Faster and cleaner real-time pure shift NMR experiments

Real-time pure shift experiments provide highly resolved proton NMR spectra which do not require any special processing. Although being more sensitive than their pseudo 2D counterparts, their signal intensities per unit time are still far below regular NMR spectra. In addition, scalar coupling evolution during the individual data chunks produces decoupling sidebands. Here we show that faster and cleaner real-time pure shift spectra can be obtained through the implementation of two parameter alterations. Variation of the FID chunk lengths between individual transients signiﬁcantly suppresses decoupling sidebands for any kind of real-time pure shift spectra and thus allows for example the analysis of minor components in compound mixtures. Shifting the excitation frequency between individual scans of real-time slice-selective pure shift spectra increases their sensitivity obtainable in unit time by allowing faster repetitions of acquisitions.


Introduction
The removal of homonuclear scalar couplings in pure shift NMR experiments significantly enhances the resolution of proton NMR spectra [1,[2][3][4][5][6][7].Broadband proton decoupling sequences, which are used routinely for removing proton couplings in heteronuclear spectra [8] can of course not be applied for homonuclear decoupling.Therefore, actual homonuclear broadband decoupling, i.e. the refocusing of scalar coupling evolution can only be achieved on a subset of spins.This could be a statistical spin subset, by using small flip angle pulses as in the time reversal [9], anti z-COSY diagonal projection [10] or the PSYCHE experiment [11,12].For these approaches it is not possible to repetitively refocus the scalar coupling evolution as it is needed for continuous decoupling during evolution.Alternatively, two methods are available which allow the continuous, real-time decoupling since they act on a specially selected subset of spins.In BIRD decoupling [13], 13 C-bound protons are decoupled from 12 C-bound protons and in slice-selective decoupling, also known as Zangger-Sterk method [1,14], different signals are selectively decoupled in different slices.In order to apply these broadband homonuclear decoupling techniques during acquisition [15][16][17][18] it is necessary to repetitively refocus the scalar coupling.Since homonuclear coupling constants are relatively small, it is sufficient to repeat the decoupling block every $20 ms.During this time, the acquisition is halted and any chemical shift evolution during the decoupling interruption must be prevented [16].Pure shift methods which are used during the acquisition (in real time) yield FIDs which do not require any special data processing and therefore increase the sensitivity per unit time [15][16][17].However, since there is some scalar coupling evolution during the individual data FID data chunks, which results in a step-like modulation of the complete FID, decoupling sidebands are introduced into the final broadband homodecoupled spectra.Additionally, for more slowly tumbling molecules, transverse relaxation during the acquisition interruption also leads to steps in the FID.The resulting decoupling sidebands appear around the actual NMR signals at frequencies corresponding to multiples of the reciprocal value of the data chunk duration d.These artifacts may prevent the analysis of low concentration impurities in pure shift NMR spectra.Another shortcoming of real-time pure shift spectra is their low sensitivity.Although the sensitivity per unit time is significantly enhanced compared to pseudo 2D decoupling, it is still way below regular proton NMR spectra.Here we present two approaches to suppress artifacts and enhance the sensitivity of real-time pure shift spectra.Decoupling sidebands in any real-time pure shift experiment can be reduced by variation of the chunking times between individual scans.
Additionally, the sensitivity of the slice-selective decoupling experiment has been addressed by introducing frequency shifted pulses, which were already used for the slice-selective decoupling experiment using pseudo 2D acquisition [19] and for following fast reactions by acquiring series of slice-selective spectra [20] without relaxation delay [21].By pairwise shifting of the excitation frequency of the slice-selective pulses, unused equilibrium magnetization can be accessed in a convenient way, thus creating very long virtual inter-scan delays and allowing the faster pulsing.As a side effect, it also increases the accuracy of the signal integrals since peaks close to the excitation frequency are typically excited to a slightly different extend compared to ones further away, especially when weak gradient fields are used.
Fig. 1.Pulse-sequence of the real-time slice-selective broadband homodecoupling (instant decoupling) approach, indicating the variable data chunking times through a variation of the number of chunks n.Frequency shifting is done for all selective pulses in parallel after each transient.Gradients of 11 and 5% (of the maximum, which is 53.5 G/cm) were used for G2 and G3, respectively.The slice-selective gradient G1 is typically between 0.5 and 2 G/cm, corresponding to 1 and 4%.The number of excitation frequencies was typically 8 and 21 different data chunking times were used.Therefore, when a higher number of scans is recorded, the excitation frequencies are combined with different chunking times.

Decoupling sideband suppression by varying data chunking durations
Real-time pure shift experiments employ scalar coupling refocusing between FID data chunks [15][16][17], which are typically $20 ms long (Fig. 1).During the interruption, the acquisition is simply halted and continued afterwards.
Scalar coupling evolves during the first half data chunk and is then inverted by either slice-selective 180°pulses or a BIRD pulse train.Therefore, the magnitude of the scalar coupling evolution reaches its initial state in the middle of the next data chunk.The overall scalar coupling evolution is zero, but it still evolves in each individual data chunk leading to a step-wise modulation of the time domain data with a frequency corresponding to the inverse of the data chunk duration d.In addition, relaxation during the interruption of the acquisition, as well as pulse-imperfections, also lead to a step-wise modulation of the resulting FID.However, since the interruption is usually rather short (typically 5-30 ms), relaxation losses are typically not severe, at least for small molecules.Therefore, we believe that scalar coupling evolution during the chunk is the major contributing factor.These steps in the FID yield chunking sidebands at frequencies Dm from the main signal according to Dm ¼ AEn=d ðn ¼ 1; 2; 3 . ..Þ: The intensity decreases rapidly with increasing n.The size of the artifacts is larger for long FID chunks since scalar coupling evolution is active for a longer duration.Shorter chunks yield less intense sidebands.However, they also produce broader signals since the acquisition is interrupted more often, leading to larger overall relaxation losses.Since the position of the artifacts depends on the chunking time, they can be reduced by variation of the FID data chunk duration d between successive scans, while still producing relatively sharp signals.By combining different values for d, the sharp decoupling sidebands are smeared out to a very broad, less prominent band of signals, which significantly decreases the average intensity of these artifacts.The practically useful lengths of d should not be too short in order to prevent excessive relaxation losses during the higher number of interruptions necessary.On the other hand, longer chunking times lead to more severe scalar coupling evolution.For small molecules we found an optimum range of d between 10 and 40 ms.Since the total acquisition time is determined by the experimental setup, i.e. the number of data points and the spectral width, a variation of the data chunk duration also requires the number of data chunks to be changed accordingly.We found it most convenient to implement the variation of chunking times by varying the number of chunks and calculating the actual chunking time on the fly.

Enhancing the sensitivity of slice-selective real-time decoupling by frequency shifting
In slice-selective decoupling, a combination of a weak pulsedfield gradient with a selective pulse leads to different signals being excited in different slices of the NMR sample tube [14].Broadband homonuclear decoupling can then be achieved by a slice selective inversion between the acquisition of individual FID data chunks.It has been shown previously that slice-selective excitation can be combined with fast pulsing by shifting the frequency of the selective pulse(s) between individual transients.This idea has been employed to follow fast reaction kinetics by recording relaxation delay free series of spectra [21] and for pseudo 2D slice-selective decoupling [19].The concept of frequency shifted pulses for slice-selective decoupling utilizes the fact that during the experiment only the magnetization that was excited in each slice is used for the acquisition of the decoupled spectrum.By shifting the offset of the selective 90°excitation pulse and in parallel the selective 180°refocusing pulse after each scan, previously unused equilibrium magnetization can be accessed without having to wait for relaxation of the freshly excited magnetization (Fig. 2).
This results in a very long virtual inter-scan delay visd which is dependent on the number of appropriately spaced excitation and refocusing frequencies m according to where aq represents the acquisition time and l ps the length of the pulse-sequence including d1.The longer the T 1 relaxation time, the higher is the obtainable sensitivity improvement.For this approach it is important that the number of non-selective 180°p ulses used during acquisition is even, so that unused magnetization is kept along the z-axis.For the same purpose, pulses need to be calibrated carefully.In slice-selective experiments, the signal  Therefore, the use of frequency shifted pulses leads to more reliable signal intensities across the whole spectral range.The use of variable data chunks and different excitation frequencies in different scans is indicated below the pulse-sequence in Fig. 1.Recently, the ASAP (acceleration by sharing adjacent polarization) principle was introduced in order to enhance the sensitivity of HSQC [22] and also slice-selective experiments [23].However, it is not possible to combine the ASAP approach with frequency shifting because a non-selective TOCSY transfer is required for ASAP.It should also be mentioned that if the pure shift spectrum does not need to be fully quantitative it is possible to use rather weak gradients in the frequency shifting approach.In this case, frequency shifting enables to excite all signals and can be thought of a combination of broadband slice-selective and band-selective decoupling.It yields higher sensitivity, however at the cost of producing not fully quantitatively reliable signal intensities.

Suppression of decoupling sidebands
Decoupling sidebands, which are formed as a result of scalar coupling evolution during individual data chunks depend both on the duration of the chunks as well as the size and multiplicity of scalar coupling.As an example the decoupling sidebands of the central CH 2 group of n-propanol in CDCl 3 in a real-time slice-selectively decoupled spectrum are shown in Fig. 3.
The longer the FID chunk, the more pronounced they are, since more anti-phase magnetization can build up.On the other hand, keeping the individual FID blocks short, reduces the chunks, but leads to broad signals, since more relaxation losses occur during the more frequent acquisition interruptions and effects accumulated by pulse imperfections.The sidebands are also more intense the longer the chunking times are and much smaller for singlets (see Supporting Figure ), pointing to evolution of scalar coupling as a significant factor determining the size of the artifacts.For short data chunks, the evolution of scalar coupling leads to a more or less sinusoidal modulation of the resulting FID, which yields anti-phase signals in the decoupled spectrum.For larger FID chunks, and especially broad multiplets (like the central CH 2 group in Fig. 3), scalar coupling evolution during one piece of the FID enables rotations of more than 180°for the outer multiplet components.This results in multiple modulations of the FID components and changes in the phases of chunking artifacts in the spectrum.A variation of the chunking time between individual scans leads to a ''smearing out" of the decoupling sidebands.As an example the variable chunking time, slice-selectively decoupled spectrum of n-propanol is shown in Fig. 4.
The artifacts are here reduced below the level of the 13 C satellites.Such a low level of chunking artifacts is typically needed when compound mixtures with large variations in concentrations are analyzed, as encountered for example in metabolomics applications or for reaction mixtures.An example is the sliceselectively decoupled spectrum of a mixture of strychnine containing degradation products (see Fig. 5).
Using any fixed chunking time there are artifacts present which prohibit the analysis of minor components in the mixture.In contrast, by variation of the chunking time, the artifacts are reduced below the intensity of signals of these minor components.The use of variable chunking times as an approach to suppress realtime homonuclear decoupling artifacts is of course not restricted to slice-selective decoupling.We also used it for real-time BIRD decoupled 1D spectra [15,17].Decoupling sidebands are very pronounced for example around the CH 2 -O group in a BIRD-decoupled spectrum of propanol.They are again largely reduced (smeared out) in the variable chunking time version (Fig. 6).
Chunking artifacts are also present in other experiments employing piecewise acquisition.A related variation of FID chunk duration was used for real-time J-upscaling experiments [24] and the proposed artifact suppression should also be advantageous for e.g.real-time band-selective decoupling [25][26][27][28][29][30] or SERF experiments [31][32][33][34].While chunking artifacts are more pronounced in real-time experiments due to the combination of scalar coupling evolution and relaxation decay between FID chunks, artifacts due to scalar coupling evolution are also present in pseudo 2D chunked pure shift experiments.A variation of the chunking times should also be useful in reducing chunking artifacts in these experiments [1,5,11,14,35,36].In particular it should be useful for other nuclei with larger homonuclear coupling constants, as encountered in pure shift 13 C experiments [37][38][39][40].

Sensitivity improvement by frequency shifting
The implementation of frequency shifted pulses is intended to address the inherently low sensitivity of the instant sliceselective decoupling experiment.By shifting the frequency of excitation it is possible to reach different signals in different scans and allow for relaxation of previously excited spins while recording newly excited ones using short relaxation delays.However, using standard strengths for the weak pulsed field gradient, the range of frequencies available for excitation pulses is rather limited.Therefore, to obtain still quantitative spectra we doubled the slice-selective gradient strength, which per se leads to a loss of 50% of the sensitivity of a regular slice-selectively decoupled Fig. 6.BIRD-decoupled spectra of 10% n-propanol in DMSO-d 6 , showing the region around the CH 2 -O group, recorded with the indicated data chunk durations or using variable data chunk durations (bottom).For all spectra 32 scans of 4096 data points for a spectral width of 10 kHz were acquired.The bottom spectrum was recorded using a variation of the chunking time between the eight values used for the spectra above.The dips around the signal, which are exaggerated by the largely increased vertical scale, are probably caused by magnetic field and/or lock disturbances caused by the repeated use of gradients during acquisition.spectrum.The intensity gained by using frequency shifted pulses is dependent on the proton T 1 values of the investigated molecules.The slower the longitudinal relaxation, the longer one would have to wait between scan and therefore the higher the gain in sensitivity by using frequency shifting of the selective pulses.This sensitivity gain results from the shorter relaxation delay needed between individual scans and the possibility to acquire more scans per unit time.The sensitivity improvement of frequency shifted slice-selective pulses on broadband homodecoupled spectra of n-propanol (in DMSO-d 6 ) and 2-(3,4-dimethoxyphenyl)ethylamine (DMPEA) (in CDCl 3 ) was investigated.For this comparison the overall measurement time was kept constant and the number of scans varied depending on the relaxation delay.The overall relative sensitivity of the individual signals is shown in Fig. 7a and b for propanol, using regular slice-selective decoupling and using frequency shifted slice-selective pulses, respectively.
Using frequency shifting the maximum signal intensity is obtained using relaxation delays around 0.6 s, while with fixed frequency pulses it is approximately 1.5-2 s depending on the individual proton T 1 times.The sensitivity per unit time is more than doubled using frequency shifting of the selective pulses for propanol, where proton T 1 values are between 4 and 4.5 s.We used 8 different excitation frequencies, varied between À1600 and +1600 Hz relative to the transmitter (see Supporting Information).The acquisition time was 410 ms and the pulse-sequence length 270 ms, amounting to a virtual interscan delay of 10.2 s.For faster relaxing molecules, the achievable sensitivity improvement is lower.The results for DMPEA, for which we found longitudinal relaxation times between 1.2 and 2.3 s, are shown in Fig. 8.
The highest sensitivity is achieved by using frequency shifted pulses with a relaxation delay around 0.5 s.The sensitivity per unit time is almost twice as high as the one achieved by keeping the excitation frequency constant.The increase in signal intensity and the shortening of the optimal inter-scan delay length are more significant for the more slowly relaxing aromatic protons.
Slice-selectively decoupled spectra typically show integrals which are not as quantitatively reliable compared to regular proton spectra.The disturbed signal uniformity derives from the non-linearity of the pulsed field gradients and relaxation during the interrupted acquisition.Variations in signal intensities across the non-linear gradient profile, can be reduced by changing the excitation frequency, leading to more uniform averaged gradient strengths.In addition, by shifting the excitation frequency between scans the effect of relaxation between delays is less pronounced, which renders the signal intensities less dependent on relaxation times.As an example the integrals of propanol and DMPEA for regular proton spectra, as well as slice-selective pure shift spectra with and without frequency shifting are shown in Fig. 9.The integrals were calibrated on the total number of visible protons (8 for n-propanol, 13 for DMPEA).
An overall estimate of the reliability of the integrals can be obtained by the average deviation per proton (dev/p).The overall accuracy for propanol is actually lowest for the regular proton spectrum ($8%), which is likely the result of the relatively short relaxation delay (1.5 s) and the additional delays in the pure shift spectrum due to the acquisition interruption.For both samples the integrals are closer to the actual values in the frequency shifted spectra, where the errors are around 5%.
The use of frequency shifted pulses enables the faster acquisition of slice-selective real-time pure shift experiments and is therefore suited for the fast acquisition of series of spectra, which is for example, necessary in reaction monitoring by NMR spectroscopy.The concept of frequency shifted pulses can easily be combined with the use of variations in data chunk durations in order to quickly obtain artifact-reduced pure shift spectra.In order to investigate the sensitivity limit of this experiment, a 1D realtime slice-selectively decoupled spectrum of a sample containing just 80 lg azithromycin aglycone (molecular weight 403 g/mol) [41] in CDCl 3 is compared with a regular proton spectrum in Fig. 10.shifted pure shift spectrum approaches for some signals about one fourth of a regular proton spectrum.Compared to a real-time sliceselectively decoupled spectrum without frequency shifting and variation of the chunking time, the sensitivity is on average increased by a factor $2-3.The signals at 3.5 and 3.9 ppm are exchangeable protons.Their intensities are significantly reduced in the real-time pure shift spectra because they are not reached by the slice-selective pulses as soon as their frequencies change during acquisition.The signal at 4.8 ppm, which is missing completely in the regular pure shift spectrum is not within the excitation range of the spatially-selective pulses used since the gradient strength was kept low for highest sensitivity.Therefore, the use of frequency-shifting not only allows for shorter relaxation delays between scans, but also for lower gradient strength and thereby even further enhanced sensitivity.As mentioned above, the sensitivity depends critically on the excitation bandwidths of the selective pulses used.In cases were mutually scalar coupled protons are closer together, for example at lower magnetic fields, more selective pulses are needed, which would decrease the overall sensitivity.
Both the variation of chunking times as well as frequency shifting could be implemented in 2D NMR experiments.While the variation of chunking times is straightforward to be used in more complex experiments, frequency shifting is only possible if all proton pulses, before the start of the acquisition, can be replaced by selective pulses, as for example in 2D real-time pure shift DOSY [42] or heteronuclear correlated experiments [7,43,44].However, it would not be possible for homonuclear correlated spectra, since magnetization needs to be transferred between different nuclei of the same kind, which prevents the replacement of all pulses by selective ones.

Experimental
Spectra of azithromycin aglycone were acquired on a Bruker Avance III 700 MHz NMR spectrometer using a cryogenically cooled 5 mm TCI probe and z-axis gradients at 298 K.All other spectra were recorded on a Bruker Avance III 500 MHz spectrometer equipped with a 5 mm TXI probe at 300 K.If not specified otherwise, a 60 ms 90°Eburp pulse (bandwidth 83 Hz) [45] was used for excitation and a 10 ms 180°Gaussian shaped pulse (bandwidth 135 Hz) for refocusing during acquisition.The strengths of the purging gradients around the non-selective and slice-selective 180°pulses were 11% and 5%, respectively.For spectra utilizing the varied data chunk durations, the weak magnetic field gradient was 1-2% of maximum strength ($0.5-1.0G/cm), and the relaxation delay was between 1 and 2 s.The variable data chunking was implemented by a variation of the number of chunks (defined through a delay list in Bruker notation; see Supporting Information).For that purpose, the number of data chunks is 20 multiplied by the current value of the delay list.For each scan a new chunking loop counter is used.The chunk duration for each scan is calculated on the fly from the current loop counter and the total acquisition time.For the BIRD-decoupled spectrum, the loop-list directly contained the actual number of data chunks.For spectra employing frequency shifted pulses, typically a spectral width of 10 kHz and a weak gradient of 2-3% ($1-1.5 G/cm) were used.The offsets were selected to prevent accessing previously excited spins, by providing sufficient frequency gaps in between the offsets.Only offset values resembling multiples of ±400 Hz are used.They were defined as shape-lists (see Supporting Information).The number of different chunking times used should not be a multiple of the number of different excitation frequencies in order to combine each excitation frequency with different chunking times when higher number of scans are used.Proton T 1 values were determined using a series of 13 1D proton saturation-recovery spectra [46] with 32 scans (DMPEA) or 16 scans (n-propanol) acquiring 16384 data points, a spectral width of 8 kHz and using the TOPSPIN (ver.

Fig. 2 .
Fig. 2. Principle of slice-selective excitation and frequency shifting.A weak pulsed-field gradient produces a spatially-dependent shift of the whole spectrum along the NMR sample tube.By shifting the excitation frequency between individual scans different signals are excited in different slices in each scan.

Fig. 3 .
Fig.3.Comparison of the central CH 2 signal in slice-selectively decoupled spectra of 10% n-propanol in DMSO-d 6 recorded with the indicated data chunk duration or employing variation of the data chunk durations.For all spectra 256 scans with 8192 data points and a spectral width of 5 kHz were acquired with G1 = 1%.The bottom spectrum was recorded using a variation of the chunking time between the seven values used for the spectra above.

Fig. 4 .
Fig. 4. Real-time slice-selectively decoupled spectra of 10% n-propanol in DMSO-d 6 with (bottom) and without (top) variation of the data chunk durations.The arrows indicate the 13 C satellites, which can be clearly distinguished from the artifacts only in the variable chunking time spectrum.

Fig. 5 .
Fig. 5. Comparison of (a) a regular spectrum, (b) a fixed chunking time (25 ms) and (c) a variable chunking time real-time slice-selectively decoupled spectrum of a mixture of strychnine with unknown degradation products in CDCl 3 .Gray circles indicate artifacts resulting from decoupling sidebands.Weak peaks visible in (c) results from additional minor compounds in the mixture, which are way below the level of artifacts in the fixed chunking time spectrum.Artifacts arising from strong coupling are seen in the region between 3.9 and 4.3 ppm in (b) and (c).

Fig. 7 .
Fig. 7. Signal intensity per second of measurement time per proton as a function of the relaxation delay.The intensity is given in arbitrary units for the individual protons of propanol in a 1D real-time slice-selectively decoupled spectrum using (a) a fixed frequency for excitation and (b) upon changing the excitation frequency after each scan.

Fig. 8 .
Fig. 8. Signal intensity per second of measurement time per proton as a function of the relaxation delay.The intensity is given in arbitrary units for the individual protons of DMPEA in a 1D real-time slice-selectively decoupled spectrum using (a) a fixed frequency for excitation and (b) upon changing the excitation frequency after each scan.

Fig. 9 .
Fig. 9. Integrated spectra of propanol and DMPEA.The actual number of protons for each signal is indicated above the integral sign in the regular proton spectrum.The overall deviation of integrals per proton (dev/p) is indicated for each spectrum.

Fig. 10 .
Fig. 10.Sensitivity comparison of a regular spectrum (a), a real-time slice-selectively decoupled spectrum using excitation frequency shifting and variable data chunking times (b) as well as a regular real-time slice-selectively decoupled spectrum (without frequency shifting and variation of chunking times in (c).All spectra were recorded in a total measurement time of 1 m and 40 s.The sample contained 80 lg of azithromycin aglycone in 80 ll CDCl 3 in a 3 mm CDCl 3 -matched Shigemi tube.The signal intensities of the pure shift spectra were increased fourfold.