We demonstrate a new phenomenon in nuclear magnetic resonance spectroscopy, in which nuclear spin transitions are induced by radio frequency irradiation at extremely low frequencies (of the order of a few Hz). Slow Rabi oscillations are observed between spin states of different exchange symmetry. These “forbidden” transitions are rendered weakly allowed by differential electronic shielding effects on the radio frequency field. We generate coherence between the singlet and triplet states of 15N-labeled nitrous oxide in solution, and estimate the scalar coupling between the two 15N nuclei with a precision of a few mHz

Carravetta, Marina

Levitt, Malcolm H.

Pileio, Giuseppe

English

Southampton (e-Prints Soton)

Extremely Low-Frequency Spectroscopy in Low-Field Nuclear Magnetic ResonanceGiuseppe Pileio, Marina Carravetta, and Malcolm H. Levitt*School of Chemistry, Southampton University, SO17 1BJ, United Kingdom(Received 28 May 2009; published 20 August 2009)We demonstrate a new phenomenon in nuclear magnetic resonance spectroscopy, in which nuclear spintransitions are induced by radio frequency irradiation at extremely low frequencies (of the order of afew Hz). Slow Rabi oscillations are observed between spin states of different exchange symmetry.These ‘‘forbidden’’ transitions are rendered weakly allowed by differential electronic shielding effects onthe radio frequency field. We generate coherence between the singlet and triplet states of 15N-labelednitrous oxide in solution, and estimate the scalar coupling between the two 15N nuclei with a precisionof a few mHz.DOI: 10.1103/PhysRevLett.103.083002 PACS numbers: 33.25.+k, 76.60.kIn nuclear magnetic resonance, radio frequency irradia-tion resonant with the nuclear Zeeman splitting is used toinduce nuclear spin transitions. In conventional high-fieldNMR, the resonant frequency is typically hundreds ofMHz, while in NMR at very low field, such as NMR inEarth’s field [1,2], the resonant frequency may be a fewkHz. Here, we demonstrate resonant nuclear spin effects atstill lower frequencies. We show that electromagnetic ir-radiation in the extremely low-frequency (ELF) region ofthe radio frequency spectrum, of the order of a few Hz, caninduce nuclear spin transitions between states of differentspin exchange symmetry. The transitions are weakly al-lowed because of differential chemical shielding of theELF field.Our demonstration system is doubly 15N-labeled nitrousoxide (15N2O, dinitrogen monoxide), which supports alow-field nuclear singlet state with a lifetime of tens ofminutes in solution [3]. Nitrous oxide is nontoxic, dis-solves in many important solvents such as water and oil,and is widely used in medicine [4] and food processing.The extraordinarily long singlet lifetime of 15N2O suggestsapplications to the characterization of slow diffusion andflow in medical and industrial materials [3]. The ELFspectroscopy of 15N2O creates further possibilities for thescientific applications of this substance.The two 15N nuclei of 15N2O are in chemically inequi-valent sites, with a chemical shift difference of  ¼82:3 ppm and a scalar spin-spin coupling JNN ’ 8 Hz[3]. In zero magnetic field, the pair of 15N nuclei becomemagnetically equivalent, with nuclear eigenstates given bythe singlet state and the three triplet states, defined asfollows:jS0i ¼ 1ﬃﬃﬃ2p ðji  jiÞ jT1i ¼ jijT0i ¼ 1ﬃﬃﬃ2p ðji þ jiÞ jT1i ¼ ji:(1)Spin-1=2 states with angular momentum ð1=2Þ@ alongthe z axis of the (arbitrarily defined) laboratory referenceframe are denoted  and , respectively. In zero magneticfield, the three degenerate triplet states are higher in energythan the singlet state by the singlet-triplet splitting2@JNN . Perturbation of the singlet-triplet splitting isvery small if the low-field chemical shift difference (inHz) is less than the scalar spin-spin coupling, as is the casefor the experiments described below.The three triplet populations mutually interconvert withthe conventional spin-lattice relaxation time constant T1.The singlet-triplet interconversion, on the other hand, is anorder of magnitude slower, since many common relaxationmechanisms are ineffective [3,5–16]. In the case of 15N2O,the time constant TS for singlet-triplet interconversion maybe as long as 26 minutes [3].The singlet state is antisymmetric, and the triplet statesare symmetric, with respect to exchange of the two nuclei.Singlet-triplet transitions are therefore symmetry-forbidden under any exchange-symmetric external pertur-bation. Conventional spin-dynamical theory assumes thatthe interaction of a spin system with an applied radiofrequency field is exchange-symmetric, i.e., exactly thesame for all resonant spins [17,18]. This assumption isplausible since each molecule is much smaller than thelength scale of radio frequency field variations. However,this assumption neglects the shielding effects of the localmolecular electrons on the applied radio frequency field.Chemical shift effects are very well known for the strongstatic magnetic fields used in conventional high-fieldNMR. However, the influence of electronic shielding onthe applied radio frequency field has been consistentlyneglected. This is reasonable, since such effects are ex-tremely small, as discussed below. Nevertheless, in thecontext of low-field NMR, the minute radio frequencychemical shift effects render singlet-triplet transitionsweakly allowed.Consider, for example, a weak magnetic field Bz alongthe z axis of the laboratory reference frame. The nuclearspin Hamiltonian describing the interaction of the 2-spinPRL 103, 083002 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending21 AUGUST 20090031-9007=09=103(8)=083002(4) 083002-1  2009 The American Physical Societysystem with the magnetic field is given byHz ¼ Bzfð1þ 1ÞI1z þ ð1þ 2ÞI2zg (2)where the spin angular momentum operators are denoted I1and I2, the chemical shifts are 1 and 2, and  is thenuclear magnetogyric ratio. The off-diagonal matrix ele-ment connecting the singlet state and the central tripletstate is given byhS0jHzjT0i ¼  12Bz (3)where  ¼ 1  2. If the field Bz is periodically modu-lated so that one of its Fourier components is resonant withthe singlet-triplet splitting, Rabi oscillations between thestates jS0i and jT0i are induced. If the modulated magneticfield has the form BzðtÞ ¼ BELF cosð!ELFtÞ where BELF isthe peak ELF field amplitude, and the modulation fre-quency !ELF exactly matches the singlet-triplet splitting,the Rabi frequency for singlet-triplet nutation is given by!STRabi ¼12BELF: (4)This corresponds to the Larmor frequency in the ELF field,scaled by the minuscule chemical shift difference  ¼82:3 ppm. For practical ELF fields, the singlet-triplet Rabifrequency is only a fraction of 1 Hz.The ELF resonance condition is extremely narrow.Nevertheless, the resonance is readily observed since ordi-nary laboratory oscillators provide mHz frequency stabil-ity, and the energy difference between the singlet state jS0iand the central triplet state jT0i is highly insensitive tomagnetic field variations.The apparatus used to detect ELF singlet-triplet transi-tions is shown in Fig. 1. This is based on a conventionalhigh-field NMRmagnet (B0 ¼ 7:05 T) equipped with con-ventional radio frequency electronics, but with the facilityof transporting the sample in and out of the magnet using astepper motor attached to a piece of string, passing over ahook in the laboratory ceiling. At the top end of its trajec-tory, the sample enters a 300-turn copper solenoid, locatedabout 1 m above the top of the NMR magnet, and with itsaxis parallel to the fringe field of the magnet. The peakfield generated by the ELF coil was BELF ’ 0:6 mT. TheELF pulses were generated by gating the sinusoidal outputof a commercial signal generator using a mechanical relay,controlled by the spectrometer software.The sample used for all experiments consisted of 15N2Odissolved in locally produced Calabrian olive oil at apressure of 3 bar.The timing sequences used for ELF experiments areshown in Fig. 2. Frames (a) and (b) indicate the timingsequences for a measurement of singlet relaxation time TS,as described in Ref. [3]. The sample is allowed to equili-brate in high magnetic field for 200 seconds before asequence of two 90 radio frequency pulses, resonantwith the 15N Larmor frequency, is applied. The pulsesequence timings and relative phases are chosen so as toinvert the magnetization of 15N nuclei at only one of thetwo chemically distinct sites. The sample is then winchedout of the NMR magnet. As described in Ref. [3], this?SampleMagnetStepper  Motor  FunctionGeneratorRelayCoilTransporttubeNMRprobe   MotorController   NMR ConsoleFIG. 1 (color online). Equipment used to perform ELF NMRexperiments.900RFELFBhigh9090 900 9045BlowELFτ1 τ2τ tr τ trτLFτevabcdτTEτ ELFτ ELF τ ELFFIG. 2. Experimental timing sequences. (a) Magnetic fields,involving transport of the sample from the high magnetic fieldBhigh to the low magnetic field Blow, and back again. Thetransport time is tr. (b) Radio frequency fields, resonant withthe 15N nuclei in Bhigh. The pulse flip angles and rf phases aregiven in degrees. The time spent in Blow is LF. (c) ELF pulsesequence for observing singlet-triplet nutation. After a time TEto allow triplet equilibration, a resonant ELF pulse is applied ofduration ELF. (d) ELF pulse sequence for observing the pre-cession of singlet-triplet coherence. Two ELF pulses, with thesame phase, are separated by a variable evolution interval ev.The ELF sequences are executed in parallel with sequences (a)and (b). The timing sequences are not to scale: the low-fieldpulses are about 4 orders of magnitude longer than the high-fieldones.PRL 103, 083002 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending21 AUGUST 2009083002-2causes a singlet-triplet population difference to be gener-ated by adiabatic transport of the sample out of the mag-netic field. The sample is left in low magnetic field for aninterval LF before the sample is let down into the magnet,a further two-pulse rf sequence is applied, and the NMRsignal is detected. In the current case, measurement of theNMR signals for a set of different low-field intervals LFprovided the following estimation of the singlet relaxationtime: TS ¼ 1585 57 s, consistent with earlier experi-ments [3].The timing sequence in Fig. 2(c) demonstrates the phe-nomenon of ELF-induced singlet-triplet nutation. Thesample is left in the low-field region for a ‘‘triplet equili-bration interval’’ TE ¼ 60 seconds. This allows the pop-ulations to redistribute within the triplet manifold, whilemaintaining the singlet-triplet population difference [3].This protocol generates a more reproducible starting pointfor the singlet-triplet nutation procedure, as will be de-scribed in detail elsewhere.Singlet-triplet nutation is observed by applying an ELFpulse of duration ELF, with a frequency matching thesinglet-triplet splitting. The sample is transported backinto the high-field region, and the NMR signal generatedby a further sequence of two 90 pulses. Fourier trans-formation of the signal generates the NMR spectrum. Theexperiment is repeated for a set of different pulse durationsELF. The amplitudes of two high-field NMR peaks areplotted as a function of the ELF pulse duration ELF inFig. 3(a).This plot shows clear Rabi oscillations indicating thecoherent driving of the singlet-triplet transitions by theextremely low-frequency field. The Rabi oscillations in-duced by the ELF pulse are extraordinarily slow: Thesinglet-triplet Rabi frequency is of the order of!STRabi=2 ¼ 116 mHz, corresponding to a 90 singlet-triplet pulse of duration 2.15 seconds. This is consistentwith the known chemical shift difference  ¼ 82:3 ppmand a peak ELF field of 0.65 mT. The asymmetric patternof peak amplitudes is consistent with spin-dynamical the-ory, as will be described elsewhere.In principle, singlet-triplet nutation could also be in-duced by an unmodulated magnetic field pulse, or a suddenmagnetic field step [19]. However, the field changes re-quired in those methods are much stronger and requirespecialized hardware.A resonant ELF pulse induces a rotation in the singlet-triplet subspace through the singlet-triplet flip angle de-fined ST ¼ !STRabiELF. For example, a 180 ELF pulse,for which ST ¼ , interchanges the populations of jS0iand jT0i. A 90 ELF pulse, for which ST ¼ =2, trans-forms the singlet state jS0i into a superposition of jS0i andjT0i. If a 90 ELF pulse is applied to a spin ensembledisplaying a singlet-triplet population difference, a coher-ent superposition of singlet and triplet states is induced.This is called singlet-triplet coherence.Figure 2(d) shows the procedure for studying the freeevolution of singlet-triplet coherence. Two 90 ELF pulsesare separated by a variable evolution interval ev. Incre-mentation of the evolution interval ev generates prominentoscillations in the NMR signal, as shown in Fig. 3(b).These oscillations may be fitted to a damped sinusoidaloscillation with frequency 50:8 0:3 mHz.Since the ELF pulses are phase-coherent at the ELFcarrier frequency, the observed oscillation frequency isgiven by j!ST !ELFj, where !ST is the singlet-tripletsplitting in angular frequency units, and !ELF is the angu-lar frequency of the ELF oscillator. A second experiment,with a slightly different ELF frequency, was performed inorder to determine whether the singlet-triplet frequencywas larger or smaller than the ELF carrier frequency. Inthis way, it was possible to determine the singlet-tripletsplitting to be !ST=2 ¼ 8:695 0:001 Hz in angularfrequency units. The decay time constant for the singlet-triplet coherence was determined to be TST2 ¼ 77 10 s.In zero magnetic field, the singlet-triplet splitting, ex-pressed in frequency units, corresponds exactly to the spin-0 2 4 6 8 10-0.50.00.51.0Signal Amplitude /s0 40 80 120Signal Amplitude -0.50.00.51.0/sabτ ELFτ evFIG. 3. Experimental peak amplitudes plotted against the tim-ing intervals of ELF pulse experiments. (a) Singlet-triplet nuta-tion experiment, varying the duration ELF of the ELF pulse inFig. 2(c). (b) Singlet-triplet coherence evolution experiment,varying the duration ev of the evolution interval in Fig. 2(d),with the two ELF pulse durations fixed to ELF ¼ 2:15 s. Blackcircles and white boxes refer to the amplitudes of the twocomponents of the high-field doublet in the 15N2O spectrum.The solid lines are best fits to exponentially decaying cosinefunctions with an added offset from zero. Experiments wereperformed on a sample of 15N2O dissolved in locally producedCalabrian olive oil using the following timings: 1 ¼ 198 s,2 ¼ 99 s, tr ¼ 10 s, and TE ¼ 60 s. The ELF irradiationfrequency was !ELF=2 ¼ 8:693 Hz in all cases.PRL 103, 083002 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending21 AUGUST 2009083002-3spin coupling, i.e., !ST ¼ 2JNN . However, in our experi-ments, the fringe field of the NMR magnet at the center ofthe ELF coil was estimated to be Blow ’ 2:0 0:1 mT byusing a Hall effect sensor. This finite ambient field leads tosmall second-order chemical shift effects. The singlet-triplet splitting in this regime is given by!ST ’ 2JNN þ ðBlowÞ24JNN: (5)When this small shift is taken into account, the J couplingbetween the two 15N nuclei was determined to be JNN ¼8:665 0:004 Hz, where the error margin takes into ac-count the uncertainty in the chemical shift values, themagnetic field inside the ELF coil, and the measuredsinglet-triplet splitting.The determination of a nuclear spin-spin coupling withsuch accuracy is possible because of the following factors:(1) Magnetic field inhomogeneity, which plays a strongrole in conventional high-field NMR, has almost no effecton the singlet-triplet splitting; (2) The decay of the singlet-triplet coherence is very slow, in part because of the longsinglet lifetime; (3) Even the diffusion of the moleculesinto sample regions that experience different magneticfields has a negligible effect.We have used singlet-triplet coherence to investigatewhether JNN depends on the solvent in which15N2O isdissolved. Important components of olive oil include thetriglyceride esters of oleic acid (9Z-octadecenoic acid) andlinoleic acid (9Z, 12Z-octadecadienoic acid). We dissolved15N2O in separate samples of oleic and linoleic acid andmeasured the singlet-triplet oscillation frequency in bothcases. The JNN couplings between the15N nuclei werefound to be 8:727 0:004 Hz and 8:698 0:004 Hz foroleic acid and linoleic acid solutions, respectively. Thesesmall but significant differences suggest that the accuratemeasurement of J couplings in low magnetic field canconvey information on the chemical environment of thenitrous oxide.The extremely long-lived singlet of 15N2O should allowhyperpolarized nuclear spin order, such as that generatedby dynamic nuclear polarization (DNP) [20], to be trans-ported through the sample with relatively little loss oforder. The experiments described here shows that this useof the singlet may be combined with singlet-triplet inter-conversion by applying resonant ELF fields of relativelylow amplitude. Since the triplet states are magnetic, theyrespond to applied magnetic field gradients, and may there-fore be used for spatial characterization.In summary, we have demonstrated a new form ofnuclear magnetic resonance spectroscopy, involving irra-diation in the extremely low-frequency (ELF) region of theelectromagnetic spectrum. The ELF pulses induce ex-tremely slow Rabi oscillations between states of differentspin exchange symmetry. In the case of 15N-labeled nitrousoxide, the ELF pulses induce singlet-triplet populationexchange, and excite singlet-triplet spin coherence, whichoscillates at a characteristic and extremely well-definedfrequency. Furthermore, the ELF pulses may be used toexchange spin order at will between magnetic triplet stateswith conventional relaxation properties, and nonmagneticsinglet states with exceptionally long lifetimes. The phe-nomenon is not restricted to 15N-labeled nitrous oxide andshould be observable for many coupled nuclear spin spe-cies in low magnetic field.We thank O.G. Johannessen, A. Glass, R. Dalley,J. James, L. Mulholland, and P. Trye for instrumentalhelp, and EPSRC(UK) for funding. M. C. would like tothank the Royal Society for financial support.*mhl@soton.ac.uk[1] S. Appelt, F.W. Ha¨sing, H. Ku¨hn, U. Sieling, andB. Blu¨mich, Chem. Phys. Lett. 440, 308 (2007).[2] S. Appelt, H. Ku¨hn, F.W. Ha¨sing, and B. Blu¨mich, NaturePhys. 2, 105 (2006).[3] G. Pileio, M. Carravetta, E. Hughes, and M.H. Levitt,J. Am. Chem. Soc. 130, 12582 (2008).[4] R. J. Traystman, J. Appl. Physiol. 97, 1601 (2004).[5] M. Carravetta, O.G. Johannessen, and M.H. Levitt, Phys.Rev. Lett. 92, 153003 (2004).[6] M. 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Extremely low-frequency spectroscopy in low-field nuclear magnetic resonance

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