing Fellowship Programme (MCDT, project FP7-625054 ODMRCHEM). A.K. appreciates the support by the German Academic Exchange Service (DAAD) via its thematic network “ACalNet”. Contents of the work do not reflect the views of the university or the European Commission.

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DOI: 10.1021/acs.jpclett.7b00349 J. Phys. Chem. Lett. 2017, 8, 1512−1516