4 DQF-COSY, Relayed-COSY, TOCSY Gerd Gemmecker 1999 Double-quantum filtered cOSY The phase problem of normal COsY can be circumvented by the dQF-COSY, using the MQc term generated by the second 90 pulse Ilz cos( @2t1) cos( t1) polarization 2l1yl2x cos(Q21t1) sin(TJt) l1/I2 double/zero quantum coherence +liy sin(@2 t1) cos(t1) single quantum coherence 211212x sin(Q2jt1 sin(tu) I2 anti-phase single quantum coherent Phase cycling can be set up to select only the dQC part at this time, which is only present in the 211yl2x term(leaving the cos(221ty sin(wty part away for the moment 2I1x=2h2(1-1)2(2+12)=h2(12+I112-l112-ll2) DOC ZOCZOC DOC Only the DQC part survives(50% loss! )and yields(after convertion back to the Cartesian basis) vh2(1+12-li12)=2{(l1x+ily)(2x+i2)-(l1x-l1y)(I2x-l2y)}=h2(2l1xl2y+2I1yl2) However, this magnetization is not observable, only after another 90 pulse 90°y h2(2I1ly-2I1l2) 12(2 11zI2y +2 IvI2z) Since we still have the cos(22) sin(Tty) modulation from the t, time evolution, our complete signal at the beginning of t2 is /22 11z l2y cos(Q21t1)sin (TJt1)+12 2 lly I2z cos( 2]t1) sin(TJt1)
44 4 DQF-COSY, Relayed-COSY, TOCSY © Gerd Gemmecker, 1999 Double-quantum filtered COSY The phase problem of normal COSY can be circumvented by the DQF-COSY, using the MQC term generated by the second 90° pulse: 90°y ¾¾® - I1z cos(W1 t1 ) cos(pJt1 ) I1 polarization + 2I1yI2x cos(W1 t1 ) sin(pJt1 ) I1 / I2 double/zero quantum coherence + I1y sin(W1 t1 ) cos(pJt1 ) I1 in-phase single quantum coherence + 2I1zI2x sin(W1 t1 ) sin(pJt1 ) I2 anti-phase single quantum coherence Phase cycling can be set up to select only the DQC part at this time, which is only present in the 2I1yI2x term (leaving the cos(W1 t1 ) sin(pJt1 ) part away for the moment): 2I1yI2x = 2 -i/2 (I1 + - I1 - ) 1 /2 (I2 + + I2 - ) = -i/2 (I1 + I2 + + I1 + I2 - - I1 - I2 + - I1 - I2 - ) DQC ZQC ZQC DQC Only the DQC part survives (50 % loss!) and yields (after convertion back to the Cartesian basis): -i/2 (I1 + I2 + - I1 - I2 - ) = -i/2 {(I1x + iI1y) (I2x + iI2y) - (I1x - iI1y) (I2x - iI2y)} = 1 /2 (2 I1x I2y + 2 I1y I2x) However, this magnetization is not observable, only after another 90° pulse: 90°y 1 /2 (-2 I1x I2y - 2 I1y I2x) ¾¾® 1 /2 (2 I1z I2y + 2 I1y I2z) Since we still have the cos(W1 t1 ) sin(pJt1 ) modulation from the t1 time evolution, our complete signal at the beginning of t2 is 1 /2 2 I1z I2y cos(W1 t1 ) sin(pJt1 ) + 1 /2 2 I1y I2z cos(W1 t1 ) sin(pJt1 )
After 2D FT, this translates into two signals both are antiphase signals at Q21 in FI (with identical absorptive/dispersive phase)and both are y antiphase signals (i.e, identical phase) in F2, the first one at Q22(cross-peak) and the second one at Q2(diagonal peak) Characteristics of the DQF-COSY experiment: the spectrum can be phase corrected to pure absorptive(although antiphase)cross- and diagonal peaks in both dimensions both cross-and diagonal peaks are derived from a dQc term requiring the presence of scalar coupling(since it can only be generated from an antiphase term with the help of another r.f. pulse: 211yI2z->211yl2x). Therefore, singulet signals-eg, solvent signals like H2O! -should be completely suppressed, even as diagonal signals Usually this suppression is not perfect(due to spectrometer instability, misset phases and pulse lengths, too short a relaxation delay between scans etc. ) and a noise ridge occurs at the frequency of intense singulets. In addition, this solvent suppression occurs only with the phase cycling during the acquisition of several scans with for the same tI increment, i. e, after digitization To cope with the
45 After 2D FT, this translates into two signals: - both are antiphase signals at W1 in F1 (with identical absorptive/dispersive phase) and - both are y antiphase signals (i.e., identical phase) in F2, the first one at W2 (cross-peak) and the second one at W1 (diagonal peak). Characteristics of the DQF-COSY experiment: - the spectrum can be phase corrected to pure absorptive (although antiphase) cross- and diagonal peaks in both dimensions - both cross- and diagonal peaks are derived from a DQC term requiring the presence of scalar coupling (since it can only be generated from an antiphase term with the help of another r.f. pulse: 2I1yI2z ¾® 2I1yI2x). Therefore, singulet signals – e.g., solvent signals like H2O! – should be completely suppressed, even as diagonal signals. Usually this suppression is not perfect (due to spectrometer instability, misset phases and pulse lengths, too short a relaxation delay between scans etc.), and a noise ridge occurs at the frequency of intense singulets. In addition, this solvent suppression occurs only with the phase cycling during the acquisition of several scans with for the same t1 increment, i.e., after digitization! To cope with the
limited dynamic range of NMR ADCS, additional solvent suppression has to be performed before digitization (i.e, presaturation) If the dQ filtering is done with pulsed field gradients(PGFs)instead of phase cycling, then this suppresses the solvent signals before hitting the digitizer. However, inserting PGFs into the dQF-COSY sequence causes other problems(additional delays and r f. pulses, phase distortions, non-absorptive lineshapes, additional 50% reduction of S/N) With the normal COsY sequence, they result in gigantic dispersive diagonal signals obscuring most of the 2D spectrum Intensity of cross-and diagonal peaks In the basic COSY experiment, diagonal peaks develop with the cosine of the scalar coupling, while cross-peaks arise with the sine of the coupling. Theoretically, this does not make any difference(FT of a sine wave is identical to that of a cosine function, except for the phase of the signal). While this is normally true for the relatively high-frequency chemical shift modulations (up to several 1000 Hz), the modulations caused by scalar coupling are of rather low frequency(max. ca. 20 Hz for JHH), with a period often significantly shorter than the total acquision time xg1o⊥lLL Time development of in-phase(cos Tty and antiphase(cos Tty) terms, with $2/=50 HE, J=2 H, for T2=10 s(left) and T2=0. 1 s(right) While the total signal intensity accumulated over a complete(or even half) period is identical for both in-phase and antiphase signals, an acquisition time much shorter than / 2j will clearly favor the in-phase over the antiphase signal in terms of S/N. This difference in sensitivity is further increased
46 limited dynamic range of NMR ADCs, additional solvent suppression has to be performed before digitization (i.e., presaturation). If the DQ filtering is done with pulsed field gradients (PGFs) instead of phase cycling, then this suppresses the solvent signals before hitting the digitizer. However, inserting PGFs into the DQF-COSY sequence causes other problems (additional delays and r.f. pulses, phase distortions, non-absorptive lineshapes, additional 50 % reduction of S/N). With the normal COSY sequence, they result in gigantic dispersive diagonal signals obscuring most of the 2D spectrum. Intensity of cross- and diagonal peaks In the basic COSY experiment, diagonal peaks develop with the cosine of the scalar coupling, while cross-peaks arise with the sine of the coupling. Theoretically, this does not make any difference (FT of a sine wave is identical to that of a cosine function, except for the phase of the signal). While this is normally true for the relatively high-frequency chemical shift modulations (up to several 1000 Hz), the modulations caused by scalar coupling are of rather low frequency (max. ca. 20 Hz for JHH), with a period often significantly shorter than the total acquision time. Time development of in-phase (cos pJt1) and antiphase (cos pJt1) terms, with W1 = 50 Hz, J = 2 Hz, for T2 = 10 s (left) and T2 = 0.1 s (right). While the total signal intensity accumulated over a complete (or even half) period is identical for both in-phase and antiphase signals, an acquisition time much shorter than 1 /2J will clearly favor the in-phase over the antiphase signal in terms of S/N. This difference in sensitivity is further increased
by fast T2(or T1) relaxation, leaving the antiphase signal not enough time to evolve into detectable magnetizatOn This phenomenon can also be explained in the frequency dimension: short acquisition times or fast relaxation leads to broad lines, which results in mutual partial cancelation of the multiplet lines in the case of an antiphase signal The simulation(next page) shows the dublet appearances for different ratios between coupling constant J and linewidth(LW). The linewidths were set constant to 2 Hz(at half-height), so that the different intensities of the dublet signal are only due to different J values Obviously, the apparent splitting in the spectrum can differ from the real coupling constant, if the two dublet lines are not baseline separated: for in-phase dublets, the apparent splitting becomes smaller, for antiphase dublets it is large than the true J value Ratio j/: 10 True J value hz 20.0 6.0 2.0 0.7 -phase sp litter 20.0 6.0 1.8 Antiphase splitting 20.0 6.0 2.2 1.3 In the basic COsY experiment the diagonal signals are in-phase and the cross-peaks antiphase, so that signals with small J couplings and broad lines(due to short AQ or fast relaxation) will show huge diagonal signals, but only very small or vanishing In the DQF-COSY, both types of signals stem from antiphase terms, so that both the cross-and diagonal peak intensity depends on the size of the coupling constants
47 by fast T2 (or T1) relaxation, leaving the antiphase signal not enough time to evolve into detectable magnetization. This phenomenon can also be explained in the frequency dimension: short acquisition times or fast relaxation leads to broad lines, which results in mutual partial cancelation of the multiplet lines in the case of an antiphase signal. The simulation (next page) shows the dublet appearances for different ratios between coupling constant J and linewidth (LW). The linewidths were set constant to 2 Hz (at half-height), so that the different intensities of the dublet signal are only due to different J values. Obviously, the apparent splitting in the spectrum can differ from the real coupling constant, if the two dublet lines are not baseline separated: for in-phase dublets, the apparent splitting becomes smaller, for antiphase dublets it is large than the true J value. Ratio J/L: 10 3 1 1 /3 True J value [Hz} 20.0 6.0 2.0 0.7 In-phase splitting 20.0 6.0 1.8 n/a Antiphase splitting 20.0 6.0 2.2 1.3 In the basic COSY experiment the diagonal signals are in-phase and the cross-peaks antiphase, so that signals with small J couplings and broad lines (due to short AQ or fast relaxation) will show huge diagonal signals, but only very small or vanishing cross-peaks. In the DQF-COSY, both types of signals stem from antiphase terms, so that both the cross- and diagonal peak intensity depends on the size of the coupling constants
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