The success of any NMR experiment is, of course, crucially dependent on the correct setting of the acquisition parameters.
In the case of 2D experiments one has to consider the parameters for each dimension separately, and we shall see that the most appropriate parameter settings for f2 are rarely optimum for f1. Likewise, one has to give rather more thought to the setting up of a 2D experiment than is usually required for 1D acquisitions to make optimum use of the instrument time available. Once again, the general considerations below will be applicable to all 2D experiments, although we restrict our discussion at this stage to COSY.
At the most basic level one has to address two fundamental questions when setting up an experiment. (1) Will the de- fined parameters enable (or limit) the detection of the desired information and exclude the unwanted? (2) How long will it
FIGURE 5.19 Bands of noise parallel to the f1-axis (t1 noise) often appear in 2D spectra.
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184 High-Resolution NMR Techniques in Organic Chemistry
take and do I have enough time? Ideally we would wish to acquire data sets rapidly yet still be able to provide the informa- tion we require, so we set up our experiment with these goals in mind.
Firstly, spectral widths, which should be the same in both dimensions of the COSY experiment, should be kept to minimum values with transmitter offsets adjusted so as to retain only the regions of the spectrum that will provide useful correlations. It is usually possible to reduced spectral widths to well below the 10 or so ppm proton window observed in 1D experiments. The use of excessively large windows leads to poorer digital resolution in the final spectrum, or requires greater data sizes, neither of which is desirable. The spectral widths in turn define the sampling rates for data in t2, in exact analogy with 1D acquisitions, and the size of the t1 increment, again according to the Nyquist criteria. The acquisition time (AQt), and hence the digital resolution (1/AQt), for each dimension is then dictated by the number of data points collected in each. For t2, this is the number of data points digitised in each FID, while for t1 this is the number of FIDs collected over the course of the experiment. The appropriate setting of these parameters is a most important aspect to setting up a 2D experi- ment, and the way in which one thinks about acquisition times and digital resolution in a 2D data set is, necessarily, quite different from that in a 1D experiment. As an illustration, imagine transferring the typical parameters used in a 1D proton acquisition into the two dimensions of COSY. The acquisition time might be 4 s, corresponding to a digital resolution of 0.25 Hz/pt, with no relaxation delay between scans. On, for example, a 400 MHz instrument with a 10 ppm spectral width, this digital resolution would require 32K words to be collected per FID. The 2D equivalent, with States quad-detection in f1 and with axial peak suppression, requires 4 scans to be collected for each t1 increment. The mean acquisition time for each would be 6 s (t2 plus the mean t1 value), corresponding to 24 s of data collection per FID. If 16K t1 increments were to be made for the f1 dimension (two data sets are collected for each t1 increment remember) this would correspond to a total experiment time of about 4ẵ days. I trust you will agree that four days for a basic COSY acquisition is quite unacceptable, so acquiring data with such high levels of digitisation in both dimensions is clearly not possible.
The key lies in deciding on what level of digitisation is required for the experiment in hand. The first point to notice is that adding data points to extend the t2 dimension leads to a relatively small increase in the overall length of the experi- ment, so we may be quite profligate with these. Adding t1 data points on the other hand requires that a complete FID of potentially many scans is required per increment, which makes a far greater increase to the total data collection time. Thus one generally aims to keep the number of t1 increments to a minimum that is consistent with resolving the correlations of interest, and increasing t2 as required when higher resolution is necessary. For this reason, the digital resolution in f2 is often greater than that in f1, particularly in the case of phase-sensitive data sets. The use of smaller t1 acquisition times (AQt1) is, in general, also preferred for reasons of sensitivity since FIDs recorded for longer values of t1 will be attenuated by relaxation and so will contribute less to the overall signal intensity. The use of small AQt1 is likely to lead to truncation of the t1 data, and it is then necessary to apply suitable window functions that force the end of the data to zero to reduce the appearance of truncation artefacts.
For COSY in particular, one of the factors that limits the level of digitisation that can be used is the presence of intrin- sically anti-phase crosspeaks, since too low a digitisation will cause these to cancel and the correlation to disappear (see Section 6.1.5 for further discussions). The level of digitisation will also depend on the type of experiment and the data one expects to extract from it. For absolute value COSY one is usually interested in establishing where correlations exist, with little interest in the fine structure within these crosspeaks. In this case it is possible to use a low level of digitisation consistent with identifying correlations. As a rule of thumb, a digital resolution of J to 2J Hz/pt (AQ of 1/J to 1/2J s) should enable the detection of most correlations arising from couplings of J Hz or greater. Thus for a lower limit of, say, 3 Hz a digital resolution of 3–6 Hz/pt (AQ of ca. 300–150 ms) will suffice. The acquisition time for t1 is typically half that for t2 in this experiment, with one level of zero-filling applied in t1 so that the final digital resolution is the same in both dimensions of the spectrum (as required for symmetrisation).
For phase-sensitive data acquisitions one may be interested in using the information contained within the crosspeak multiplet structures, and a higher degree of digitisation is required to adequately reflect this, a more appropriate target being around J/2 Hz/pt or better (AQ of 2/J s or greater). Again, digitisation in t2 is usually 2 or even 4 or 8 times greater than that in t1. In either dimension, but most often in t1, this may be improved by zero filling, although one must always remember that it is the length of the time domain acquisition that places a fundamental limit on peak resolution and the effective linewidths after digitisation, regardless of zero-filling. The rule as ever is that high resolution requires long data-sampling periods. An alternative approach for extending the time-domain data is to use forward linear prediction when processing the data (Section 3.2.3). It is now also possible to reduce the sampling requirements in t1 through the use of non-uniform sam- pling, as described in the following section, potentially leading to significant time savings. Following recent developments, the acquisition of 2D spectra in a single scan is also possible and the simultaneous acquisition of multiple nuclei (requiring dual instrument receiver channels) also has the potential to accelerate data acquisition; these topics are introduced briefly in Sections 5.4.5 and 7.7, respectively.
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Having decided on suitable digitisation levels and data sizes, one is left to choose the number of scans or transients to be collected per FID and the repetition rates and hence relaxation delays to employ. The minimum number of transients is dictated by the minimum number of steps in the phase cycle used to select the desired signals. Further scans may include additional steps in the cycle to suppress artefacts arising from imperfections. Beyond this, further transients should only be required for signal averaging when sensitivity becomes a limiting factor. Since most experiments are acquired under
‘steady-state’ conditions, it is also necessary to include ‘dummy’ scans prior to data acquisition to allow the steady-state to establish. On modern instruments dummy scans are required only at the very beginning of each experiment so make a negligible increase to the total time required. On older instruments it is necessary to add dummy scans for each t1 increment, and these may then make a significant contribution to the total duration of the experiment. The repetition rate will depend upon the T1 s of the excited spins (protons in the case of COSY and many of the heteronuclear correlation experiments) and since the sequence uses 90 degree pulses, the optimum sensitivity is achieved by repeating every 1.3 T1 s.
Returning to the example 400 MHz acquisition discussed earlier, we can apply more appropriate criteria to the selection of parameters. Table 5.3 compares the result from above with more realistic data, and it is clear that under these conditions COSY becomes a viable experiment, requiring only minutes to collect, rather than days. The introduction of PFGs to high- resolution spectroscopy (Section 5.4) allows experiments to be acquired with only one transient per FID where sensitivity is not limiting so further reducing the total time required for data collection. Although illustrated for COSY spectra, the general line of reasoning presented here is applicable to the set-up of any 2D experiment. These issues are briefly consid- ered with reference to different classes of techniques in the following chapters describing other 2D methods.
5.2.4.1 Non-Uniform Sampling
The classical sampling of 2D (and more generally multi-dimensional) NMR experiments requires the uniform sampling of data in the indirect dimension(s) that allows for the processing of the data by the discrete Fourier transform. This means a sequential, stepwise increment of the t1 period of a 2D data set is made to the limit t1(max) which dictates the resolution in this dimension. The number of such t1 increments employed ultimately defines the total duration of the experiment. The method of non-uniform sampling (NUS) seeks to reduce the number of data points collected in the indirect dimension(s) and so reduces the total experiment time. The development of NUS in NMR spectroscopy has been largely driven by the widespread use of 3D experiments in biomolecular NMR, where single experiments may last days with conventional data sampling and where time savings through NUS can be very significant. Nevertheless, NUS may also be applied to 2D experiments and can yield time savings that become significant when many samples are being analysed, and it is in this context that we consider this approach.
A typical approach to collecting NUS experiments is to randomly acquire only a subset of the usual t1 data traces. Most often only 50–25% of data points may be sampled (Fig. 5.20), leading to a time saving of two to fourfold. Such sampling means, however, that it is then not possible to process the t1 time domain data with the conventional Fourier transform, and
TABLE 5.3 Illustrative Data Tables for COSY Experiments
Experiment Spectral Width (ppm) N (t2) N (t1) Hz/pt (t2) Hz/pt (t1) Experiment Time
(a) Phase sensitive 10 × 10 32K 32K 0.25 0.25 4.5 day
(b) Phase sensitive 6 × 6 2K 1K 2.3 2.3 55 min
(c) Absolute value 6 × 6 1K 256 4.6 4.6 22 min
Scenario (a) transplants acquisition parameters from a typical 1D proton spectrum into the second dimension leading to unacceptable time requirements, where- as (b) and (c) use parameters more appropriate to 2D acquisitions. All calculations use phase cycles for f1 quad-detection and axial peak suppression only and, for (b) and (c), a recovery delay of 1 s between scans. A single zero-filling in f1 was also employed for (b) and (c).
FIGURE 5.20 Non-uniform data sampling. Filled circles show the randomly distributed t1 data points of a 2D data set sampled at 25%, open circles represent those additional points that would also be collected for conventional t1 data sampling (128 complex points in total).
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186 High-Resolution NMR Techniques in Organic Chemistry
reconstruction of the missing data points is required. Many approaches to the processing of non-uniformly sampled data have been proposed [22], although in reality you are likely to employ that provided by your software vendor (for which specific licences may be required). The critical element required for these to succeed is adequate signal-to-noise in the col- lected data points, and NUS spectra are most likely to contain artefacts when this is too low, or when too few t1 data points have been sampled.
The benefits of using NUS for 2D experiments may be viewed in two ways. Firstly, it may allow the collection of a spectrum in a shorter time when compared to a conventionally sampled data set with the same f1 resolution. This is illustrated in the comparison of the 2D heteronuclear correlation spectra (see Section 7.3) in Fig. 5.21. The conventionally sampled (128 complex points) and the 25% sampled (32 complex points) NUS spectra appear indistinguishable, although that later required only one-quarter of the time for data acquisition; this sample provided high 1H signal to noise, allowing such sparse sampling. Alternatively the gain from NUS could be to increase resolution in the indirect dimension when compared to a conventionally sampled data set of the same overall duration. The heteronuclear single quantum correla- tion (HSQC) spectrum of Fig. 5.21c was collected in the same total time as that for Fig. 5.21a but has fourfold greater points in the reconstructed t1 domain (512 vs. 128 complex points) due to the use of 25% NUS. This may appear to be gaining resolution for no penalty, but as ever, the compromise here is sensitivity, since the non-uniformly sampled points are now spread over a larger total t1 duration, meaning the later points will suffer reduced intensity from greater relax- ation losses. Some sampling schemes, especially those used for protein samples, are therefore optimised to concentrate the NUS points towards the earlier time points to mitigate such sensitivity losses, although this is likely to be less of a problem for small molecules where transverse relaxation rates are low compared to those of macromolecules. Too great a reduction in the number of sampled points will ultimately lead to corruption of the final spectrum, as illustrated for the HSQC spectrum of Fig. 5.21d, for which only 10% sampling was employed. Due to the requirement of sufficiently high signal-to-noise ratios, NUS methods may be less satisfactory for data sets with intrinsically low sensitivity, such as 2D nuclear Overhauser effect spectroscopy (NOESY) (see Section 9.6). When sample quantities are not restrictive, anecdotally they appear more robust for heteronuclear correlation experiments such as HSQC and possibly heteronuclear multiple bond correlation (HMBC).