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Suppression of artifacts in two-dimensional J spectroscopy
JOURNAL
OF MAGNETIC
RESONANCE
27,5
11-5 14
(1977)
Suppressionof Artifacts in Two-Dimensional J Spectroscopy In homonuclear coupled spin systems, NMR spin echoes are found to carry modulation caused by spin-spin coupling (I, 2) and in heteronuclear systems, a similar modulation can be introduced by the application of a 180° pulse on the nonresonant spins, synchronized with the refocusing pulse (3). Where several coupling constants are involved, the resulting modulation is correspondingly complex and is best analyzed by Fourier transformation (4). The resulting “J spectrum” is insensitive to chemical shifts and field inhomogeneity effects (provided that spin diffusion is negligible) and therefore benefits from much higher resolution than conventional NMR. A particularly promising application is to proton-coupled 13C spectroscopy (5,6). J spectroscopy may profitably be combined with the new technique of double Fourier transformation (7,8) in order to separate the effects of spin-spin coupling from those of the chemical shift. The result is a spectrum with two orthogonal frequency axes, one reserved for the conventional spectrum, the other for the J spectrum. Carbon13 spin echoes are generated by a single 180° refocusing pulse, and monitored as a function of the time parameter t, = r, + r,, where r, is the “defocusing interval” between the 90 and 180’ pulses, and ra is an equal “refocusing interval” extending to the center of the spin echo. The second half of the spin echo is acquired as a function of the running-time variable t,, and the sequence is repeated for a series of different values of the variable t,. Successive Fourier transformations with respect to t, and then t, generate a spectrum S(F,, FJ where intensity is displayed as a function of the two orthogonal frequency parameters F, and F,. The J spectrum appears in the F, dimension. ‘Phantom” and “Ghost” Signals
Spurious responses often appear in these two-dimensional J spectra, and since they are usually weak replicas of the main signals, they have come to be known as “phantom” and “ghost” responses. They can be shown to arise from imperfections in the radiofrequency pulses applied to 13C, either from a missetting of the 90° or 180° flip angles, or more commonly through spatial inhomogeneities in the radiofrequency field. These artifacts appear in both the “proton flip” and “gated decoupler” modes of J spectroscopy, but exhibit different behavior in the two experiments (9). For simplicity only the “proton flip” technique is considered here. The 13C J spectrum of methyl iodide is used to illustrate these effects, spin echoes being acquired in the absence of proton decoupling, with the result that spin multiplet structure also appears in the F, dimension, the 1: 3 : 3 : 1 quartet lying on a 4S” diagonal A phantom multiplet appears when the refocusing pulse deviates from its nominal 180° flip angle; any Z magnetization is flipped into a position where it has a finite XY component in the rotating frame. Such Z magnetization can arise either from an imperfect initial pulse or by spin-lattice relaxation during rD. If 6 is the chemical shift of methyl iodide measured with respect to the transmitter frequency, the four transverse Copyright @ 1977 by Academic Press, Inc. All rights of reproduction in any form reserved. Primed in Great Britain
511
1SSN 0022-2364
COMMUNICATIONS
512
vectors precess at frequencies 6 - 3Jl2, 6 - J/2, 6 + J/2, and 6 + 3512 during tR. Since the transformation is made with respect to t, = 22,, the J spectrum responses are at one half of these frequencies. The two-dimensional spectrum shows a phantom quartet which lies on a diagonal at an angle arctan 0.5 to the F, axis. The center of the quartet has the coordinates F, = +6/2 Hz, F,= +S Hz. A ghost quartet also appears when the 180° refocusing pulse applied to 13C is imperfect. This can be treated (IO) by breaking down the total magnetization into three parts, one which experiences a perfect refocusing pulse, one which reverts to Z magnetization, and a third which experiences no carbon refocusing pulse at all. This third part is responsible for the ghost response. In the interval r, the four vectors precess at 6 - 3Jf2, 6 - J/2, 6 + J/2, and 6 + 3Jl2, but because of the proton flip pulse (assumed here to be perfect) they precess at 6 + 3J/2, 6 + J/2, 6 - J/2, and 6 - 3J/2 in the refocusing interval r,. Consequently there is no net splitting in the F, dimension, simply a displacement of all four lines by +6 Hz. The ghost quartet thus lies parallel to the Fz axis with its center at F, = S, F, = 6. Elimination of Artifacts Phantom signals arise from transverse magnetization created by an imperfect refocusing pulse, and since the sign of this signal is reversed by inverting the phase of the refocusing pulse, phantoms are easily canceled by phase alternation followed by coherent addition of an even number of echoes. This is analogous to the method used to eliminate the interfering transverse signal in an inversion-recovery spin-lattice relaxation experiment (II). The magnetization which gives rise to ghost multiplets does not experience the 180° carbon refocusing pulse at all. This makes it possible to shift the phase of the refocusing pulse without affecting ghost responses, and a 90° phase shift has the effect of inverting the sense of the spin echo (12). When such a 90° shift is combined with inversion of the receiver reference phase (or digital subtraction of the signal in the computer) the echoes add coherently while the ghosts cancel after an even number of acquisitions. The two procedures can be combined into a four-step sequence where the phase of the carbon refocusing pulse is cycled through 0, 90, 180, 270° while the receiver reference phase is alternated (see Table 1). Addition of the second part of the echoes from steps (a) and (c) or steps (b) and (d) cancels phantoms; while the combination (a) + (b) or (c) + (d) cancels ghosts. Summation over all four steps cancels both TABLE A PHASE-CYCLING
1
SEQUENCE WHICH CANCELS RESPONSES IN TWO-DIMENSIONAL Phase angles
90° Carbon 0 0 0 0
pulse
HO0
Carbon 0 90 180 270
“PHANTOM” J SPECTRA
AND “GHOST”
(deg) pulse
Receiver
reference 0 180 0 180
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forms of artifact. For therefore be a multiple A practical test of CFT-20 spectrometer
513
any given setting of t,, the total number of acquisitions should of 4. We dub this sequence “Exorcycle.” this phase-cycling sequence has been carried out on a Varian with the software adapted for double Fourier transformation P G
FIG. 1. Two-dimensional J spectra of “C in methyl iodide obtainedO rather by thethan proton 180”.tlipIntechnique, spectrum but (a) with the “C refocusing pulse deliberately misset to a flip angle ofwhereas 135 in spectrum (b) they have been the phantom (P) and ghost (G) multiplets are clearly visible, canceled by using the phase-cycled pulse sequence.
(9) and hardware modifications that shift the phase of the transmitter and receiver signals (13). (Circuit diagrams are available on request.) reference Figure la shows the two-dimensional proton flip J spectrum with phantom and ghost multiplets emphasized by a deliberate missetting of the refocusing pulse to 135”, while Fig. lb presents the same spectrum under the same pulse conditions but with these
514
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spurious responses eliminated by the use of Exorcycle. Some extremely weak artifacts remain, two of which can be observed at F, = ?J, F2 = ?3Jl2. These are ascribed to the effect of missetting the proton pulse flip angle, and will be the subject of a later investigation. ACKNOWLEDGMENTS This work was made possible by an equipment grant from the British Science Research Council, and has been supported by a Salters’ Company Scholarship (G.B.) and the Science Research Council (D.L.T.). The authors acknowledge a useful discussion on phase-alternated pulse sequences with Dr. S. Patt. REFERENCES Rev. 88,107O (1952). in “Dynamic Nuclear Magnetic Resonance Spectroscopy” (L. M. Jackman and F. A. Cotton, Eds.), Chap. 5, Academic Press, New York/London, 1975. G. BODENHAUSEN, R. FREEMAN, R. NEIDERMAYER, AND D. L. TURNER, J. Magn. Resonance, 24, 291 (1976); L. MOLLER, A. KUMAR, AND R. R. ERNST, J. Magn. Resonance 25,383 (1977). R. FREEMAN AND H. D. W. HILL, J. Chem. Phys. 54,301 (1971). R. FREEMAN, G. A. MORRIS, AND D. L. TURNER, J. Magn. Resonance 26,373 (1977). G. BODENHAUSEN, R. FREEMAN, G. A. MORRIS, AND D. L. TURNER, J. Magn. Resonance (1977), in press. J. JEENER, Ampere International Summer School, Basko Polje, Poland (1971); Second European Experimental NMR Conference, Enschede, Holland (1975). L. MUELLER, A. KUMAR, AND R. R. ERNST, J. Chem. Phys. 63, 5490 (1975); W. P. AUE, E. BARTHOLDI AND R. R. ERNST, J. Chem. Phys. 64,2229 (1976). G. BODENHAUSEN, R. FREEMAN, R. Niedermeyer, AND D. L. TURNER, J. Magn. Resonance 26, 133 (1977). R. KAISER, E. BARTHOLDI, AND R. R. ERNST, J. Chem. Phys. 60,2966 (1974). D. E. DEMCO, P. VAN HECKE, AND J. S. WAUGH, J. Magn. Resonance 16,467 (1974). S. MEI~OOM AND D. GILL, Rev. Sci. Instrum. 29,688 (1958). G. BODENHAUSEN, R. FREEMAN, G. A. MORRIS, R. NIEDERMEYER, AND D. L. TURNER, J. Magn. Resonance 25,559 (1977).
1. E. L. HAHN AND D. E. MAXWELL,P@S. 2. R. FREEMAN AND H. b. W. HILL, 3. 4. 5.
6. 7.
8. 9. 10. II. 12.
13.
GEOFFREY
BODENHAUSEN RAY
DAVID
Physical Chemistry Laboratory South Parks Road Oxford, England Received May 18.1977
FREEMAN
L. TURNER
OF MAGNETIC
RESONANCE
27,5
11-5 14
(1977)
Suppressionof Artifacts in Two-Dimensional J Spectroscopy In homonuclear coupled spin systems, NMR spin echoes are found to carry modulation caused by spin-spin coupling (I, 2) and in heteronuclear systems, a similar modulation can be introduced by the application of a 180° pulse on the nonresonant spins, synchronized with the refocusing pulse (3). Where several coupling constants are involved, the resulting modulation is correspondingly complex and is best analyzed by Fourier transformation (4). The resulting “J spectrum” is insensitive to chemical shifts and field inhomogeneity effects (provided that spin diffusion is negligible) and therefore benefits from much higher resolution than conventional NMR. A particularly promising application is to proton-coupled 13C spectroscopy (5,6). J spectroscopy may profitably be combined with the new technique of double Fourier transformation (7,8) in order to separate the effects of spin-spin coupling from those of the chemical shift. The result is a spectrum with two orthogonal frequency axes, one reserved for the conventional spectrum, the other for the J spectrum. Carbon13 spin echoes are generated by a single 180° refocusing pulse, and monitored as a function of the time parameter t, = r, + r,, where r, is the “defocusing interval” between the 90 and 180’ pulses, and ra is an equal “refocusing interval” extending to the center of the spin echo. The second half of the spin echo is acquired as a function of the running-time variable t,, and the sequence is repeated for a series of different values of the variable t,. Successive Fourier transformations with respect to t, and then t, generate a spectrum S(F,, FJ where intensity is displayed as a function of the two orthogonal frequency parameters F, and F,. The J spectrum appears in the F, dimension. ‘Phantom” and “Ghost” Signals
Spurious responses often appear in these two-dimensional J spectra, and since they are usually weak replicas of the main signals, they have come to be known as “phantom” and “ghost” responses. They can be shown to arise from imperfections in the radiofrequency pulses applied to 13C, either from a missetting of the 90° or 180° flip angles, or more commonly through spatial inhomogeneities in the radiofrequency field. These artifacts appear in both the “proton flip” and “gated decoupler” modes of J spectroscopy, but exhibit different behavior in the two experiments (9). For simplicity only the “proton flip” technique is considered here. The 13C J spectrum of methyl iodide is used to illustrate these effects, spin echoes being acquired in the absence of proton decoupling, with the result that spin multiplet structure also appears in the F, dimension, the 1: 3 : 3 : 1 quartet lying on a 4S” diagonal A phantom multiplet appears when the refocusing pulse deviates from its nominal 180° flip angle; any Z magnetization is flipped into a position where it has a finite XY component in the rotating frame. Such Z magnetization can arise either from an imperfect initial pulse or by spin-lattice relaxation during rD. If 6 is the chemical shift of methyl iodide measured with respect to the transmitter frequency, the four transverse Copyright @ 1977 by Academic Press, Inc. All rights of reproduction in any form reserved. Primed in Great Britain
511
1SSN 0022-2364
COMMUNICATIONS
512
vectors precess at frequencies 6 - 3Jl2, 6 - J/2, 6 + J/2, and 6 + 3512 during tR. Since the transformation is made with respect to t, = 22,, the J spectrum responses are at one half of these frequencies. The two-dimensional spectrum shows a phantom quartet which lies on a diagonal at an angle arctan 0.5 to the F, axis. The center of the quartet has the coordinates F, = +6/2 Hz, F,= +S Hz. A ghost quartet also appears when the 180° refocusing pulse applied to 13C is imperfect. This can be treated (IO) by breaking down the total magnetization into three parts, one which experiences a perfect refocusing pulse, one which reverts to Z magnetization, and a third which experiences no carbon refocusing pulse at all. This third part is responsible for the ghost response. In the interval r, the four vectors precess at 6 - 3Jf2, 6 - J/2, 6 + J/2, and 6 + 3Jl2, but because of the proton flip pulse (assumed here to be perfect) they precess at 6 + 3J/2, 6 + J/2, 6 - J/2, and 6 - 3J/2 in the refocusing interval r,. Consequently there is no net splitting in the F, dimension, simply a displacement of all four lines by +6 Hz. The ghost quartet thus lies parallel to the Fz axis with its center at F, = S, F, = 6. Elimination of Artifacts Phantom signals arise from transverse magnetization created by an imperfect refocusing pulse, and since the sign of this signal is reversed by inverting the phase of the refocusing pulse, phantoms are easily canceled by phase alternation followed by coherent addition of an even number of echoes. This is analogous to the method used to eliminate the interfering transverse signal in an inversion-recovery spin-lattice relaxation experiment (II). The magnetization which gives rise to ghost multiplets does not experience the 180° carbon refocusing pulse at all. This makes it possible to shift the phase of the refocusing pulse without affecting ghost responses, and a 90° phase shift has the effect of inverting the sense of the spin echo (12). When such a 90° shift is combined with inversion of the receiver reference phase (or digital subtraction of the signal in the computer) the echoes add coherently while the ghosts cancel after an even number of acquisitions. The two procedures can be combined into a four-step sequence where the phase of the carbon refocusing pulse is cycled through 0, 90, 180, 270° while the receiver reference phase is alternated (see Table 1). Addition of the second part of the echoes from steps (a) and (c) or steps (b) and (d) cancels phantoms; while the combination (a) + (b) or (c) + (d) cancels ghosts. Summation over all four steps cancels both TABLE A PHASE-CYCLING
1
SEQUENCE WHICH CANCELS RESPONSES IN TWO-DIMENSIONAL Phase angles
90° Carbon 0 0 0 0
pulse
HO0
Carbon 0 90 180 270
“PHANTOM” J SPECTRA
AND “GHOST”
(deg) pulse
Receiver
reference 0 180 0 180
COMMUNICATIONS
forms of artifact. For therefore be a multiple A practical test of CFT-20 spectrometer
513
any given setting of t,, the total number of acquisitions should of 4. We dub this sequence “Exorcycle.” this phase-cycling sequence has been carried out on a Varian with the software adapted for double Fourier transformation P G
FIG. 1. Two-dimensional J spectra of “C in methyl iodide obtainedO rather by thethan proton 180”.tlipIntechnique, spectrum but (a) with the “C refocusing pulse deliberately misset to a flip angle ofwhereas 135 in spectrum (b) they have been the phantom (P) and ghost (G) multiplets are clearly visible, canceled by using the phase-cycled pulse sequence.
(9) and hardware modifications that shift the phase of the transmitter and receiver signals (13). (Circuit diagrams are available on request.) reference Figure la shows the two-dimensional proton flip J spectrum with phantom and ghost multiplets emphasized by a deliberate missetting of the refocusing pulse to 135”, while Fig. lb presents the same spectrum under the same pulse conditions but with these
514
COMMUNICATIONS
spurious responses eliminated by the use of Exorcycle. Some extremely weak artifacts remain, two of which can be observed at F, = ?J, F2 = ?3Jl2. These are ascribed to the effect of missetting the proton pulse flip angle, and will be the subject of a later investigation. ACKNOWLEDGMENTS This work was made possible by an equipment grant from the British Science Research Council, and has been supported by a Salters’ Company Scholarship (G.B.) and the Science Research Council (D.L.T.). The authors acknowledge a useful discussion on phase-alternated pulse sequences with Dr. S. Patt. REFERENCES Rev. 88,107O (1952). in “Dynamic Nuclear Magnetic Resonance Spectroscopy” (L. M. Jackman and F. A. Cotton, Eds.), Chap. 5, Academic Press, New York/London, 1975. G. BODENHAUSEN, R. FREEMAN, R. NEIDERMAYER, AND D. L. TURNER, J. Magn. Resonance, 24, 291 (1976); L. MOLLER, A. KUMAR, AND R. R. ERNST, J. Magn. Resonance 25,383 (1977). R. FREEMAN AND H. D. W. HILL, J. Chem. Phys. 54,301 (1971). R. FREEMAN, G. A. MORRIS, AND D. L. TURNER, J. Magn. Resonance 26,373 (1977). G. BODENHAUSEN, R. FREEMAN, G. A. MORRIS, AND D. L. TURNER, J. Magn. Resonance (1977), in press. J. JEENER, Ampere International Summer School, Basko Polje, Poland (1971); Second European Experimental NMR Conference, Enschede, Holland (1975). L. MUELLER, A. KUMAR, AND R. R. ERNST, J. Chem. Phys. 63, 5490 (1975); W. P. AUE, E. BARTHOLDI AND R. R. ERNST, J. Chem. Phys. 64,2229 (1976). G. BODENHAUSEN, R. FREEMAN, R. Niedermeyer, AND D. L. TURNER, J. Magn. Resonance 26, 133 (1977). R. KAISER, E. BARTHOLDI, AND R. R. ERNST, J. Chem. Phys. 60,2966 (1974). D. E. DEMCO, P. VAN HECKE, AND J. S. WAUGH, J. Magn. Resonance 16,467 (1974). S. MEI~OOM AND D. GILL, Rev. Sci. Instrum. 29,688 (1958). G. BODENHAUSEN, R. FREEMAN, G. A. MORRIS, R. NIEDERMEYER, AND D. L. TURNER, J. Magn. Resonance 25,559 (1977).
1. E. L. HAHN AND D. E. MAXWELL,P@S. 2. R. FREEMAN AND H. b. W. HILL, 3. 4. 5.
6. 7.
8. 9. 10. II. 12.
13.
GEOFFREY
BODENHAUSEN RAY
DAVID
Physical Chemistry Laboratory South Parks Road Oxford, England Received May 18.1977
FREEMAN
L. TURNER