Spin echo NMR spectra without J modulation

being used to suppress the effects of chemical shifts and field inhomogeneity, to measure spin–spin relaxation times T2, and to discriminate between signals with different T2s. Echo modulation was responsible for the original discovery of J couplings, but significantly restricts their use. It is well-known that homonuclear 15 J modulation can be quenched by rapid refocusing. In the Carr– Purcell–Meiboom–-Gill (CPMG) experiment of Fig. 1a, modulation is suppressed (at the cost of high RF power deposition) if it arises from couplings between spins with chemical shift differences Δν << 1/τ. It has recently been shown 20 10 that the cumulative effect of pulse imperfections can reduce or even suppress modulations in CPMG experiments at favourable resonance offsets, even for interpulse spacings 2τ much longer than 1/Δν (the "SITCOM" effect, ‘stabilization by interconversion within a triad of coherences under multiple 25 refocusing’). It is also known that J modulation can be refocused in the special case of a weakly-coupled two-spin system AX, in what Takegoshi et al. call a "perfect echo" (recently rediscovered), by inserting a 90° pulse at the midpoint of a double spin echo; and that this can reduce J modulation for 30 other spin systems. A zero/double quantum filtration method for two-spin systems has also been proposed recently, but is less general than the perfect echo. J modulation can in favourable cases also be avoided by using multiplet-selective 180° pulses, but only for one multiplet at a time. 35

refocusing').It is also known 11,12 that J modulation can be refocused in the special case of a weakly-coupled two-spin system AX, in what Takegoshi et al. call a "perfect echo" 11 (recently rediscovered 13 ), by inserting a 90° pulse at the midpoint of a double spin echo; and that this can reduce J modulation for other spin systems. 12A zero/double quantum filtration method for two-spin systems has also been proposed recently, 14 but is less general than the perfect echo.J modulation can in favourable cases also be avoided by using multiplet-selective 180° pulses, but only for one multiplet at a time.
The extra 90° pulse in Fig. 1b exchanges coherence between spins and reverses the apparent sense of J modulation, so that the second half of the double spin echo refocuses the modulation caused by the first.The effect is not in fact restricted to AX spin systems; it extends to arbitrary spin systems provided that   modulation.Intriguingly, the bracketed cyclic perfect echo component of Fig. 1b has been used previously as a planar mixing sequence for propagating spin waves in linear spin chains, 18 though not for T 2 weighting.At present, T 2 in coupled spin systems is normally measured using very short interpulse spacings 2τ, which can cause severe sample heating and suppresses the effects of slow chemical exchange processes.It has recently been shown 8 that measurements can be made at significantly longer spacings (approaching 1 ms) provided that these intervals are carefully 10 chosen with respect to resonance offsets.Here we show, for the first time for arbitrary spin systems, that with the sequence of Fig. 1b, interpulse spacings 2τ can be used that are an order of magnitude greater than this, irrespective of offset.T 2 -weighting is frequently used to suppress interfering signals 50 from high molecular weight, relatively low mobility species, for example in NMR metabolomics 19 and in drug discovery methods such as saturation transfer difference. 20Long CPMG sequences with high duty cycles are commonly used to attenuate such signals, but cause undesirable sample heating.Fig. 3 shows, for 55 an aqueous sample of beef and yeast extract, that good suppression of broad spectral components can be achieved with very little RF power deposition (here only 25 mW during the echo train).It should be straightforward to adapt such methods for use if strong T 2 -weighting is required in vivo.

60
The applications of "perfect echo" pulse sequence elements are by no means confined to the above; in particular, the first section of the sequence, -τ -180 -τ -90°y, may be regarded as a "prefocusing" unit, resulting in J modulation equivalent to a time minus 2τ, and hence allowing J modulation to be refocused at a 65 time 2τ later.Such a sequence element can for example be used to suppress the troublesome J modulation seen in experiments such as WATERGATE, 21 or as an alternative to a 45° purge pulse in stimulated echo DOSY sequences such as Oneshot. 22he theoretical background is as follows.Spin echo J 70 modulation in a system of spins-1/2 arises because the 180° pulse has the double effect of rotating the coherence of one ("active") spin, and of exchanging α and β spin states for its coupling partners ("passive" spins).For a weakly coupled two-spin system IS, the effect of a standard Carr-Purcell spin echo experiment in 75 the product operator formalism 23 is where the chemical shifts are refocused and hence have been ignored, and θ J = 2πJ IS τ.If a 90° pulse is now applied about the y axis, the effect is to leave the in-phase y terms unchanged but to exchange the I and S antiphase terms, changing their signs so that the net effect of J modulation has been reversed: If a second echo is now generated, the J modulation is refocused: Thus for an AX spin system, as is already known, adding a 90° pulse at the midpoint of a double spin echo completely refocuses the J modulation.The effect does, however, rely on equal initial magnetisations for the two coupled spins, as for example when the spin system is initially at equilibrium.
Consider now the effect of J modulation in such an experiment for general spin system of N weakly coupled spins-1/2 I 1 .. I N .If the quantity θ Jij = 2πJ ij τ 1 (a much easier condition to fulfill than that for the sequence of Fig. 1a, in which J is replaced by the chemical shift difference), then sinθ Jij ≃ θ Jij << 1, so that multiply antiphase terms, which are proportional to higher powers of sinθ Jij , can be neglected, and the effect of J evolution during the first spin echo reduces to Applying a 90°y pulse at this point once again exchanges and inverts the antiphase terms, and a second echo refocuses the J modulation: Thus for short τ the additional 90° pulse fully refocuses J modulation for arbitrary networks of weakly coupled spins-1/2.
In the case of strong coupling, a different mechanism of modulation suppression comes into play.Because in the strong 35 coupling case τ is short compared to the inverse of the chemical shift difference Δδ ij as well as to 1/J ij , the effect of differential precession of the chemical shifts of coupled pairs is small, and as a result the effects of the three terms in the coupling Hamiltonian

Experimental Section
All

Fig. 1 85 Fig. 1 .
Fig.1bwith n = 1; the cyclic analogue n > 1 is here distinguished by the name PROJECT (Periodic Refocusing of J Evolution by Coherence Transfer), as it does not form perfect echoes for systems of more than two spins but does still suppress J

Fig. 2 .Fig. 3 .
Fig. 2. 500 MHz 1 H T 2 measurements on 75 mM clarithromycin in dimethylsulfoxide-d 6 .a) and b), spectra obtained using the sequences of Fig. 1a and 1b respectively with a delay τ = 8 ms and a total echo time of 4nτ = 128 ms (n = 4).c) and d), results for the two