Zero filling prediction

Second, the resolution achieved in a 2-D experiment, particularly in the carbon domain is nowhere near as good as that in a 1-D spectrum. You might remember that we recommended a typical data matrix size of 2 k (proton) x 256 (carbon). There are two persuasive reasons for limiting the size of the data matrix you acquire - the time taken to acquire it and the shear size of the thing when you have acquired it This data is generally artificially enhanced by linear prediction and zero-filling, but even so, this is at best equivalent to 2 k in the carbon domain. This is in stark contrast to the 32 or even 64 k of data points that a 1-D 13C would typically be acquired into. For this reason, it is quite possible to encounter molecules with carbons that have very close chemical shifts which do not resolve in the 2-D spectra but will resolve in the 1-D spectrum. So the 1-D experiment still has its place. 

Data shown as examples in this review were typically acquired as 2K X 128 or 2K x 160 point files. Data were processed with linear prediction or zero-filling prior to the first Fourier transform. Data were uniformly linear predicted to 512 points in the second dimension followed by zero-filling to afford final data matrices that were 2K x IK points. 

Figure 9 1,/i-ADEQUATE spectrum of strychnine (1) optimized for 5 Hz. The data were acquired using a sample of 1.8 mg in 40 j.Lof deuterochloroform in a 1.7-mm NMR tube at 600 MHz using a 1.7-mm Micro CryoProbe. The data were acquired as IK x 160 points with 320 transients/q increment and a 3-s interpulse delay giving an acquisition time of 48 h 17 min. The data were linear predicted to IK points in the first dimension and from 160 to 512 point in the second frequency domain followed by zero-filling to give a final IK x IK data matrix. 

Later section.s of this chapter deal with more advanced and specialised processing options such as zero filling, linear prediction, deconvolution and the manipulation of 2D data sets. The chapter concludes with a set of tables containing recommendations for the type of processing function and the corresponding parameters to be used in a number of ID and 2D experiments. 

There are three main processing options based on the addition of a processing or correction function to the FID DC- or Baseline-Correction, Zero-Filling and Linear Prediction LP. 

With 2D forward LP (see Fig. 5.25) the number of measured data points used for prediction is TD. If LPBIN is zero, the predicted data points (SI - TD) are added to the TD measured data points. If LPBIN is greater than TD but less than SI then LPBIN defines the upper limit of predicted points and (LPBIN - TD) data points are calculated and added to the measured TD data points (a combination of LP and zero filling). If TDeff is greater than zero, then TD is replaced by TDeff,... 

With ID backward LP (see Fig. 5.26) the range and the number of measured data points used for prediction is again defined by the Last Point used for LP and the First Point used for LP respectively. With LP backward to Point positive, the first measured data points ( LP backward to Point up to First Point used for LP) are replaced by predicted points. With LP backward to Point negative, LP backward to Point data points are added to the beginning of the FID and an equal number of points are discarded from the end of the (zero-filled) FID. 

Like acquisition, data processing is performed differently in 2D, compared with ID, NMR experiments. The principal reason is that signal truncation is a much more serious problem in 2D than ID experiments. Zero filling also is used in 2D experiments, as is the relatively new technique of linear prediction. 

If computer speed and memory permit, 2D NMR experiments generally are planned so that at least a 2K (2,048-point) FT is carried out in each dimension. In this approach, np2 should be 1,024 and zero filled by one level, to 2,048, prior to the FT2. In addition, ni should then be linear predicted two- to fourfold, to 1,024, and zero filled by one level, to 2,048, before FTl. RT s of 0.8-1.2 s are generally sufficient, and most experiments call for the use of steady-state scans. 

The same raw data was used in each spectrum, with the F (carbon) dimension processed with (a) no data extension, (b) one zero-fill and (c) linear prediction in place of zero-filling. 

Thus the stabilization energy calculation agrees with the deduction from the disposition of filled MOs (i.e. with the 4n + 2 rule) that the cyclobutadiene dication should be stabilized by electron delocalization, which is in some agreement with experiment [45], More sophisticated calculations indicate that cyclic 4n systems like cyclobutadiene (where planar cyclooctatetraene, for example, is buckled by steric factors and is simply an ordinary polyene) are actually destabilized by n electronic effects their resonance energy is not just zero, as predicted by the SHM, but less than zero. Such systems are antiaromatic [17,46],... 

While methods of spectrum analysis capable of super-resolution exist, that is, methods that can achieve resolution greater than l/Wx, the most common of these, linear prediction (LP) extrapolation, has substantial drawbacks. LP extrapolation is used to extrapolate signals beyond the measured interval. While this can dramatically suppress truncation artifacts associated with zero-filling as well as improve resolution, because LP extrapolation implicitly assumes exponential decay it can lead to subtle frequency bias when the signal decay is not perfectly exponential [8]. This bias can have detrimental consequences for applications that require the determination of small fi-equency differences, such as measurement of residual dipolar couplings (RDCs). 

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