2D experiments

For quadnipolar nuclei, the dependence of the pulse response on Vq/v has led to the development of quadnipolar nutation, which is a two-dimensional (2D) NMR experiment. The principle of 2D experiments is that a series of FIDs are acquired as a fimction of a second time parameter (e.g. here the pulse lengdi applied). A double Fourier transfomiation can then be carried out to give a 2D data set (FI, F2). For quadnipolar nuclei while the pulse is on the experiment is effectively being carried out at low field with the spin states detemiined by the quadnipolar interaction. In the limits Vq v the pulse response lies at v and... 

The key dimension m NMR is the frequency axis All of the spectra we have seen so far are ID spectra because they have only one frequency axis In 2D NMR a stan dard pulse sequence adds a second frequency axis Only pulsed FT NMR spectrometers are capable of carrying out 2D experiments... 

Parameter B3LYP/6-31G(d) B3LYP/6-31+G(d) B3LYP/6-311G(2d) Experiment... 

The evolution period tl is systematically incremented in a 2D-experiment and the signals are recorded in the form of a time domain data matrix S(tl,t2). Typically, this matrix in our experiments has the dimensions of 512 points in tl and 1024 in t2. The frequency domain spectrum F(o l, o 2) is derived from this data by successive Fourier transformation with respect to t2 and tl. 

In practice it is usually unnecessary to determine exact pulse widths for each sample we can use approximate values determined for each probe-head, except in certain 2D experiments in which the accuracy of pulse widths employed is critical for a successful outcome. Proper tuning of the probehead is advisable, since pulse widths will normally not vary beyond 10% with well-tuned probeheads. 

Some of the most important 2D experiments involve chemical shift correlations between either the same type of nuclei (e.g., H/ H homonu-clear shift correlation) or between nuclei of different types (e.g., H/ C heteronuclear shift correlation). Such experiments depend on the modulation of the nucleus under observation by the chemical shift frequency of other nuclei. Thus, if H nuclei are being observed and they are being modulated by the chemical shifts of other H nuclei in the molecule, then homonuclear shift correlation spectra are obtained. In contrast, if C nuclei are being modulated by H chemical shift frequencies, then heteronuclear shift correlation spectra result. One way to accomplish such modulation is by transfer of polarization from one nucleus to the other nucleus. Thus the magnitude and sign of the polarization of one nucleus are modulated at its chemical shift frequency, and its polarization transferred to another nucleus, before being recorded in the form of a 2D spectrum. Such polarization between nuclei can be accomplished by the simultaneous appli-... 

When there is only one time variable during a 2D experiment, i.e., U, why do we need to process the data through two Fourier transformation operations ... 

Figure 3.5 Schematic representation of data processing in a 2D experiment (one zero-filling in and two zero-fillings in F ). (a) A(, FIDs composed of Afj quadrature data points, which are acquired with alternate (sequential) sampling, (b) On a real...

At the end of the 2D experiment, we will have acquired a set of N FIDs composed of quadrature data points, with N /2 points from channel A and points from channel B, acquired with sequential (alternate) sampling. How the data are processed is critical for a successful outcome. The data processing involves (a) dc (direct current) correction (performed automatically by the instrument software), (b) apodization (window multiplication) of the <2 time-domain data, (c) Fourier transformation and phase correction, (d) window multiplication of the t domain data and phase correction (unless it is a magnitude or a power-mode spectrum, in which case phase correction is not required), (e) complex Fourier transformation in Fu (f) coaddition of real and imaginary data (if phase-sensitive representation is required) to give a magnitude (M) or a power-mode (P) spectrum. Additional steps may be tilting, symmetrization, and calculation of projections. A schematic representation of the steps involved is presented in Fig. 3.5. 

It is easier to obtain a higher digital resolution in 2D experiments in the domain than in the domain, since doubling the acquisition time <2 results in little overall increase in the experiment time. This is so because... 

In three-dimensional experiments, two different 2D experiments are combined, so three frequency coordinates are involved. In general, the 3D experiment may be made up of the preparation, evolution (mixing periods of the first 2D experiment, combined with the evolution t ), mixing, and detection ( ) periods of the second 2D experiment. The 3D signals are therefore recorded as a function of two variable evolution times, t and <2, and the detection time %. This is illustrated in Fig. 6.1. 

Since there are two time variables, i and h, to be incremented in a 3D experiment (in comparison to one time variable to increment in the 2D experiment), such experiments require a considerable data storage space in the computer and also consume much time. It is therefore practical to limit such experiments to certain limited frequency domains of interest. Some common pulse sequences used in 3D time-domain NMR spectroscopy are shown in Fig. 6.2. 

The peak shapes in 3D spectra can be obtained from the phases of the corresponding signals in the two 2D experiments from which the 3D spectrum is derived. This, if the two 2D spectra have pure phases, e.g., absorption signals, then the 3D cross-peaks will also be in the pure-... 

Figure 7.1 Selective excitation of only one multiplet by a selective pulse transforms a 2D experiment into a ID technique. A selective pulse generates the transverse magnetization. The result is a trace of the corresponding 2D spectrum. (Reprinted from Mag. Reson. Chem. 29, H. Kessler ei al., 527, copyright (1991), with permission from John Wiley and Sons Limited, Baffins Lane, Chichester, Sussex P019 lUD, England.)...

COSY (H-H correlation spectroscopy) An important 2D experiment that allows us to identify the protons coupled to one another. 

Cross-peaks The off-diagonal peaks in a 2D experiment that appear at the coordinates of the correlated nuclei. 

Detection period The FID is acquired in the last segment of the pulse sequence. This is the detection period, and, in 2D experiments, this is the <2 domain. 

J-spectroscopy A 2D experiment in which the chemical shifts are plotted along one axis F2 axis) while the coupling constants are plotted along the other axis axis). This is an excellent procedure for uncoding overlapping multiplets. 

Mixing period The third time period in 2D experiments, such as NOESY, during which mixing of coherences can occur between correlated nuclei. 

It is my opinion that this approach has considerable merit, provided that the questions posed in the problems are wisely selected, as indeed they are in this text. The authors themselves are well versed in natural-product chemistry, an area that presents a wide array of small molecule structural problems. They are therefore concerned that the reader reach the practical goal of applying the full power of NMR spectroscopy to problems of this type. To this end they have selected problems that address methods for solving structures as well as those that pertain to basic theory. The authors have wisely made a point of treating the more widely used ID and 2D experiments in considerable detail. Nevertheless, they also introduce the reader to many of the less common techniques. 

Hence, a series of measurements with several Tcp values will provide a data set with variable decays due to both diffusion and relaxation. Numerical inversion can be applied to such data set to obtain the diffusion-relaxation correlation spectrum [44— 46]. However, this type of experiment is different from the 2D experiments, such as T,-T2. For example, the diffusion and relaxation effects are mixed and not separated as in the PFG-CPMG experiment Eq. (2.7.6). Furthermore, as the diffusion decay of CPMG is not a single exponential in a constant field gradient [41, 42], the above kernel is only an approximation. It is possible that the diffusion resolution may be compromised. 

In summary, the new 2D experiments of relaxation and diffusion appear to offer a new method to identify and quantify the components in dairy products. The two components are well separated in the 2D maps while they can be heavily overlapped in the ID spectrum. We find that some microscopic properties of the products can be reflected in the relaxation and diffusion properties. These new techniques are likely to be useful to assist the characterization of the products for quality control and quality assurance. 

One of the fastest growing areas in NMR over the past decade has been the use of pulsed field gradients , or PFG-NMR, for selective ID and 2D experiments. The basic pulsed gradient spin-echo (PGSE) experiment [174] relies on the use of pulsed linear magnetic field gradients (of amplitude g, duration 8 and separation A) that are applied during a spin-echo experiment [184],... 

The study of molecular diffusion in solution by NMR methods offers insights into a range of physical molecular properties. Different mobility rates or diffusion coefficients may also be the basis for the separation of the spectra of mixtures of small molecules in solution, this procedure being referred to as diffusion-ordered spectroscopy (DOSY) [271] (Figure 5.11). In this 2D experiment, the acquired FID is transformed with respect to 2 (the acquisition time). 

NOE effects can naturally also be investigated by 2D experiments these are known as NOESY and ROESY. 

The NMR spectrum is recorded during the chromatographic separation. Data are collected as in a 2D experiment, the two dimensions being the chemical shift and the retention time of the chromatogram. 

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